Question

Consider the following hypothetical aqueous reaction. A flask is charged with .065 mol of A in a total volume of 100.0 mL. The following data are collected:
Time (min) 0 10 20 30 40
Moles of A 0.065 0.051 0.042 0.036 0.031
This is a second order reaction.
What is the value of the rate constant for the reaction?

Answer 1

Answer: 0.422 M⁻¹s⁻¹

Explanation: Reaction Rate is the speed of decomposition of the reactant(s) per unit of time.

A Rate Law relates concentration of reactants, rate reaction and rate constant:

$r=k[A]^{x}[B]^{y}$

where

[A] and [B] are reactants concentration

x and y are reaction order, not related to the stoichiometric coefficients

k is rate constant

r is rate

Before calculating rate constant, first we have to determine reaction order.

In this question, the reactio order is 2. So, the rate law for it is

$-\frac{d[A]}{dt} =k[A]^{2}$

and the integrated formula is

$\frac{1}{[A]} =\frac{1}{[A]_{0}} +kt$

in which

[A]₀ is initial concentration of reactant

Then, using initial concentration at initial time and final concentration at final time:

$\frac{1}{0.031} =\frac{1}{0.065} +k(40)$

$40k=\frac{1}{0.031}-\frac{1}{0.065}$

$40k=32.26-15.38$

k = 0.422

The rate constant for the reaction is 0.422 M⁻¹.s⁻¹