Data for the following reaction are given in the table...

Data for the following reaction are given in the table below. $$\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{NO}(\mathrm{g})$$ $$\begin{array}{cccl}\text { Experiment } & \begin{array}{c}\text { Concentration }(\mathrm{mol} / \mathrm{L}) \\{[\mathrm{CO}]} {\quad \quad \quad \quad} \left[\mathrm{NO}_{2}\right]\end{array} & \begin{array}{c}\text { Initial Rate } \\(\mathrm{mol} / \mathrm{L} \cdot \mathrm{h})\end{array} \\\hline 1 & 5.0 \times 10^{-4} {\quad \quad} 0.36 \times 10^{-4} & 3.4 \times 10^{-8} \\ 2 & 5.0 \times 10^{-4} {\quad \quad} 0.18 \times 10^{-4} & 1.7 \times 10^{-8} \\ 3 & 1.0 \times 10^{-3} {\quad \quad} 0.36 \times 10^{-4} & 6.8 \times 10^{-8} \\ 4 & 1.5 \times 10^{-3} {\quad \quad} 0.72 \times 10^{-4} & ? \\\hline\end{array}$$ (a) What is the rate law for this reaction? (b) What is the rate constant for the reaction? (c) What is the initial rate of the reaction in experiment $4 ?$

Data for the following reaction are given in the table below. $$\mathrm{CO}(\mathrm{g})+\mathrm{NO}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+\mathrm{NO}(\mathrm{g})$$
$$\begin{array}{cccl}\text { Experiment } & \begin{array}{c}\text { Concentration }(\mathrm{mol} / \mathrm{L}) \\{[\mathrm{CO}]} {\quad \quad \quad \quad} \left[\mathrm{NO}_{2}\right]\end{array} & \begin{array}{c}\text { Initial Rate } \\(\mathrm{mol} / \mathrm{L} \cdot \mathrm{h})\end{array} \\\hline
1 & 5.0 \times 10^{-4} {\quad \quad} 0.36 \times 10^{-4} & 3.4 \times 10^{-8} \\
2 & 5.0 \times 10^{-4} {\quad \quad} 0.18 \times 10^{-4} & 1.7 \times 10^{-8} \\
3 & 1.0 \times 10^{-3} {\quad \quad} 0.36 \times 10^{-4} & 6.8 \times 10^{-8} \\
4 & 1.5 \times 10^{-3} {\quad \quad} 0.72 \times 10^{-4} & ? \\\hline\end{array}$$
(a) What is the rate law for this reaction?
(b) What is the rate constant for the reaction?
(c) What is the initial rate of the reaction in experiment $4 ?$

Key Concepts

Rate Law

The rate law in chemical kinetics expresses the mathematical relationship between the rate of a reaction and the concentrations of the reactants. It specifies which reactant concentrations affect the rate and to what power they are raised, indicating the reaction order with respect to each reactant. Understanding the rate law is crucial because it provides insights into the reaction mechanism and helps in predicting how changes in conditions will impact the reaction rate.

Reaction Order

Reaction order is the sum of the exponents of the concentration terms in the rate law. It tells us how the rate is affected by changes in the concentration of the reactants and can be determined experimentally by measuring initial rates under different reactant concentrations. The orders may be zero, first, second, or fractional, and they are essential in understanding how variations in reactant levels influence the overall speed of the reaction.

Initial Rate Method

The initial rate method is a technique used to determine the reaction order and rate constant by measuring the rate of reaction at the very beginning when the concentrations of reactants are known and unaltered by the reaction progress. By comparing the initial rates of reaction under different conditions, one can deduce how the rate depends on the reactant concentrations, thus establishing the exponents in the rate law.

Rate Constant

The rate constant (often denoted as k) is a proportionality factor in the rate law that links the rate of reaction to the concentrations of reactants. It is a measure of the intrinsic speed of the reaction at a given temperature and is determined experimentally. The value of the rate constant is crucial for predicting reaction kinetics and comparing the reactivity of different chemical processes.

Transcript

00:01 So in order to derive the rate equation, we need to figure out the order with respect to each of the reactants.

00:08 And so first, let's deal with co.

00:12 To figure out the order of carbon monoxide, we want to find two experiments where the concentration of no2, the other reactant, are constant.

00:22 And so the experiments that we can see here, well, let's take a look.

00:29 We'll do experiment 1 and 5.

00:32 The first and last one.

00:34 The concentration of no2 is the same there.

00:36 And so the concentration of co goes from being 5 .1 times 10 to the negative fourth to being 1 .5 times 10 to negative thirds.

00:47 In other words, it increased by a factor of three.

00:50 So now let's see how the rate changed.

00:54 The rate went from being 3 .4 times 10 to negative a to 10 .2 times 10 to negative a if.

01:05 And if you plug this into calculator take this divided by that you will find that it's also increased by a factor of three and so since these are values are the same this is a first order with respect to carbon monoxide let's do the same process for n .2 we're looking for two experiments where the concentration of c .o.

01:31 Is constant so we can just do one and two and we can see that the concentration of no2 in those two reactions went from 0 .35 times 10 to negative 4 to 0 .7 times 10 to negative 4th so it went up by a factor of 2.

01:53 Let's see what happened to the rate.

01:58 While the rate went from 3 .4 times 10 to negative 8th to 6 .8 times 10 to negative 8th, you can do this for a calculator you can see pretty easily by inspection.

02:10 This also went up by a factor of 2.

02:12 So this is also first order with respect to no2...

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