### How To Find Rate Law From Mechanism?

- Marvin Harvey
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Rate law is an equation that relates the reaction rate to the concentration of the reactants. It is usually expressed as a first order, second order or zero order equation. Rate law can be determined experimentally or theoretically. Theoretically, rate law is determined from the mechanism of the reaction.

- The rate law is determined from the mechanism by taking the derivatives of the reaction rate with respect to the concentration of the reactants and equating them to zero.
- The order of the reaction is determined by the highest order of the derivatives.
- The rate constant is determined by the lowest order of the derivatives.

The rate law can also be determined experimentally by plotting the reaction rate against the concentration of the reactants and fitting a line to the data. The order of the reaction is determined by the slope of the line and the rate constant is determined by the y-intercept.

- The order of a reaction is the number of molecules of the reactant that are involved in the reaction.
- The rate constant is the proportionality constant that relates the reaction rate to the concentration of the reactants.
- The order of a reaction can be determined from the rate law.
- The rate law is expressed as a first order, second order or zero order equation.

The order of a reaction can be determined from the rate law. The rate constant is determined by the lowest order of the derivatives. The rate law can also be determined experimentally by plotting the reaction rate against the concentration of the reactants and fitting a line to the data.

What are the rate laws for each step in the mechanism? – For elementary reactions, the order of reaction for a reactant equals its stoichiometric coefficient (Remember: this is true only for elementary reactions!) Thus, the rate laws for each step in the proposed mechanism can be written down by inspection: Step 1 Rate = k 1 Step 2 Rate = k –1 2 Step 3 Rate = k 2 2 The slow step is rate limiting, so if this is an acceptable mechanism, then the rate law should match the experimental rate law. If we substitute this into the rate law from step 3 Now the observed rate law matches the rate law predicted by the mechanism, so this is a plausible mechanism.

## How do you write a rate law for a reaction?

From Elementary Steps – Write the rate law for the following reaction given the reaction mechanism elementary steps: 2NO 2 (g) + F 2 (g) → 2NO 2 F (g)

- NO 2 + F 2 → NO 2 F + F (slow)
- F + NO 2 → NO 2 F (fast)

Explanation: Since step 1 is the slower step, it is the rate-determining step for this reaction. Write the rate law by plugging in the reactants into the rate law equation. Answer: R = k

## How does the rate law work?

Molar Concentrations of Reactants – R = k n m The rate law uses the molar concentrations of reactants to determine the reaction rate. Typically, increased concentrations of reactants increases the speed of the reaction, because there are more molecules colliding and reacting with each other.

## How do you find the rate law from a table?

From a Table – To determine the rate law from a table, you must mathematically calculate how differences in molar concentrations of reactants affect the reaction rate to figure out the order of each reactant. Then, plug in values of the reaction rate and reactant concentrations to find the specific rate constant.

Finally, rewrite the rate law by plugging in the specific rate constant and the orders for the reactants. A table given will list the different tests of a reaction. Each different test will have different concentrations of reactants, and as a result, and the reaction rates for that test will be different.

Here’s an example of a data table for the experiment: 2HI (g) → H 2 (g) + I 2 (g)

Experiment | (M) | Rate (M/s) |

1 | 0.015 | 1.1 * 10 -3 M/s |

2 | 0.030 | 4.4 * 10 -3 M/s |

3 | 0.045 | 9.9 * 10 -3 M/s |

#### Are there rate laws that are consistent with a particular mechanism?

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Page ID 152013 Because a proposed mechanism can only be valid if it is consistent with the rate law found experimentally, the rate law plays a central role in the investigation of chemical reaction mechanisms. The discussion above introduces the problems and methods associated with collecting rate data and with finding an empirical rate law that fits experimental concentration- versus -time data.

We turn now to finding the rate laws that are consistent with a particular proposed mechanism. For simplicity, we consider reactions in closed constant-volume systems. In principle, numerical integration can be used to predict the concentration at any time of each of the species in any proposed reaction mechanism.

This prediction can be compared to experimental observations to see whether they are consistent with the proposed mechanism. To do the numerical integration, it is necessary to know the initial concentrations of all of the chemical species and to know, or assume, values of all of the rate constants.

- The initial concentrations are known from the procedure used to initiate the reaction.
- However, the rate constants must be determined by some iterative procedure in which initial estimates of the rate constants are used to predict concentration- versus -time data that can be compared to the experimental results to produce refined estimates.

In practice, we tailor our choice of reaction conditions so that we can use various approximations to test whether a proposed mechanism can explain the data. We now consider the most generally useful of these approximations. In this discussion, we assume that the overall reaction goes to completion; that is, at equilibrium the concentration of the reactant whose concentration is limiting has become essentially zero.

- If the overall reaction involves more than one elementary step, then an intermediate compound is involved.
- A valid mechanism must include this intermediate, and more than one differential equation may be needed to characterize the time rate of change of all of the species involved in the reaction.
- We focus on conditions and approximations under which the rate of appearance of the final products in a multi-step reaction mechanism can be described by a single differential equation, the rate law.

We examine the application of these approximations to a particular reaction mechanism. When we understand the application of these approximations to this mechanism, the ways in which they can be used in other situations are clear. Consider the following sequence of elementary steps \ whose kinetics are described by the following simultaneous differential equations: \+k_2\left \\ \frac &=k_1-k_2\left-k_3\left \\ \frac &=k_3\left \end \] The general analytical solution for this system of coupled differential equations can be obtained, but it is rather complex, because \(\left\) increases early in the reaction, passes through a maximum, and then decreases at long times.

In principle, experimental data could be fit to these equations. The numerical approach requires that we select values for \(k_1\), \(k_2\), \(k_3\), \( _0\), \( _0\), \( _0\), and \( _0\), and then numerically integrate to get \(\), \(\), \(\left\), and \(\left\) as functions of time. In principle, we could refine our estimates of \(k_1\), \(k_2\), and \(k_3\) by comparing the calculated values of one or more concentrations to the experimental ones.

In practice, the approximate treatments we consider next are more expedient. When we begin a kinetic study, we normally have a working hypothesis about the reaction mechanism, and we design our experiments to simplify the differential equations that apply to it.

For the present example, we will assume that we always arrange the experiment so that \( _0=0\) and \( _0=0\). In consequence, at all times: \+\left+\left.\] Also, we restrict our considerations to experiments in which \( _0\gg _0\). This exemplifies the use of flooding, The practical effect is that the concentration of \(B\) remains effectively constant at its initial value throughout the entire reaction, which simplifies the differential equations significantly.

In the present instance, setting \( _0\gg _0\) means that the rate-law term \(k_1\) can be replaced, to a good approximation, by \(k_ \), where \(k_ =k_1 _0\). Once we have decided upon the reaction conditions we are going to use, whether the resulting concentration- versus -time data can be described by a single differential equation depends on the relative magnitudes of the rate constants in the several steps of the overall reaction.

### What is the definition of rate law?

What is the Rate Law? The rate law (also known as the rate equation) for a chemical reaction is an expression that provides a relationship between the rate of the reaction and the concentrations of the reactants participating in it.