Problem 8 - Chemistry in 30 days

Question

The rate of a reaction increases eight times when the concentration increases four times. 'The order of the reaction is (a) \(2.5\) (b) \(2.0\) (c) \(1.5\) (d) \(0.5\)

Step-by-Step Solution

Answer

The order of the reaction is 1.5 (option c).

Step 1: Understanding the Problem

We need to find the order of the reaction given that the rate increases eight times when the concentration is increased four times. The relationship between rate and concentration for a reaction is given by the rate law: \( \text{Rate} = k [A]^n \), where \([A]\) is the concentration and \(n\) is the order we need to find.

Step 2: Set Up the Equation

According to the problem, the rate increases eight times when the concentration increases four times. We can set up the equation as: \( 8 \times \text{Rate}_0 = k (4 \times [A]_0)^n \). The original rate is \( \text{Rate}_0 = k [A]_0^n \).

Step 3: Simplify the Equation

We can equate the new rate to 8 times the original rate: \( 8 = 4^n \). This equation comes from dividing the new rate equation by the original rate equation \( (8 = \frac{k (4 \times [A]_0)^n}{k [A]_0^n}) \).

Step 4: Solve for Order of Reaction

To solve for n, the order of the reaction, take the logarithm on both sides: \( n \log(4) = \log(8) \). Simplifying gives: \( n = \frac{\log(8)}{\log(4)} = \frac{3\log(2)}{2\log(2)} = \frac{3}{2} = 1.5 \).

Step 5: Conclusion

After solving the equation, we find that the order of the reaction \( n = 1.5 \). Thus, the correct answer is \( c \) which is \( 1.5 \).

Key Concepts

Understanding Rate Law

The rate law is an essential concept in chemical kinetics. It provides the relationship between the rate of a chemical reaction and the concentration of reactants. The general formula for rate law is \( \text{Rate} = k [A]^n \) where:

• \( k \) is the rate constant, which is specific to a particular reaction and temperature.
• \([A]\) represents the concentration of a reactant.
• \( n \) is the reaction order with respect to that reactant.

The reaction order \( n \) indicates how the rate is affected by the concentration. For example, if \( n = 1 \), the reaction is first order, meaning the rate is directly proportional to the concentration. Understanding this relationship allows chemists to predict how changing concentrations will affect the rate.

Dive into Chemical Kinetics

Chemical kinetics is the branch of chemistry that studies the speed or rate at which chemical reactions occur. It aims to understand the steps that lead to the transformation of reactants into products. The key components of chemical kinetics include:

• Reaction Mechanism: A detailed description of the steps involved in a chemical reaction.
• Rate Laws: Equations that describe the relationship between the rate of a reaction and the concentrations of reactants.
• Reaction Rate: The speed at which reactants are converted to products, typically measured in concentration per unit of time.

By studying chemical kinetics, we can make predictions about how fast a reaction will proceed under different conditions, which is crucial for controlling industrial processes and understanding biological systems.

Exploring the Concentration Effect

The concentration effect in reactions is an important concept that explains how changes in the concentration of reactants influence the reaction rate. In many reactions, increasing the concentration of reactants increases the rate of the reaction. This is because:

• Higher concentration leads to more frequent collisions between reactant molecules.
• More collisions increase the probability of successful reactions, hence accelerating the reaction rate.

In our specific problem, when the concentration increases four times, and the rate increases eight times, we infer that the reaction order plays a significant role in this enhancement. Understanding the concentration effect helps to optimize reaction conditions in various scientific and industrial applications. It allows researchers to control reaction speeds efficiently for desired outcomes.