### In Hooke’S Law, What Does K Represent?

Home FAQs What does the k mean in Hooke’s law? Published on September 17th, 2021 Published on September 17th, 2021 by aleksander.malaszkiewicz K represents the constant of proportionality, also known as the ‘spring constant.’ In layman’s terms, the k variable in Hooke’s law (F = -kx) indicates stiffness and strength.

## What does the K value of a spring represent?

PHYS 1405 Conceptual Physics I Laboratory # 2 Hookes Law Investigation: How does the force felt by a spring vary as we stretch it, and how can we determine the stiffness of a spring? What to measure: Distance a spring is stretched, force felt by the spring Measuring devices: A meter stick, a force sensor, two unknown springs Calculations: The spring constant INTRODUCTION In the first part of this unit, we will be discussing and getting familiar with forces.

Simply put, a force is a push or a pull. Some forces involve things touching (contact forces), while others do not require contact (force at a distance). In this experiment, we will investigate the forces exerted on and by a spring. These forces were first investigated by the British physicist Robert Hooke, and the equation he used to describe the so-called elastic force has been dubbed Hookes Law: F Spring = – k x In this equation, F is the force exerted by something stretching or compressing the spring, and x is the distance that the spring is stretched or compressed from its rest position.

The letter k represents the spring constant, a number which essentially tells us how stiff a spring is. If you have a large value of k, that means more force is required to stretch it a certain length than you would need to stretch a less stiff spring the same length.

Once you have determined the spring constant of a spring, you can use that k value for all future calculations, unless the spring is damaged in some way. The negative sign is in the equation because force is a vector quantity. The negative sign tells us that the direction of the elastic force is always opposite to the direction of the stretching motion.

In other words, if you stretch a spring downward, you feel the spring pull upward. If you want to stretch the spring out and hold it in place, you must apply the same amount of force the spring is, but in the opposite direction. That is, to stretch a spring with spring constant k a distance x and hold it there in equilibrium, you must apply a constant force with a size given by F Applied = + k x This force that you are applying exactly balances the opposite force exerted by the spring, to achieve an equilibrium situation.

In this experiment, we will exploit this fact to find out the values of the spring constants of two springs. PART 1: General Properties Note that you have two springs for this lab, color-coded green and blue. The green spring should already be hanging next to the meter stick. The spring is hanging from a device called a force sensor, which is hooked to the computer.

The sensor will tell the computer exactly how much force (measured in newtons) the spring is feeling. We will not use the sensor for this part of the lab. Just pull a little on each spring (do not pull either to its limits!). Pull each spring out 10 centimeters from its rest” position.

• Question 1: Which spring is more difficult to stretch? Which spring do you think will have the higher spring constant? Question 2: When you pull the spring out and hold it, you should feel a force being exerted on you by the spring.
• How does that force compare to the force you are applying? What makes you say that? Question 3: If you let go of the spring, what will happen to it? Explain why, in terms of forces.

PART 2: Green Spring The first thing we must do is calibrate the force sensor, so that it will only read the force that we are exerting on the spring, and no other forces. Hang the green spring from the force sensor next to the meter stick. Do not stretch the spring yet.

Hit the Collect button on the computer screen and let the sensor record data for a brief time. Select five data points and average them. Question 4: What is the size of the force felt by the unstretched spring? Where does this force come from? It is important to find out what this unstretched force is, because in this lab we are only concerned with the force that you exert on the spring.

If you were to pull on the spring now, the force sensor would register both the force you were exerting and the force the unstretched spring feels. We can get rid of the extra force by zeroing the force sensor with the spring on it. With the spring hanging from the force sensor, click the Zero button that is next to the Collect button.

• When you hit the Collect button again, the sensor should read close to 0.000.
• Once you have zeroed out the force sensor, click on the Collect button and gradually stretch the spring.
• The force felt by the spring will be displayed on the graph, and as a stream of numbers on the right of the screen.
• Question 5: How does the force change with distance stretched? Explain this behavior in terms of Hookes Law.

Now stretch the spring to 10 centimeters past its rest length. Click on the collect button and gather a few seconds worth of data. Its very important to keep the end of the spring steady at all times. Values for the force should appear in the data table at the right of the screen.

• Average five values and determine the force that you exerted on the spring.
• Dividing that force by the distance stretched (10 cm) should give the large springs spring constant, in units of newtons per centimeter (N/cm).
• Repeat your observations for 20, 30, 40, and 50 centimeters.
• Calculate a value for the spring constant each time.

Average all six spring constant values. Construct a data table with the following information for each trial: distance stretched (x in cm), average force (F in N), spring constant (in N/cm).

 Distance (cm) Force (N) k (N / cm) 10 20 30 40 50 Average =

PART 3: Blue Spring Remove the green spring from the force sensor and replace it with the blue spring. Zero out the sensor with the blue spring hanging from it. Take force measurements for stretches of 10, 20, 30, 40 and 50 centimeters. Determine a spring constant value for all trials, then an average spring constant.

Create a data table as you did in Part 2 for this spring. Question 6: Which spring was stiffer? Which spring really had the higher spring constant? PART 4: Graphs Create two graphs to finish the lab report, one for each spring. On each graph, the x-axis will be distance stretched, and the y-axis will be the force felt by the spring.

Plot as many data points as you have on each graph. Draw the best line you can through all the data points. Calculate the slope (rise/run) for each line. Question 7: What number is the slope of the graph roughly equal to?

### What is K in spring constant?

The extension of an elastic object, such as a spring, is described by Hooke’s law.

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The spring constant, k, is a measure of the stiffness of the spring. It is different for different springs and materials. The larger the spring constant, the stiffer the spring and the more difficult it is to stretch. Question A force of 3 N is applied to a spring.

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### What does the K represent in physics?

The kelvin (abbreviation K), less commonly called the degree Kelvin (symbol, o K), is the Standard International ( SI ) unit of thermodynamic temperature. One kelvin is formally defined as 1/273.16 (3.6609 x 10 -3 ) of the thermodynamic temperature of the triple point of pure water (H 2 O).

The kelvin scale differs from the more familiar Celsius or centigrade ( o C) temperature scale; there is no such thing as a below-zero Kelvin figure. A temperature of 0 K represents absolute zero, the absence of all heat. However, the size of the kelvin “degree” is the same as the size of the Celsius “degree.” A change of plus-or-minus 1 o C is the same as a change of plus-or-minus 1 K.

At standard Earth-atmospheric sea-level pressure, water freezes at 0 o C or +273.15 K, and boils at +100 o C or +373.15 K. A temperature of 0 K thus corresponds to -273.15 o C. A temperature of 273.15 K corresponds to 0 o C. To convert a kelvin temperature figure to Celsius, subtract 273.15.

#### What is K elasticity?

F = –kx. In the equation, F is the force, x is the extension in length, k is the constant of proportionality known as the spring constant in N/m.

### What does K value stand for?

What is a K-Value in construction? The K-value is basically a shortened phrase for thermal conductivity, which is the time rate that heat steadily flows through a unit that is induced by the unit temperature in a direction that is perpendicular to the area.

1. Okay, so that sounds really complicated, but honestly, it isn’t.
2. Start to consider the amount of heat that flows when you are running hot water and you basically know what thermal conductivity is and how it works.
3. Values K-values are important, because they allow you to assess what the heat transfer is between the outside and inside of a building.
See also:  How Is It Possible For Living Organisms To Comply With The Second Law Of Thermodynamics?

Since you are using many different materials, your K-values can be different, so this is something that truly is important to know.

• As soon as you have fully researched the definition of a K-value, you will see that it is units of Btu per inch per hour per square foot per Fahrenheit degree for the temperature.
• Once you know the K-values for the building you are working on, you can easily use that information to determine the other values that you will need to know.
• C-Values

A C-value is different than a K-value, because it focuses on thermal conductance. This value depends on the thickness of the material, whereas the K-value does not care how thick the material is. The C-value is determined by Btu per hour per square foot per Fahrenheit degree for the temperature.

• When you are looking at the C-value of a building, you will instantly notice that the C-value is going to be cut in half if you use a one inch thick insulation board instead of a two inch thick piece of the same board.
• R-Values An R-value is considered thermal resistance between two defined surfaces of material.

It can also be any type of construction that induces unit heat flow through any area. To determine the R-value of any item, you must divide one by the C-value or divide the thickness by the K-value. Therefore, you can see that a C-value of 0.5 will have an R-value of 2.0, while the R-value is 4 when the K-value is 0.25 and the thickness of the material is 1.

1. U-Values U-values are basically thermal transmittance and it is where the heat transmission goes through material construction and the boundary air firms according to the environment on each side of the building.
2. The lower the U-value is, the lower the rate of heat flow, and that means heat is not escaping and the building is staying warm.

Of course, higher U-values usually pop up in poorly insulated buildings and in those scenarios, the heat will be on much more. It is a lot of work to determine the U-value for any building, but when you do, you must know these things first:

• The C-value of both the indoor and outdoor air film
• K-value of the 3 and ½ inch wide wood studs
• The spacing between the studs
• The K-value of the fiberglass insulation batts and the thickness of them
• The K-value, as well as the thickness of the wood siding material
1. The Rules of These Values
2. The lower the K-value is, the greater the insulating value for the given thickness and the set of conditions.
3. The better the performance of insulation means a greater R-value and a lower C-value.
4. The better the insulation is, the lower the U-value will be.
5. All these values are used to create energy savings, protect those who are in the building, and control condensation.

Therefore, it is important to know all these values inside any building that you construct. The K-values are necessary so you can figure out all the rest, so do not try to take shortcuts. The results of a shortcut can be skewed numbers that will not truly represent what the value really is and that can create more problems in the future. : What is a K-Value in construction?

### What do K values show?

Summary –

• The equilibrium constant expression is a mathematical relationship that shows how the concentrations of the products vary with the concentration of the reactants.
• If the value of \(K\) is greater than 1, the products in the reaction are favored. If the value of \(K\) is less than 1, the reactants in the reaction are favored. If \(K\) is equal to 1, neither reactants nor products are favored.

### What is the K constant?

The Coulomb constant, the electric force constant, or the electrostatic constant (denoted k e, k or K) is a proportionality constant in electrostatics equations. In SI base units it is equal to 8.9875517923(14)×10 9 kg⋅m 3 ⋅s − 4 ⋅A − 2.

## What is the value of constant k?

Having dimensions of energy per degree of temperature, the Boltzmann constant has a defined value of 1.380649 × 10 − 23 joule per kelvin (K), or 1.380649 × 10 − 16 erg per kelvin.

### What determines k of a spring?

W = kx. W is the weight of the added mass. Therefore, the spring constant k is the slope of the straight line W versus x plot. Weight is mass times the acceleration of gravity or W = mg where g is about 980 cm/sec2.

## Why is k represented constant?

Where does the k prefix for constants come from? It’s a historical oddity, still common practice among teams who like to blindly apply coding standards that they don’t understand. Long ago, most commercial programming languages were weakly typed; automatic type checking, which we take for granted now, was still mostly an academic topic.

1. This meant that is was easy to write code with category errors; it would compile and run, but go wrong in ways that were hard to diagnose.
2. To reduce these errors, a chap called Simonyi suggested that you begin each variable name with a tag to indicate its (conceptual) type, making it easier to spot when they were misused.

Since he was Hungarian, the practise became known as “Hungarian notation”. Some time later, as typed languages (particularly C) became more popular, some idiots heard that this was a good idea, but didn’t understand its purpose. They proposed adding redundant tags to each variable, to indicate its declared type.

The only use for them is to make it easier to check the type of a variable; unless someone has changed the type and forgotten to update the tag, in which case they are actively harmful. The second (useless) form was easier to describe and enforce, so it was blindly adopted by many, many teams; decades later, you still see it used, and even advocated, from time to time.

“c” was the tag for type “char”, so it couldn’t also be used for “const”; so “k” was chosen, since that’s the first letter of “konstant” in German, and is widely used for constants in mathematics. : Where does the k prefix for constants come from?

### What does k represent in the equation?

 The vertex form of a quadratic function is given by f ( x ) = a ( x – h ) 2 + k, where ( h, k ) is the vertex of the parabola.

FYI: Different textbooks have different interpretations of the reference ” standard form ” of a quadratic function. Some say f ( x ) = ax 2 + bx + c is “standard form”, while others say that f ( x ) = a ( x – h ) 2 + k is “standard form”. To avoid confusion, this site will not refer to either as “standard form”, but will reference f ( x ) = a ( x – h ) 2 + k as “vertex form” and will reference f(x ) = ax 2 + bx + c by its full statement.

When written in ” vertex form “: • (h, k) is the vertex of the parabola, and x = h is the axis of symmetry. • the h represents a horizontal shift (how far left, or right, the graph has shifted from x = 0). • the k represents a vertical shift (how far up, or down, the graph has shifted from y = 0). • notice that the h value is subtracted in this form, and that the k value is added.

If the equation is y = 2( x – 1) 2 + 5, the value of h is 1, and k is 5. If the equation is y = 3( x + 4) 2 – 6, the value of h is -4, and k is -6. To Convert from f ( x ) = ax 2 + bx + c Form to Vertex Form: Method 1: Completing the Square To convert a quadratic from y = ax 2 + bx + c form to vertex form, y = a ( x – h ) 2 + k, you use the process of completing the square. Let’s see an example. Convert y = 2 x 2 – 4 x + 5 into vertex form, and state the vertex.

 Equation in y = ax 2 + bx + c form. y = 2 x 2 – 4 x + 5 Since we will be ” completing the square ” we will isolate the x 2 and x terms, so move the + 5 to the other side of the equal sign. y – 5 = 2 x 2 – 4 x We need a leading coefficient of 1 for completing the square, so factor out the current leading coefficient of 2. y – 5 = 2( x 2 – 2 x ) Get ready to create a perfect square trinomial. BUT be careful!! In previous completing the square problems with a leading coefficient not 1, our equations were set equal to 0. Now, we have to deal with an additional variable, “y”, so we cannot “get rid of ” the factored 2. When we add a box to both sides, the box will be multiplied by 2 on both sides of the equal sign. Find the perfect square trinomial. Take half of the coefficient of the x -term inside the parentheses, square it, and place it in the box, Simplify and convert the right side to a squared expression. y – 3 = 2( x – 1) 2 Isolate the y -term, so move the -3 to the other side of the equal sign. y = 2( x – 1) 2 + 3 In some cases, you may need to transform the equation into the “exact” vertex form of y = a ( x – h ) 2 + k, showing a “subtraction” sign in the parentheses before the h term, and the “addition” of the k term. (This was not needed in this problem.) y = 2( x – 1) 2 + 3 Vertex form of the equation. Vertex = ( h, k ) = (1, 3) (The vertex of this graph will be moved one unit to the right and three units up from (0,0), the vertex of its parent y = x 2,)

Here’s a sneaky, quick tidbit: Method 2: Using the “sneaky tidbit”, seen above, to convert to vertex form:

 y = ax 2 + bx + c form of the equation. y = 2 x 2 – 4 x + 5 Find the vertex, ( h, k ), and, a = 2 and b = -4 Vertex: (1,3) Write the vertex form. y = a ( x – h ) 2 + k y = 2( x – 1) 2 + 3

To Convert from Vertex Form to y = ax 2 + bx + c Form:

 Simply multiply out and combine like terms: y = 2( x – 1) 2 + 3 y = 2( x 2 – 2 x + 1) + 3 y = 2 x 2 – 4 x + 2 + 3 y = 2 x 2 – 4 x + 5

Graphing a Quadratic Function in Vertex Form:

 1. Start with the function in vertex form : y = a ( x – h ) 2 + k y = 3( x – 2) 2 – 4 2. Pull out the values for h and k, If necessary, rewrite the function so you can clearly see the h and k values. ( h, k ) is the vertex of the parabola. Plot the vertex. y = 3( x – 2) 2 + (-4) h = 2; k = -4 Vertex: (2, -4) 3. The line x = h is the axis of symmetry, Draw the axis of symmetry. x = 2 is the axis of symmetry 4. Find two or three points on one side of the axis of symmetry, by substituting your chosen x -values into the equation. For this problem, we chose (to the left of the axis of symmetry): x = 1; y = 3( 1 – 2) 2 – 4 = -1 x = 0; y = 3( 0 – 2) 2 – 4 = 8 Plot (1, -1) and (0,8) 5. Plot the mirror images of these points across the axis of symmetry, or plot new points on the right side. Draw the parabola. Remember, when drawing the parabola to avoid “connecting the dots” with straight line segments. A parabola is curved, not straight, as its slope is not constant.

NOTE: The re-posting of materials (in part or whole) from this site to the Internet is copyright violation and is not considered “fair use” for educators. Please read the ” Terms of Use “.

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### Why is k called a constant?

In mathematics the letter k often is used to represent an arbitrary constant since it sounds like the first letter of ‘constant’, while ‘c’ is used for many other tasks and usually is not available.

### What is K in Young’s modulus?

The ratio of interatomic force to that of change in interatomic distance is defined as the interatomic force constant K=ΔrF. It is also given as K=Y×r0. Here Y is the Young’s modulus and r0 is the interatomic distance.

#### What is K in the elastic formula?

Elastic Potential Energy Calculator This elastic potential energy calculator makes it easy to determine the potential energy of a spring when stretched or compressed. Read on to get a better understanding of this concept, including an elastic potential energy definition and an example of calculations.

Make sure to check out our, too! Imagine a simple helical spring. You can compress or stretch it (to some extent, of course). To do it, though, you need to perform some work – or, in other words, to provide it with some energy. This energy is then stored in the spring and released when it comes back to its equilibrium state (the initial shape and length).

Remember that the elastic potential energy is always positive. Why exactly is this called ‘potential energy’? You can think of it like this: the spring doesn’t spend the energy at once (in contrary to ), but has the potential to do so. Don’t forget that you cannot compress or stretch a spring to infinity and expect it to return to its original shape.

• k is the constant. It is a proportionality constant that describes the relationship between the strain (deformation) in the spring and the force that causes it. However, in the case of rotational forces the is of interest. The value of spring constant is always real and positive. The units are Newtons per meter;
• Δx is the deformation (stretch or compression) of the spring, expressed in meters; and
• U is the elastic potential energy in Joules.

Try the if you want to calculate the force in the spring as well. Follow these steps to find its value in no time!

1. Determine the spring constant k, We can assume a spring of k = 80 N/m,
2. Decide how far you want to stretch or compress your spring. Let’s say that we compress it by x= 0.15 m, Note that the initial length of the spring is not essential here.
3. Substitute these values to the spring potential energy formula: U = ½kΔx 2,
4. Calculate the energy. In our example it will be equal to U = 0.5 * 80 * 0.15² = 0.9 J,
5. You can also type the values directly into the elastic potential energy calculator and save yourself some time 🙂

The elastic potential energy stored in a stretched wire is half of the product of the stretching force (F) and the elongation (Δx): The compression or stretching of any string involves storing supplied energy in the form of potential energy. Hence, this results in an increase in the elastic potential energy.

u = (1/2) × (F/A) × (Δx/x)

But, (F/A) is stress, and (Δx/x) is the strain. Thus,

u = (1/2) × stress × strain

No, elastic potential energy is due to the deformation of an object’s shape and so does not depend upon the object’s mass. The elongation of a stretched string with a constant k and a strain energy, or elastic potential energy, of 98 J is: Thus, the given string has an elongation of: √(2 × 98 J/ 15 Nm -1 ) = 3.6 m, : Elastic Potential Energy Calculator

#### Why is K negative in Hooke’s law?

Want to join the conversation? –

At 9:44 you wrote that F=-2x, but if k=-2, then F = -(-2)x = 2x

k, being the spring constant, is always a positive number. the negative sign indicates that the restorative force is in the opposite direction of the applied force. in actuality the equation should be -F=2x but it is still algebraically correct.

F=-Kx, Sal explains what x and F are, but not what -K is. Does it have a name or any further description in physics besides just -K?

K indicates the spring constant of that spring. It is just a constant that varies depending on the spring. A common exercise in an introductory physics lab is measuring the spring constant of a spring experimentally.

I have a simple question: On a microscopic level, what force(s) makes the spring want to restore itself to its original position?

The equilibrium position of the string minimizes the potential energy of the metal atoms from which the spring is constructed. I don’t know how much inorganic chemistry you know, but what it basically comes down to is that chemical bonds have a sort of “best distance of separation.” Atoms consist of subatomic constituents that carry electric charges (nuclei are positively charged due to protons and the space around the exterior of the atom has a negative charge due to the electrons). Bring two nuclei too close together and their positive like charges will repel-this is the case with spring compression. Separate the bound atoms by too great a distance and the “electron glue” that holds them together will create tension that draws the atoms back together-this is stretching the spring. Keep in mind that this is a very very simplified explanation of what really happens, to truly understand the nature of this elastic energy you must study the wave-nature of subatomic particles and quantum mechanics.

What does the constant K of the spring determine ? Does it vary from spring to spring depending on the material it’s made of ? If not, then what ?

K is a constant that represents the elasticity of a spring (and therefore stiffness). It varies between spring to spring, depending on what it is made of, the shape of the spring, and the width of the wire.

Elastomers are polymers that are designed to be highly elastic (they can stretch far without breaking). For example, yoga pants, running tights, nylons, and the rubber bands are all composed of elastomers. The concept was first discovered with the sap of the rubber tree, which was distilled into highly flexible material. Today, manufacturing companies can artificially design/construct their own materials.

As Sal explained in the video that the restoring for is ‘ F = -kx”, he also take the restoring force to be equal to the force applied by Newton’s 3rd Law. But how is it necessary to be the same. If k has big value, we will have to apply large force for very small displacement in that case restoring force will be lesser because of very small value of ‘x’.

Sal is right. If k has a big value, you will have to apply a huge force to cause a small displacement. But that also means (k having a big value) that for a small displacement the restoring force will be huge. In the end everything is balanced and Newton’s 3rd law still holds 😀

well what does x stand for?

x is the displacement of the spring’s end from its equilibrium point – how much the spring is stretched (or, in the other direction, compressed)

At the end, wouldn’t the restoration force be -2N because we have defined right as positive?

Yep. You’re correct – and Sal briefly says that near the end.

I have a query regarding springs in a series combination. Say, there’s a thread attached to the ceiling, connecting three springs vertically and a block of mass ‘M’ connected at the bottom. It is said that the force is same for all springs in series (=Mg in this case). How is this possible if we have mass-full springs? Or is it applicable solely for ‘mass-less’ springs?

great point. yes, usually we have ‘mass-less’ springs. ie their mass is very very small compared to the mass being suspended by the springs. OR we may be given the ‘mass per unit length’ of each spring and therefore able to figure out the extension due to the mass of the springs, but this is probably an unlikely situaiton (though not impossible in some courses) ok??

I saw F= k*x^2/2 what is that different from Hooke’s law?

I believe you mean U = k*x^2/2. This is equivalent to Hooke’s law. (U is potential energy stored by spring device)

## What does K mean in interest?

Compound Interest –

P N is the balance in the account after N years. P 0 is the starting balance of the account (also called initial deposit, or principal) r is the annual interest rate in decimal form k is the number of compounding periods in one year

If the compounding is done annually (once a year), k = 1. If the compounding is done quarterly, k = 4. If the compounding is done monthly, k = 12. If the compounding is done daily, k = 365.

The most important thing to remember about using this formula is that it assumes that we put money in the account once and let it sit there earning interest. In the next example, we show how to use the compound interest formula to find the balance on a certificate of deposit after 20 years.

## What does it mean if K is less than 1?

Equilibrium Constant Overview – A large equilibrium constant means that the reaction proceeds in the forward direction, from reactants to products, until almost all the reactants have been converted to products. A small equilibrium constant, or when K eq is less than one, means that the chemical reaction will favor the reactants and the reaction will proceed in the opposite direction.

An equilibrium constant of 1 indicates that the reactants and products will be equal when the reaction reaches equilibrium. Scientists use the equilibrium constant of an equation to better understand how quickly the equilibrium will be reached, and whether the equilibrium will favor reactants or products.

The constant can be calculated using the ratio of products to reactants when the equation has reached equilibrium. The equilibrium constant is often represented by the variable K eq, which is defined by the equilibrium constant expression seen below.

### What does a higher K value mean?

In terms of a reaction, a high K value tells us that there are more products than reactants in the chemical reaction, and therefore a greater equilibrium concentration of the products.

### What does a high K value mean?

Video transcript – – The magnitude of the equilibrium constant tells us the relative amounts of products and reactants at equilibrium. For example, let’s look at a hypothetical reaction where gas A turns into gas B. And for the first example, let’s say that gas A is represented by a red sphere and gas B is represented by a blue sphere.

And down here, we have a particulate diagram showing an equilibrium mixture of our hypothetical reaction. Let’s write the equilibrium constant expression for this hypothetical reaction. So we’re gonna write Kc is equal to, and we think products over reactants. So our product is B. So this can be the concentration of B.

And since the coefficient is a one in the balanced equation, it’s the concentration of B raised to the first power divided by the concentration of our reactant, which is A. And A in the balanced equation also has a coefficient of one. So this is the concentration of A raised to the first power.

If we assume that each particle in our particulate diagram represents 0.1 moles of a substance, and the volume is one liter, we can calculate the concentration of both A and B. For example, for B, there are five blue spheres. So that’ll be five times 0.1 moles or 0.5 moles. So for the concentration of B, we have 0.5 moles divided by a volume of one liter.

So 0.5 divided by one is 0.5 molar. So we can go ahead and plug that in for our concentration of B. It’s 0.5 molar. Next, we can do the same thing for A. There are also five red spheres. And so therefore the concentration of A is also 0.5 molar. So we can plug that into our equilibrium constant expression.0.5 divided by 0.5 is equal to one.

• So therefore, Kc, the equilibrium constant is equal to one at whatever temperature we have for our hypothetical reaction.
• So our equilibrium constant Kc is equal to one.
• And we saw in our particulate diagram at equilibrium, we have equal amounts of reactants and products.
• Therefore just by knowing the value for the equilibrium constant, we know about the relative amounts of reactants and products at equilibrium.

Let’s look at another hypothetical reaction, which also has gas A turning into gas B. However, this time gas A is green and gas B is red. And let’s calculate the equilibrium constant Kc for this reaction. And once again, our particulate diagram shows an equilibrium mixture.

So Kc is equal to the concentration of B over the concentration of A. And it’s a lot faster to simply count our particles. So for B, B is red, we have one red particle here, so we can go ahead and put in one. And then for gas A, we have one, two, three, four, five, six, seven, eight, nine, 10 particles.

So one divided by 10 is equal to 0.1. So Kc is equal to 0.1 for this hypothetical reaction at a certain temperature. So the magnitude of the equilibrium constant tells us about the reaction mixture at equilibrium. For this reaction, Kc is equal to 0.1. So K is less than one.

And if we think about what that means, K is equal to products over reactants. So if K is less than one, that means we have a smaller number in the numerator and a larger number in the denominator, which means there are more reactants than products at equilibrium. Let’s look at another hypothetical reaction where gas A turns into gas B.

This time gas A is yellow and gas B is blue. If we look at our particulate diagram, showing our reaction mixture at equilibrium, there are 10 blue particles and only one yellow particle. So when plug into our equilibrium constant expression, this time it’s going to be 10 over one.

• Therefore the equilibrium constant Kc is equal to 10 for this particular reaction at a certain temperature.
• Once again, the magnitude of the equilibrium constant tells us something about the reaction mixture at equilibrium.
• For this hypothetical reaction, Kc is equal to 10.
• So K is greater than one.
• And when K is greater than one, once again, we have products over reactants.

So the numerator must be larger than the denominator, which means we have a lot more products than reactants at equilibrium. Let’s look at the reaction of carbon monoxide and chlorine gas to form phosgene. At 100 degrees Celsius, the equilibrium constant for this reaction is 4.56 times 10 to the ninth.

• Since the equilibrium constant K is greater than one, we know there are more products than reactants at equilibrium.
• And with the extremely large value for K, like 10 to the ninth, we could even assume this reaction essentially goes to completion.
• For the reaction of hydrogen gas and iodine gas to form hydrogen iodine, the equilibrium constant Kc is equal to 51 at 448 degrees Celsius.

Since the equilibrium constant is relatively close to one. This means at equilibrium, we have appreciable amounts of both our reactants and our products. Let’s look at the reaction of nitrogen gas plus oxygen gas plus bromine gas to form NOBr. At 298 Kelvin, the equilibrium constant for this reaction is 9.5 times 10 to the negative 31st.

### What does a very high value of K indicate?

A very high value of K indicates that at equilibrium most of the reactants are converted into products. The equilibrium constant K is the ratio of the concentrations of products to the concentrations of reactants raised to appropriate stoichiometric coefficients.

#### What is K in potential energy of spring?

K is the spring constant. x is the spring displacement.

## What determines k of a spring?

W = kx. W is the weight of the added mass. Therefore, the spring constant k is the slope of the straight line W versus x plot. Weight is mass times the acceleration of gravity or W = mg where g is about 980 cm/sec2.