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Question: The reaction \(A\left( g \right) + 2B\left( g \right) \to C\left( g \right) + D\left( g \right)\) is...

The reaction A(g)+2B(g)→C(g)+D(g)A\left( g \right) + 2B\left( g \right) \to C\left( g \right) + D\left( g \right) is an elementary process. In an experiment, the initial partial pressure of A and B are PA=0.6{P_A} = 0.6 and PB=0.8atm{P_B} = 0.8atm. Calculate the ratio of rate of reaction relative to initial rate when PC{P_C} becomes 0.2atm0.2atm.
A.14\dfrac{1}{4}
B.110\dfrac{1}{{10}}
C.16\dfrac{1}{6}
D.22

Explanation

Solution

Rate of reaction: The rate of a reaction is the speed at which a chemical reaction happens.
Order of the reaction: It is defined as the power dependence of the rate of reaction on the concentration of the reactants.
Elementary reaction: It is defined as a chemical reaction in which one or more chemical species react directly with each other to form the product in a single step.

Complete step by step solution:
Let us first define elementary reaction.
Elementary reaction: It is defined as a chemical reaction in which one or more chemical species react directly with each other to form the product in a single step.
Now we will study the rate of reaction and order of reaction.
Order of the reaction: It is defined as the power dependence of the rate of reaction on the concentration of the reactants. For example: if order of reaction is one then rate of reaction depends linearly on the concentration of one reactant. The unit of first order of reaction is s−1{s^{ - 1}}. The unit of second order of reaction is 1/Ms1/Ms.
Rate of reaction: The rate of a reaction is the speed at which a chemical reaction happens. Rate of reaction is directly proportional to the product of all reactants in the reaction raised to the power of their order. Here the proportionality constant is known as rate constant and is represented by kk.
For example: if reaction is of first order then rate of reaction will be as r=k[A]r = k[A], where rr is rate of reaction, [A][A] is concentration of the reactant and kk is rate constant of the reaction.
Now here we are given the elementary reaction as: A(g)+2B(g)→C(g)+D(g)A\left( g \right) + 2B\left( g \right) \to C\left( g \right) + D\left( g \right). So the rate of reaction will be as: r=kPAPB2r = k{P_A}{P_B}^2.
The initial partial pressure of A and B are PA=0.6{P_A} = 0.6 and PB=0.8atm{P_B} = 0.8atm. So initially the rate of reaction is r=k(0.6)(0.8)2r = k\left( {0.6} \right){\left( {0.8} \right)^2}. And after the reaction when PC{P_C} becomes 0.2atm0.2atm then PA=0.4{P_A} = 0.4 and PB=0.4{P_B} = 0.4 (by the stoichiometry). So the rate of reaction will be r=k(0.4)(0.4)2r = k\left( {0.4} \right){\left( {0.4} \right)^2}. So the ratio will be as (0.4)2(0.4)(0.8)2(0.6)=16\dfrac{{{{\left( {0.4} \right)}^2}\left( {0.4} \right)}}{{{{\left( {0.8} \right)}^2}\left( {0.6} \right)}} = \dfrac{1}{6}

Hence, option c is correct.

Note: Half-time: It is defined as the time duration in which the concentration of a reactant drops to one-half of its initial concentration. It is represented by t12{t_{\dfrac{1}{2}}}.
Half-time of a reaction is inversely proportional to the concentration of the reactant raised to the power of its order of reaction minus one.