Question

Consider this initial-rate data at a certain temperature for the reaction described by N2O3(

Answer 1

N2O3(g)→NO(g)+NO2(g)

[N2O3] Initial Rate
0.1 M     r(t)=0.66 M/s
0.2 M     r(t)=1.32 M/s
0.3 M     r(t)=1.98 M/s

We can have the relationship:

([N2O3]/[N2O3]0)^m=r(t)/r0(t)
However,
([N2O3]/[N2O3]0) = 2

Also, we assume m=1 which is the order of the reaction.

Thus, the relationship is simplified to,

r(t)/r0(t) = 2

r(t)=k[N2O3]

0.66 M/s=k×0.1 M

k=6.6 s−1

Answer 2

The value of k is $\boxed{\text{6.6 s}^{-1}}$ .

Further Explanation:

Order of reaction:

It is sum of exponents of concentration of each of the reactants that are present in chemical reaction. In other words, order indicates power dependence of order of reaction on reactant concentration.

Given reaction is as follows:

 $\text{N}_2\text{O}_3(\text{g})\rightarrow\text{NO}(\text{g})+\text{NO}_2(\text{g})$

When concentration of  $\text{N}_2\text{O}_3$ changes from 0.1 M to 0.2 M, rate of reaction becomes doubled. This implies order of reaction with respect to  $\text{N}_2\text{O}_3$ is one.

The expression for rate of given reaction is as follows:

$\text{Rate}=\text{k}[\text{N}_2\text{O}_3]$                                         ...... (1)

Where, k is the rate constant of reaction.

Rearrange equation (1) to calculate the value of k.

$\text{k}=\dfrac{\text{Rate}}{[\text{N}_2\text{O}_3]}$                                                     ...... (2)

Any of the three given concentrations of  $\text{N}_2\text{O}_3$ can be considered for calculation of rate constant along with the respective initial rates of reaction.

Here, we take concentration of $\text{N}_2\text{O}_3$ as 0.1 M so rate corresponding to this is 0.66 M/s.

Substitute 0.1 M for  $[\text{N}_2\text{O}_3]$ and 0.66 M/s for rate in equation (2).

 $\begin{aligned}{\text{k}&=\dfrac{\text{0.66 M/s}}{\text{0.1 M}}\\&=\text{6.6 s}^{-1}}\end{aligned}$

 

Therefore the value of rate constant (k) for the given reaction comes out to be $\text{6.6 s}^{-1}}$.

Learn More:  

1. What is the half-life of the reaction? brainly.com/question/8907464  2. Rate of chemical reaction: brainly.com/question/1569924  

Answer Details:  

Grade: Senior School  

Subject: Chemistry  

Chapter: Chemical Kinetics  

Keywords: k, rate, order, N2O3, NO, NO2, 0.1 M, 0.66, 0.2 M, 1.32, 0.3 M, 1.98, rate constant, sum, exponents.