244. The rate of change in concentration of C in the reaction 2A + B → 2C + 3D was reported 1.0 M sec^–1. Calculate the reaction rate as well as rate of change of concentration of A, B and D.

Rate of reaction =

$-\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=-\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{D}\right]}{\mathrm{dt}}$


$\because$                   $\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}=1.0 \mathrm{mol} {\mathrm{litre}}^{-1} {\sec }^{-1}$

$\therefore$               
                $$\begin{gathered} -\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}=1.0 \mathrm{mol} {\mathrm{litre}}^{-1}{\sec }^{-1} \\ -\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{dt}}=\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}=0.5 \mathrm{mol} {\mathrm{litre}}^{-1}{\sec }^{-1} \\ \frac{\mathrm{d}\left[\mathrm{D}\right]}{\mathrm{dt}}=\frac{3}{2}\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}} = \frac{3}{2}\times 1 = 1.5 \mathrm{mol} {\mathrm{litre}}^{-1}{\sec }^{-1} \end{gathered}$$


Also, Because            $\mathrm{Rate}=\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}$

$\therefore$                               $\mathrm{Rate}=\frac{1}{2}\times 1 = 0.5 \mathrm{mol} {\mathrm{litre}}^{-1} {\sec }^{-1}.$

Dependence of rate on concentration of reactants: The rate of a chemical reaction at a given temperature may depend on the concentration of one or more reactants and sometimes on products. The representation of rate of a reaction in the terms of the concentration of the reactants is given by rate law. The rate for a given reaction is established by experimental study of the rate of reaction over a wide range of concentration of the reactants and products. Rate law expression differs for the same reaction under different experimental conditions. Rate constants and order of reaction:

(i) Rate constant or specific reaction rate: It is the rate of reaction when the concentration of each reactant is 1 mol/L. For a given reaction it is constant at a particular temperature and is independent of the concentration of reactants. The units of the rate constant of a reaction depends on the order of the reaction. For an nth order of reaction,

$$\begin{gathered} \frac{\mathrm{dx}}{\mathrm{dt}}= \mathrm{k}(\mathrm{conc}{)}^{\mathrm{n}} \\ \mathrm{k} = \frac{\mathrm{dx}}{\mathrm{dt}}\times \frac{1}{(\mathrm{conc}{)}^{\mathrm{n}}}=\frac{\mathrm{conc}.}{\mathrm{time}}\times \frac{1}{(\mathrm{conc}{)}^{\mathrm{n}}}=\frac{1}{\mathrm{time}}\times \frac{1}{(\mathrm{conc}.{)}^{\mathrm{n}-1}} \end{gathered}$$

For zero order of reaction, units of k is mol L^–1 time^–1, for first order reaction, unit of k is time^–1, for second order reaction, unit of k is L mol^–1 time^–1.

In terms of gaseous reactions, concentration is expressed terms of pressure having units of atmosphere. Let us consider the general reaction: aA + bB → Products
where A and B are the reactants and a and b are the stoichiometric coefficients in the balanced chemical equations.

The rate law is written as,
Rate = Δ[A] / Δ t = k[A]^α [B]^β
where k is called the rate constant. Rate constant (k) is the constant of proportionality within the empirical rate law linking the rate of reaction and concentration of reactants involved in the reaction. The rate law can be written in the form
Rate ∝ [A]^α[B]^β

The exponents ‘α’ and ‘β’ in the rate law indicate how sensitive the rate is to change in [A] and [B] and they are usually unrelated to the coefficients a and b in the balanced equation. In general, exponents are positive. But for complex reactions it can be negative, zero or even fractions. If exponent is one, it means rate depends linearly on the concentration of the reactant. If concentration of A is doubled, rate is also doubled. This means a = 1. If α = 2 and [A] is also doubled, rate increases by the factor of 4(z²). When exponent is zero {[A]⁰ = 1}, rate is independent of concentration.