Problem 212 - A Complete Resource Book in Chemistry for JEE Main

Question

A reaction was found to be second-order with respect to the concentration of carbon monoxide. If the concentration of carbon monoxide is doubled, with everything else kept the same, the rate of reaction will \([2006]\) (a) remain unchanged (b) triple (c) increase by a factor of 4 (d) double

Step-by-Step Solution

Answer

The rate of reaction will increase by a factor of 4. Option (c) is correct.

Step 1: Understanding the Order of Reaction

The problem states that the reaction is second-order with respect to the concentration of carbon monoxide. This means the rate of reaction depends on the square of the concentration of carbon monoxide. Mathematically, this is represented as: \[ ext{Rate} = k [ ext{CO}]^2 \]where \( k \) is the rate constant.

Step 2: Determine the Effect of Doubling Concentration

Since the rate of reaction depends on \( [ ext{CO}]^2 \), doubling the concentration of carbon monoxide means you replace \( [ ext{CO}] \) with \( 2[ ext{CO}] \).The new rate will then be:\[ ext{New Rate} = k (2[ ext{CO}])^2 \]

Step 3: Calculate the Factor of Increase

Expanding the expression for the new rate gives:\[ ext{New Rate} = k imes 4[ ext{CO}]^2 = 4 imes k [ ext{CO}]^2 \]This shows the new rate is four times the original rate, indicating the rate of reaction increases by a factor of 4.

Key Concepts

Rate of Reaction

Understanding the rate of reaction is key to interpreting how fast or slow a chemical reaction proceeds. The rate is essentially the speed at which reactants are consumed or products are formed. In mathematical terms, this is often represented by the change in concentration of a reactant or product over time. For instance, if you have a reaction where a substance A converts into products, the rate can be expressed as \[\text{Rate} = \frac{- \Delta [A]}{\Delta t} \]where \([A]\) is the concentration of the reactant. In words, this equation signifies that the rate is the change in concentration of A over the change in time. When reactions occur faster, this rate value is higher and when slower, it's lower.

• It's crucial to note that external conditions like temperature and the presence of a catalyst can affect the rate.
• For each type of reaction order, such as first, second, or zero order, the dependence on concentration will change, hence affecting the speed of the reaction.

Thus, understanding the rate of reaction helps in predicting and controlling the behavior of a chemical process.

Second-Order Reactions

Second-order reactions are a fascinating type of reaction where the rate is proportional to the square of the concentration of one reactant, or to the product of the concentrations of two different reactants. For a reaction that is second-order with respect to a single reactant, such as carbon monoxide in the given exercise, the rate equation can be described as:\[ \text{Rate} = k [\text{CO}]^2 \]where \(k\) is the rate constant and \([\text{CO}]\) is the concentration of carbon monoxide. This indicates a direct relationship where doubling the concentration of carbon monoxide leads to a quadrupling of the reaction rate, due to the squaring factor.

• The units for a second-order rate constant typically are \(\text{M}^{-1}\text{s}^{-1}\), reflecting how concentration changes influence rate.
• Second-order kinetics are commonly seen in reactions involving a single reactant undergoing a transformation that's part of a complex mechanism.

Recognizing a second-order reaction enables chemists to predict outcomes and manipulate conditions optimally for desired rates.

Concentration Effects

Concentration effects explain how changing the amount of reactants affects the overall rate of a reaction. In the second-order reaction example provided, this becomes particularly important. For reactions dependent on concentration, any increase in concentration can significantly accelerate the rate.

• In a first-order reaction, the rate change is directly proportional to concentration change.
• However, in a second-order reaction, the impact is more pronounced because the rate is proportional to the square of the concentration.

When the concentration of carbon monoxide is doubled, the rate becomes \(4\) times faster; this demonstrates the profound impact of concentration in second-order reactions. Understanding these effects is critical for industrial applications where time efficiency can influence economic viability. Adjusting concentration becomes a powerful tool in controlling chemical kinetics. This knowledge is invaluable when improving processes, optimizing reactions and developing more efficient chemical production systems.