Problem 19 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

\(\mathrm{A}+2 \mathrm{~B} \rightarrow \mathrm{C}\), the rate equation for this reaction is given as Rate \(=\mathrm{k}[\mathrm{A}]\) [B] [Main Online April 11, 2015] If the concentration of \(\mathrm{A}\) is kept the same but that of \(\mathrm{B}\) is doubled what will happen to the rate itself? (a) halved (b) the same (c) doubled (d) quadrupled

Step-by-Step Solution

Answer

The rate is doubled.

Step 1: Understanding the Reaction Rate

The given rate equation is Rate \( = k[A][B] \). This indicates that the rate of the reaction depends on the concentration of both \(A\) and \(B\), specifically, it is first order with respect to both \(A\) and \(B\). Since the rate is proportional to both \([A]\) and \([B]\), any change in these concentrations will affect the rate according to these proportionalities.

Step 2: Analyzing the Effect of Doubling \(B\)

The problem states that the concentration of \(A\) is kept constant and the concentration of \(B\) is doubled. We represent the initial rate equation as Rate = \( k[A][B] \). When \([B]\) is doubled, it becomes \([2B]\), which changes the rate equation to Rate = \( k[A][2B] \).

Key Concepts

Rate Equation

The rate equation is an essential concept in reaction kinetics. It provides us a precise mathematical expression that describes how the concentration of reactants affects the rate of a chemical reaction. In simple terms, the rate equation shows us the speed at which reactants convert into products. For the reaction given as \( \mathrm{A}+2 \mathrm{~B} \rightarrow \mathrm{C} \), the rate equation is expressed as:\[\text{Rate} = k[A][B]\]Here, \( k \) is the rate constant, \([A]\) and \([B]\) are the concentrations of reactants \(A\) and \(B\), respectively. The equation demonstrates that the reaction rate depends directly on both the concentrations of \(A\) and \(B\). This allows us to predict how changes in these concentrations will influence the overall reaction speed.

Order of Reaction

The order of reaction indicates how the rate is influenced by the concentration of reactants. It is important in deducing the kinetics of a reaction. In the rate equation \( \text{Rate} = k[A][B] \), we can see that the order of reaction with respect to \(A\) is 1, and with respect to \(B\) is also 1. This is because the exponents of \([A]\) and \([B]\) in the rate equation are both 1.

• If the concentration of a reactant changes, the extent to which the rate changes gives us the reaction order concerning that reactant.
• The total order of reaction is the sum of the exponents, which in this case, is 2.

This indicates that the reaction is a second-order reaction overall. Knowing the order helps us understand and control the conditions to influence the reaction rate effectively.

Concentration Effect

The concentration effect is about understanding how changes in the amount of reactants alter the reaction rate. In our example, if the concentration of \(B\) is doubled, while \(A\) remains constant, it will directly impact the rate. Originally, with the concentration of \(B\) being \([B]\), the rate is \( k[A][B] \). By doubling \([B]\) to \([2B]\), the new rate expression becomes:\[\text{Rate} = k[A][2B] = 2 \times k[A][B]\]This shows that doubling \([B]\) leads to the rate being doubled. Thus, the reaction rate increases proportionally with the concentration of \(B\). This relationship allows chemists to control reaction speeds by adjusting concentrations to achieve desired reaction rates.