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Question: A gaseous reaction, \(2A(g) + B(g) \to 2C(g)\), shows a decrease in pressure from 120mm to 100mm in ...

A gaseous reaction, 2A(g)+B(g)→2C(g)2A(g) + B(g) \to 2C(g), shows a decrease in pressure from 120mm to 100mm in 10min The rate of appearance of C is :
A. 2mmmin⁡2\dfrac{{mm}}{{\min }}
B. 4mmmin⁡4\dfrac{{mm}}{{\min }}
C. 10mmmin⁡10\dfrac{{mm}}{{\min }}
D. 12mmmin⁡12\dfrac{{mm}}{{\min }}

Explanation

Solution

Basically, the rate of reaction refers to the speed at which the products are formed from the reactants in a chemical reaction. We can say that it is the speed at which the reactants are converted into products. To solve this question, we need to know the rate law equation.

Formula used:
Rate of reaction =change in pressurechange in time = \dfrac{{change\,in\,pressure}}{{change\,in\,time}}

Complete step by step answer:
When we talk about a chemical reaction, it is a fact that the rate at which these reactions occur varies by a great deal. Some chemical reactions are very instantaneous while others usually take time to reach the final product. Now, let us consider a simple example and determine its rate.
aA+bB→pP+qQaA + bB \to pP + qQ
Here, A and B denote reactants and P and Q denote products while a, b, p and q are stoichiometric coefficients. So, the rate of reaction will be:
r=−1ad[A]dt=−1bd[B]dt=1pd[P]dt=1qd[Q]dtr = - \dfrac{1}{a}\dfrac{{d[A]}}{{dt}} = - \dfrac{1}{b}\dfrac{{d[B]}}{{dt}} = \dfrac{1}{p}\dfrac{{d[P]}}{{dt}} = \dfrac{1}{q}\dfrac{{d[Q]}}{{dt}}
The negative sign is used to indicate the decreasing concentration of the reactant.
Now, let’s solve the given question.
2A(g)+B(g)→2C(g)2A(g) + B(g) \to 2C(g)
According to rate law, the rate of the reaction will be:
r=−12d[A]dt=−d[B]dt=12d[C]dt=k[A]n[B]nr = - \dfrac{1}{2}\dfrac{{d[A]}}{{dt}} = - \dfrac{{d[B]}}{{dt}} = \dfrac{1}{2}\dfrac{{d[C]}}{{dt}} = k{[A]^n}{[B]^n}
Now, we can see that the units are mm min⁡−1mm\,{\min ^{ - 1}}. So, the order of the reaction is zero.
Hence, rate =K
Therefore, according to the formula, rate of reaction =change in pressurechange in time = \dfrac{{change\,in\,pressure}}{{change\,in\,time}}
Now, we substitute the values of pressure and time that are given in the question.
=(120−100)10= \dfrac{{(120 - 100)}}{{10}}
=2010=2mmmin⁡= \dfrac{{20}}{{10}} = 2\dfrac{{mm}}{{\min }}
So, rate =12d[C]dt = \dfrac{1}{2}\dfrac{{d[C]}}{{dt}}
=d[C]dt=2×2=4mmmin⁡= \dfrac{{d[C]}}{{dt}} = 2 \times 2 = 4\dfrac{{mm}}{{\min }}

Hence, option D is correct.

Note: There are various factors that affect the rate of a chemical reaction. It highly depends on the nature of the reaction. Moreover, other factors such as number of reactants, complexity of reactions highly influence the reaction rate as well.