Chemistry, 24.07.2019 12:30, jayowens20

For the reaction x2 + y + z → xy + xz, it is found that doubling the concentration of x2 doubles the reaction rate, tripling the concentration of y triples the rate, and doubling the concentration of z has no effect. what is the rate law for this reaction?

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answered: Bloom247

The rate law for the given reaction is $\boxed{rate=k\left[ {{{\text{X}}_2}}\right]\left[ {\text{Y}} \right]}$ .

Further explanation:

The rate of reaction is defined decrease in concentrations of reaction in unit time or increase in products concentration in unit time. Rate of reaction is determined by the rate law. The rate law is a relationship between rate constant and reactants of the reaction.

Consider a reaction,

$a{\text{A}}+b{\text{B}}\to{\text{Products}}$

The rate law for the general equation is expressed as,

${\text{rate}}=k{\left[{\text{A}}\right]^a}{\left[{\text{B}}\right]^b}$ ...... (1)

Here,

rate is the rate of the reaction.

k is the rate constant.

[A] and [B] are the concentration of reactant species.

a is the order of reaction with respect to reactant A.

b is the order of reaction with respect to reactant A.

The given reaction is,

${{\text{X}}_2}+{\text{Y}}+{\text{Z}}\to{\text{XY}}+{\text{XZ}}$

The rate law for this reaction is can be written as follows:

${\text{rate}}=k{\left[{{{\text{X}}_2}}\right]^a}{\left[{\text{Y}}\right]^b}{\left[ {\text{Z}} \right]^c}$ …… (2)

Here, a, b, and c are order of reaction with respective to reactant ${{\text{X}}_2}$ , Y, and Z respectively.

Since it is found that rate of reaction is doubled on doubling the concentration of ${{\text{X}}_2}$ thus the order of reaction with respect to the ${{\text{X}}_2}$ is 1, and therefore, the value of a is 1.

The rate of reaction is doubled on doubling the concentration of Y thus, order of reaction with respect to reactant Y is 1, and therefore, the value of b is also 1.

The rate of reaction does not affect on doubling the concentration of reactant Z thus order of reaction is not depended on the reactant Z, and therefore, the value of c is 0.

Substitute these values in equation (2).

$\begin{aligned}{\text{rate}}&=k{\left[{{{\text{X}}_2}}\right]^a}{\left[{\text{Y}}\right]^b}{\left[ {\text{Z}}\right]^c}\\&=k{\left[{{{\text{X}}_2}}\right]^1}{\left[ {\text{Y}}\right]^1}{\left[ {\text{Z}}\right]^0}\\&=k\left[{{{\text{X}}_2}}\right]\left[ {\text{Y}}\right]\\\end{aligned}$