Which Law Can Be Used To Calculate The Number Of Moles Of A Contained Gas?

Which Law Can Be Used To Calculate The Number Of Moles Of A Contained Gas
Section Summary –

  • The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
  • The ideal gas law can be written in terms of the number of molecules of gas: PV = NkT, where P is pressure, V is volume, T is temperature, N is number of molecules, and k is the Boltzmann constant k = 1.38 × 10 –23 J/K.
  • A mole is the number of atoms in a 12-g sample of carbon-12.
  • The number of molecules in a mole is called Avogadro’s number NA, NA = 6.02 × 10 23 mol −1,
  • A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
  • The ideal gas law can also be written and solved in terms of the number of moles of gas: PV = nRT, where n is number of moles and R is the universal gas constant, R = 8.31 J/mol ⋅ K.
  • The ideal gas law is generally valid at temperatures well above the boiling temperature.

Which law will you use to calculate the number of moles?

Summary –

Calculations for relationships between volume and number of moles of a gas can be performed using Avogadro’s Law.

How do you find the number of moles in a gas?

The formula to find out the number of moles at STP is Number of moles = Molar volume at STP litres /V o l u m e ITP litres.

Which law can be used to calculate the number of moles of a contained gas Boyle’s law combined gas law ideal gas law?

Key Takeaways: Combined Gas Law –

The combined gas law is one of the ideal gas laws.It gets its name because it combines Boyle’s law, Charles’ law, and Gay-Lussac’s law.When using this law, only pressure, volume, and temperature can change. The amount or number of moles of gas is held constant.Essentially, the law states that the ratio between pressure, volume, and absolute temperature of a gas equals some constant. So, if you change one of these variables, you can predict how the other factors are affected.

Which law helps us find the moles of gas?

Avogadro’s law – The volume (\(V\)) of an ideal gas varies directly with the number of moles of the gas ( n ) when the pressure ( P ) and the number of temperature ( T ) are constant. We can express this mathematically as: \ \ As before, we can use Avogadro’s law to predict what will happen to the volume of a sample of gas as we change the number of moles.

Are moles constant in Charles law?

Is this consistent with pV = nRT? You have a fixed mass of gas, so n (the number of moles) is constant.

What is Avogadro’s law used for?

Avogadro’s law, a statement that under the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules, This empirical relation can be derived from the kinetic theory of gases under the assumption of a perfect (ideal) gas,

  1. The law is approximately valid for real gases at sufficiently low pressures and high temperatures.
  2. The specific number of molecules in one gram- mole of a substance, defined as the molecular weight in grams, is 6.02214076 × 10 23, a quantity called Avogadro’s number, or the Avogadro constant,
  3. For example, the molecular weight of oxygen is 32.00, so that one gram-mole of oxygen has a mass of 32.00 grams and contains 6.02214076 × 10 23 molecules.

The volume occupied by one gram-mole of gas is about 22.4 litres (0.791 cubic foot) at standard temperature and pressure (0 °C, 1 atmosphere) and is the same for all gases, according to Avogadro’s law. The law was first proposed in 1811 by Amedeo Avogadro, a professor of higher physics at the University of Turin for many years, but it was not generally accepted until after 1858, when an Italian chemist, Stanislao Cannizzaro, constructed a logical system of chemistry based on it.

What is R constant in ideal gas law?

The factor ‘R’ in the ideal gas law equation is known as the ‘gas constant’. R = PV. nT. The pressure times the volume of a gas divided by the number of moles and temperature of the gas is always equal to a constant number.

How do you use ideal gas law?

The Ideal Gas Law explained Learn about the concept of the Ideal Gas Law Learn about Avogadro’s number and the ideal gas law. Encyclopædia Britannica, Inc. Although we can’t see them, we are surrounded by gas molecules. If we look at gas molecules in a balloon, we would see the gas molecules in motion, constantly bouncing up against the inside surface of the balloon.

How can we use math to understand gas in a closed system like this? The Ideal Gas Law states that for any gas, its volume (V) multiplied by its pressure (P) is equal to the number of moles of gas (n) multiplied by its temperature (T) multiplied by the ideal gas constant, R. PV=nRT But what exactly is R? If we rewrite the ideal gas law to solve for R, we find that R equals the value of P times V, divided by the value of n times T.

Because R is a constant, we can use the qualities of any gas — its temperature, pressure, volume, and number of moles — to determine the value of R. Avogadro’s law states that equal volumes of all gases, at the same temperature and pressure, have the same number of molecules.

This means four balloons, at the same temperature, filled to the same volume, with four different gasses, all contain the same number of moles of gas. People have used this law to find the number of molecules of gas at a standard temperature and pressure, abbreviated as STP. STP is 273 Kelvin and 1 atmosphere (atm), the standard unit for atmospheric pressure.

At STP, 1 mole of gas takes up 22.4 liters. Let’s plug those numbers into the ideal gas law. R equals the value of 1 atmosphere multiplied by 22.4 liters, divided by the value of 1 mole multiplied by 273 degrees kelvin equals 0.0821 atmosphere liters per moles Kelvin.

What is ATM in gas law?

Gas Laws

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    Gases behave differently from the other two commonly studied states of matter, solids and liquids, so we have different methods for treating and understanding how gases behave under certain conditions. Gases, unlike solids and liquids, have neither fixed volume nor shape.

    • They are molded entirely by the container in which they are held.
    • We have three variables by which we measure gases:, volume, and temperature.
    • Pressure is measured as force per area.
    • The standard SI unit for pressure is the pascal (Pa).
    • However, atmospheres (atm) and several other units are commonly used.

    The table below shows the conversions between these units.1 pascal (Pa) 1 N*m -2 = 1 kg*m -1 *s -2 1 atmosphere (atm) 1.01325*10 5 Pa 1 atmosphere (atm) 760 torr 1 bar 10 5 Pa Volume is related between all gases by Avogadro’s hypothesis, which states: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

    See also:  Explain How Corn Can Be Used As An Example Of Mendel'S Law Of Independent Assortment?
    V m = Vn = 22.4 L at 0°C and 1 atm


  • Where:
  • V m = molar volume, in liters, the volume that one mole of gas occupies under those conditions V =volume in liters n =moles of gas
  • An equation that chemists call the Ideal Gas Law, shown below, relates the volume, temperature, and pressure of a gas, considering the amount of gas present.
  • PV = nRT Where: P =pressure in atm T =temperature in Kelvins R is the molar gas constant, where R=0.082058 L atm mol -1 K -1, The Ideal Gas Law assumes several factors about the molecules of gas. The volume of the molecules is considered negligible compared to the volume of the container in which they are held.

    • We also assume that gas molecules move randomly, and collide in completely elastic collisions.
    • Attractive and repulsive forces between the molecules are therefore considered negligible.
    • Example Problem: A gas exerts a pressure of 0.892 atm in a 5.00 L container at 15°C.
    • The density of the gas is 1.22 g/L.

    What is the molecular mass of the gas?

      PV = nRT
      T = 273 + 15 = 228
      (0.892)(5.00) = n(.0821)(288)
      n = 0.189 mol
    ,189 mol5.00L x x grams1 mol = 1.22 g/L

    /td>   x = Molecular Weight = 32.3 g/mol

    We can also use the Ideal Gas Law to quantitatively determine how changing the pressure, temperature, volume, and number of moles of substance affects the system. Because the gas constant, R, is the same for all gases in any situation, if you solve for R in the Ideal Gas Law and then set two Gas Laws equal to one another, you have the Combined Gas Law: Where:

    1. values with a subscript of “1” refer to initial conditions values with a subscript of “2” refer to final conditions
    2. If you know the initial conditions of a system and want to determine the new pressure after you increase the volume while keeping the numbers of moles and the temperature the same, plug in all of the values you know and then simply solve for the unknown value.

    Example Problem: A 25.0 mL sample of gas is enclosed in a flask at 22°C. If the flask was placed in an ice bath at 0°C, what would the new gas volume be if the pressure is held constant?

      Because the pressure and the number of moles are held constant, we do not  need to represent them in the equation because their values will cancel. So the   combined gas law equation becomes:
      V 2 = 23.1 mL

    We can apply the Ideal Gas Law to solve several problems. Thus far, we have considered only gases of one substance, pure gases. We also understand what happens when several substances are mixed in one container. According to Dalton’s law of, we know that the total pressure exerted on a container by several different gases, is equal to the sum of the pressures exerted on the container by each gas.

    • Where:
    • P t =total pressure P 1 =partial pressure of gas “1” P 2 =partial pressure of gas “2” and so on
    • Using the Ideal Gas Law, and comparing the pressure of one gas to the total pressure, we solve for the,
    P 1 P t = n 2 RT/V n t RT/V = n 1 n t = X 1


  • Where:
  • X 1 = mole fraction of gas “1”
  • And discover that the partial pressure of each the gas in the mixture is equal to the total pressure multiplied by the mole fraction.
  • Example Problem: A 10.73 g sample of PCl 5 is placed in a 4.00 L flask at 200°C. a) What is the initial pressure of the flask before any reaction takes place? b) PCl 5 dissociates according to the equation: PCl 5 (g) -> PCl 3 (g) + Cl 2 (g). If half of the total number of moles of PCl 5 (g) dissociates and the observed pressure is 1.25 atm, what is the partial pressure of Cl 2 (g)?

      a) 10.73 g PCl 5 x 1 mol208.5 g = 0.05146 mol PCl 5

    /td>      PV = nRT      T = 273 + 200 = 473      P(4.00) = (.05146)(.0821)(473)      P = 0.4996 atm   b) PCl 5 → PCl 3 + Cl 2      Start: .05146 mol 0 mol 0 mol      Change: -.02573 mol +.02573 mol +.02573 mol      Final: .02573 mol .02573 mol .02573 mol

         X Cl 2 = n Cl 2 n total = P Cl 2 P total


          P Cl 2 1.25 atm = ,02573 mol.07719 mol

    /td>       P Cl 2 =,4167 atm

    As we stated earlier, the shape of a gas is determined entirely by the container in which the gas is held. Sometimes, however, the container may have small holes, or leaks. Molecules will flow out of these leaks, in a process called, Because massive molecules travel slower than lighter molecules, the rate of effusion is specific to each particular gas.

    We use Graham’s law to represent the relationship between rates of effusion for two different molecules. This relationship is equal to the square-root of the inverse of the molecular masses of the two substances. Where: r 1 =rate of effusion in molecules per unit time of gas “1” r 2 =rate of effusion in molecules per unit time of gas “2” u 1 =molecular mass of gas “1” u 2 =molecular mass of gas “2” Previously, we considered only ideal gases, those that fit the assumptions of the ideal gas law.

    Gases, however, are never perfectly in the ideal state. All atoms of every gas have mass and volume. When pressure is low and temperature is low, gases behave similarly to gases in the ideal state. When pressure and temperature increase, gases deviate farther from the ideal state.

    • Where the van der Waals constants are:
    • a accounts for molecular attraction b accounts for volume of molecules
    • The table below shows values for a and b of several different compounds and elements.
    Species a (dm 6 bar mol -2 ) b (dm 3 mol -1 )
    Helium 0.034598 0.023733
    Hydrogen 0.24646 0.026665
    Nitrogen 1.3661 0.038577
    Oxygen 1.3820 0.031860
    Benzene 18.876 0.11974

    Practice Ideal Gas Law Problem: 2.00 g of hydrogen gas and 19.2 g of oxygen gas are placed in a 100.0 L container. These gases react to form H 2 O(g). The temperature is 38°C at the end of the reaction. a) What is the pressure at the conclusion of the reaction? b) If the temperature was raised to 77° C, what would the new pressure be in the same container?,

    1. Practice Pressure Problem: 1 mole of oxygen gas and 2 moles of ammonia are placed in a container and allowed to react at 850°C according to the equation:

    4 NH 3 (g) + 5 O 2 (g) -> 4 NO(g) + 6 H 2 O(g)

    • b) Using Graham’s Law, what is the ratio of the effusion rates of NH 3 (g) to O 2 (g)?

    a) If the total pressure in the container is 5.00 atm, what are the partial pressures for the three gases remaining?, An Online Interactive Tool Developed by in cooperation with the,

    1. Copyright © 1996-2008 Shodor Please direct questions and comments about this page to

    : Gas Laws

    What is Charles Law and Boyle’s law?

    Introduction – The three fundamental gas laws discover the relationship of pressure, temperature, volume and amount of gas. Boyle’s Law tells us that the volume of gas increases as the pressure decreases. Charles’ Law tells us that the volume of gas increases as the temperature increases.

    What does Boyle’s law calculate?

    Home Science Physics Matter & Energy Alternate titles: Mariotte’s law, first gas law Boyle’s law, also called Mariotte’s law, a relation concerning the compression and expansion of a gas at constant temperature, This empirical relation, formulated by the physicist Robert Boyle in 1662, states that the pressure ( p ) of a given quantity of gas varies inversely with its volume ( v ) at constant temperature; i.e., in equation form, p v = k, a constant.

    The relationship was also discovered by the French physicist Edme Mariotte (1676). The law can be derived from the kinetic theory of gases assuming a perfect (ideal) gas ( see perfect gas ). Real gases obey Boyle’s law at sufficiently low pressures, although the product p v generally decreases slightly at higher pressures, where the gas begins to depart from ideal behaviour.

    The Editors of Encyclopaedia Britannica This article was most recently revised and updated by Adam Augustyn,

    What does Henry’s law find?

    Henry’s Law – Statement, Formula, Constant, Solved Examples Henry’s law is a gas law which states that at the amount of gas that is dissolved in a liquid is directly proportional to the partial pressure of that gas above the liquid when the temperature is kept constant.

    ‘P’ denotes the partial pressure of the gas in the atmosphere above the liquid. ‘C’ denotes the concentration of the dissolved gas. ‘k H ‘ is the Henry’s law constant of the gas.

    Is Avogadro’s law the same as ideal gas law?

    PV = nRT – Where:

    P is pressure V is volume n is the number of gas molecules in moles R is a number known as the ideal gas constant (The value for R is often, but not always, 8.314 J/mol ˖ K) T is temperature (which has to be in Kelvin)

    The chart below shows how all the above gas laws are present in this ideal gas law.

    Law Variables Symbols in Formula
    Boyle pressure & volume P, V
    Charles volume & temperature V, T
    Gay-Lussac pressure & temperature P, T
    Avogadro volume & amount V, n

    Although in reality no gas is an ‘ideal gas’, some do come very close. Therefore, the Ideal Gas Law allows us to roughly predict the behaviour of a gas. This formula is often used when you want to determine the amount of gas that is present in a container.

    For example, you could find the mass of gas in a container by weighing the gas in the container, pumping out the gas and then reweighing the container. However, since gases have such low weight, the difference would be so small it would be hard to measure. Instead, all you need to know is the pressure – which can be obtained from a pressure gauge – the volume of the container, and the temperature of the gas.

    Then put these values into the formula and solve for n, from which the mass can be obtained.

    What is the gas law called?

    Home Science Physics Matter & Energy gas laws, laws that relate the pressure, volume, and temperature of a gas, Boyle’s law —named for Robert Boyle —states that, at constant temperature, the pressure P of a gas varies inversely with its volume V, or P V = k, where k is a constant.

    1. Charles’s law —named for J.-A.-C.
    2. Charles (1746–1823)—states that, at constant pressure, the volume V of a gas is directly proportional to its absolute (Kelvin) temperature T, or V / T = k,
    3. These two laws can be combined to form the ideal gas law, a single generalization of the behaviour of gases known as an equation of state, P V = n R T, where n is the number of gram-moles of a gas and R is called the universal gas constant,

    Though this law describes the behaviour of an ideal gas, it closely approximates the behaviour of real gases. See also Joseph Gay-Lussac, Erik Gregersen

    What formula is used in Charles Law?

    Charles Law states that the volume of a given mass of a gas is directly proportional to its Kevin temperature at constant pressure. In mathematical terms, the relationship between temperature and volume is expressed as V1/T1=V2/T2. Alright. One of the gas laws that you might come across is called Charles Law, and Charles law was formed by Jacque Charles in France in the 1800s.

    1. And he discovered that the volume of a given mass of a gas is directly proportional to its kelvin temperature at constant pressure.
    2. There are two things that you want to make sure you know or you notice when you’re reading this gas law.
    3. One is the kelvin temperature where you make sure our temperature is always always always in kelvin or else we are going to get the wrong answer when dealing with this Charles law and you also want to notice it’s a constant pressure.

    So two variables that are changing is volume and, volume and temperature. Okay, those are the two variables we’re dealing with. So let’s say we have two canisters. They are at this, notice they are at the same pressure. So this, this canister we have gas pressure.

    We know normal temperature and pressure and then we actually heat it up. Okay. So now we’re increasing the kinetic energy. Those gas particles are now moving at a faster rate and they are able, if we want to make sure the pressure is constant. They are actually going to push against this the top of this thing and actually move making the volume larger.

    So if you notice, the relationship between temperature and volume as we increase temperature, we also increase the volume as long as pressure is constant. Okay? So, Charles law, its relationship is – we have a direct relationship as stated in the actual law and we can now actually make it mathematically equal.

    Volume one over divided by the temperature of one equals the volume of the second one divided by the temperature of the second scenario. So this is actually Charles law mathematically. If you were to make a graph, the graph of Charles law is at zero kelvin and we’re going to have zero volume because it’s zero kelvin, nothing moves and the volume of a gas is actually going to be zero, and it increases as the other one increases also.

    So you’re going to have linear relationship that looks like this. As temperature increases so does the volume of the gas. It also increases. Also as temperature decreases, volume of the gas actually decreases. Let’s actually do a demonstration that shows this.

    • Okay. So over here I have a candle floating in some water.
    • I’m going to light that candle.
    • Let me just put safety goggles on first.
    • And let’s do that. Okay. Alright.
    • I’m going to put this in here just to be safe.
    • Make sure I don’t burn anything down.
    • Okay, so what’s happening, the air particles around this candle are actually heating up, okay.

    So they’re expanding. I’m going to capture this, I’m going to capture this. I’m going to put this glass on top of this candle and what that’s going to do is going to end up going out because it’s going to all the oxygen in this glass container is going to go away.

    • It’s going to be used up.
    • So as it’s being used up the candle is going to go out.
    • And notice, when it went out, a lot of the volume in the water level rose inside the canister.
    • Now why did that happen? Because when the candle went out, the temperature of the gas particles inside the ga- inside this glass chamber actually dropped and that made the temp- the gas particles actually have a lower volume.

    Because the gas particles had a lower volume, they had, that volume had to replaced by something. And it was replaced by the water at the bottom. So the water is actually able to be sucked in to the glass container to replace that volume that was then lost due to the drop in temperature.

    1. Okay. So let’s do a problem that you might see in class. Okay.
    2. Something that you might see in class I’m going to take off my glass my goggles.
    3. Don’t need them anymore.
    4. A gas at 40 degrees celsius occupies a volume at 2.32 litres.
    5. If the temperature is raised to 75 degrees celsius, what will the new volume be if the pressure is constant.

    So I’m dealing with temperature and volume. So I know in my head that’s Charles law. Charles law deals with temperature and volume. Okay. It also deals with temperature in kelvins. So I want to make sure I change these temperatures to kelvin. So knowing that my formula is v1 over t1 equals v2 over t2.

    The first volume that we’re going to deal with is 2.32 litres. The first temperature is 40 degrees celsius. We add 273 to that and we get 313 kelvin and then our second volume is, we don’t know. It’s what we’re looking for. It’s what we’re looking for. Our second temperature is I’m just going to turn this on real quick.

    Our second temperature is 75 degrees celsius. We’re going to add 273 to that and we get two, 348 kelvin. We cross multiply 348 times 232 divided by 313, we get our new volume which is 2.58 litres and let’s see if that makes sense, okay? So we increased the temperature.

    What remains constant and Charles Law?

    Charles’s law, a statement that the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature, if the pressure remains constant.

    What remains constant in Boyle’s law?

    Boyle’s Law – Robert Boyle (1627-1691), an English chemist, is widely considered to be one of the founders of the modern experimental science of chemistry. He discovered that doubling the pressure of an enclosed sample of gas, while keeping its temperature constant, caused the volume of the gas to be reduced by half.

    Boyle’s law states that the volume of a given mass of gas varies inversely with the pressure when the temperature is kept constant. An inverse relationship is described in this way. As one variable increases in value, the other variable decreases. Physically, what is happening? The gas molecules are moving and are a certain distance apart from one another.

    An increase in pressure pushes the molecules closer together, reducing the volume. If the pressure is decreased, the gases are free to move about in a larger volume. Figure \(\PageIndex \): Robert Boyle. (CC BY-NC; CK-12) Mathematically, Boyle’s law can be expressed by the equation: \ The \(k\) is a constant for a given sample of gas and depends only on the mass of the gas and the temperature. The table below shows pressure and volume data for a set amount of gas at a constant temperature.

    Table \(\PageIndex \): Pressure-Volume Data

    Pressure \(\left( \text \right)\) Volume \(\left( \text \right)\) \(P \times V = k\) \(\left( \text \cdot \text \right)\)
    0.5 1000 500
    0.625 800 500
    1.0 500 500
    2.0 250 500
    5.0 100 500
    8.0 62.5 500
    10.0 50 500

    A graph of the data in the table further illustrates the inverse relationship nature of Boyle’s Law (see figure below). Volume is plotted on the \(x\)-axis, with the corresponding pressure on the \(y\)-axis. Which Law Can Be Used To Calculate The Number Of Moles Of A Contained Gas Figure \(\PageIndex \): The pressure of a gas decreases as the volume increases, making Boyle’s law an inverse relationship. (CC BY-NC; CK-12) Boyle’s Law can be used to compare changing conditions for a gas. We use \(P_1\) and \(V_1\) to stand for the initial pressure and initial volume of a gas.

    Which of the below is the Dalton’s law?

    According to Dalton’s law of partial pressures, the total pressure by a mixture of gases is equal to the sum of the partial pressures of each of the constituent gases.

    What is Avogadro gas law formula?

    Avogadro’s Law is stated mathematically as follows: Vn=k, where V is the volume of the gas, n is the number of moles of the gas, and k is a proportionality constant.

    What does the ideal gas law states?

    Ideal Gas Law Definition – The ideal gases obey the ideal gas law perfectly. This law states that: the volume of a given amount of gas is directly proportional to the number on moles of gas, directly proportional to the temperature and inversely proportional to the pressure.i.e. pV = nRT.

    How do you find moles in Avogadro’s law?

    One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions). The number 6.022 × 10²³ is known as Avogadro’s number or Avogadro’s constant. The concept of the mole can be used to convert between mass and number of particles Created by Sal Khan.

    What is Avogadro’s Law number?

    Molar Volume of a Gas – As per Avogadro’s law, the ratio of volume and amount of gaseous substance is a constant (at constant pressure and temperature). The value of this constant (k) can be determined with the help of the following equation: k = (RT)/P Under standard conditions for temperature and pressure, the value of T corresponds to 273.15 Kelvin and the value of P corresponds to 101.325 kilo Pascals.

    What does Avogadro’s law formula?

    💡 Summary –

    • Avogadro’s law states that the total number of atoms or molecules of any gas is directly proportional to the gaseous volume occupied at constant pressure and temperature.
    • Avogardro’s equation is written as V = k ྾ n or V1/n1 = V2/n2.