What Will the Initial Rate Be If [A] Is Halved and [B] Is Tripled?

Understanding how the reaction rate changes when reactant concentrations are modified is essential in chemical kinetics. What will the initial rate be if [A] is halved and [B] is tripled? This question is commonly encountered when analyzing reaction mechanisms and rate laws. To answer this, let’s break down the rate law, the impact of concentration changes, and the final calculation of the new reaction rate.

Understanding the Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentrations of its reactants. The equation usually gives it:

Where:

• Rate is the reaction rate.
• k is the rate constant, which depends on temperature and other conditions.
• [A] and [B] are the molar reactants A and B concentrations.
• m and n are the reaction orders concerning A and B, respectively.

The reaction orders (m and n) are determined experimentally and indicate how the concentration of each reactant affects the reaction rate. A higher exponent means the reactant has a more significant influence on the rate.

Effect of Halving [A]

When the concentration of [A] is halved, we modify its contribution to the rate law:

• If m = 1 (first-order concerning A), the rate will be reduced by 1/2.
• If m = 2 (second-order concerning A), the rate will be reduced by (1/2)^2 = 1/4.
• If m = 0, then A does not affect the rate, and halving it has no impact.

Thus, the effect of halving [A] depends on the reaction order.

Effect of Tripling [B]

When the concentration of [B] is tripled, we adjust its contribution:

• If n = 1, the rate will increase by a factor of 3.
• If n = 2, the rate will increase by 3² = 9.
• If n = 0, then B does not affect the rate, and tripling it has no impact.

The impact of increasing [B] also depends on its reaction order.

Calculating the Overall Rate Change

To determine the new reaction rate, we multiply the effects of both changes:

Example Calculation

Let’s assume:

• m = 1 (first-order in A)
• n = 2 (second-order in B)

Applying the formula:

This means the new reaction rate is 4.5 times the initial rate after halving [A] and tripling [B].

Key Takeaways

• Halving [A] reduces the rate by (1/2)^m, depending on the order of A.
• Tripling [B] increases the rate by (3)^n, depending on the order of B.
• The overall effect is found by multiplying these factors with the initial rate.
• The actual numerical effect depends on the reaction orders m and n.
• The rate constant k remains unchanged unless external conditions (like temperature) are altered.

Practical Applications

Understanding rate changes is crucial in the pharmaceutical, environmental science, and chemical engineering industries. Scientists can optimize processes, control reactions, and improve efficiency by knowing how reactant concentrations influence reaction speed.

For example:

• Chemists use kinetics to enhance reaction rates without excessive waste in drug synthesis.
• In environmental chemistry, controlling pollutants in water treatment relies on reaction rate adjustments.
• In industrial manufacturing, optimizing reactant concentrations helps improve yield and reduce costs.

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Final Review

The question “what will the initial rate be if [A] is halved and [B] is tripled?” can be answered using the rate law. The rate change depends on the reaction orders m and n. You can accurately predict the new reaction rate by applying the correct formula. Understanding this concept in laboratories or real-world applications is essential for controlling and optimizing chemical reactions.