What will the initial Rate be if [a] is halved and [b] is tripled?

Understanding the behavior of a chemical reaction when the concentrations of its reactants change is essential for predicting how the reaction rate will shift. In this article, we will explore the impact of halving the concentration of one reactant, [a], and tripling the concentration of another reactant, [b], on the initial reaction rate. This scenario is quite common in reaction rate studies. It can be explained by the rate law, a mathematical expression that describes the relationship between the concentrations of reactants and the Rate at which a reaction proceeds.

The Rate Law Explained

Before diving into the specifics of the initial Rate if [a] is halved and [b] is tripled?, let’s first break down the rate law, which governs the relationship between the Rate of a reaction and the concentrations of its reactants. The general form of the rate law is:

Rate=k[A]m[B]n\text{Rate} = k[A]^m[B]^nRate=k[A]m[B]n

Here, Rate refers to the speed at which the reaction occurs, k is the Rate constant (which is specific to the response and temperature), and [A] and [B] are the concentrations of reactants A and B, respectively. The exponents m and n represent the reaction orders concerning reactants A and B, typically determined experimentally.

The reaction order, m, tells us how sensitive the Rate of reaction is to changes in the concentration of A. Similarly, n reflects how changes in the concentration of B affect the Rate. These orders can be different for each reactant.

Impact of Halving [A] and Tripling [B]

Now, let’s address the core question: what will the initial Rate be if [a] is halved and [b] is tripled?

Halving [A]

The effect of halving the concentration of reactant A depends on the reaction order concerning A (denoted as m). If m is 1, halving [A] will halve the reaction rate. If m is 2, halving [A] will reduce the Rate by a factor of four. If you halve [A], the Rate will be multiplied by (1/2)^m.

Let’s break it down further:

If m = 1, halving [A] multiples the Rate by 1/2.
If m = 2, halving [A] reduces the Rate to a quarter of its original value (multiplied by 1/4).

Tripling [B]

Similarly, tripling the concentration of reactant B will impact the Rate, and this effect depends on the reaction order concerning B (denoted as n). If n is 1, tripling [B] will result in the Rate being tripled. If n is 2, tripling [B] will increase the Rate by a factor of nine. If you triple [B], the Rate will be multiplied by 3^n.

For example:

If n = 1, tripling [B] multiples the Rate by 3.
If n = 2, tripling [B] increases the Rate by a factor of nine (multiplied by 9).

Combined Effect on the Initial Rate

To calculate the overall effect on the initial Rate when both [A] and [B] are changed, we combine the individual effects from halving [A] and tripling [B]. The new initial Rate can be determined using the following formula:

New Initial Rate=Initial Rate×(12)m×3n\text{New Initial Rate} = \text{Initial Rate} \times \left(\frac{1}{2}\right)^m \times 3^nNew Initial Rate=Initial Rate×(21)m×3n

Let’s consider a specific example to make this more transparent.

Example Calculation

Imagine the following scenario:

The rate law is given by: Rate=k[A]2[B]\text{Rate} = k[A]^2[B]Rate=k[A]2[B], so m = 2 and n = 1.
The initial Rate of the reaction is Initial Rate\text{Initial Rate}Initial Rate.

Now, if the concentration of A is halved and the concentration of B is tripled, the new initial Rate can be calculated as:

New Initial Rate=Initial Rate×(12)2×31\text{New Initial Rate} = \text{Initial Rate} \times \left(\frac{1}{2}\right)^2 \times 3^1New Initial Rate=Initial Rate×(21)2×31New Initial Rate=Initial Rate×14×3\text{New Initial Rate} = \text{Initial Rate} \times \frac{1}{4} \times 3New Initial Rate=Initial Rate×41×3New Initial Rate=34×Initial Rate\text{New Initial Rate} = \frac{3}{4} \times \text{Initial Rate}New Initial Rate=43×Initial Rate

In this example, the new initial Rate would be three-quarters (3/4) of the original initial Rate. This demonstrates how halving the concentration of A and tripling the concentration of B leads to a decrease in the overall reaction rate due to the more significant influence of [A] in this specific case.

Factors to Consider

When analyzing, what will the initial Rate be if [a] is halved and [b] is tripled? Knowing the specific values of the reaction orders m and n for your reaction is crucial. These values dictate how the concentrations of reactants influence the Rate. If you don’t know the reaction orders, conducting experiments or obtaining this information from literature sources is essential to making accurate predictions.

Also, remember that the rate constant k may vary with temperature, and temperature changes can also influence the rate law. This should be considered if you’re conducting real-world experiments or the reaction is temperature-sensitive.

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Climax

In summary, what will the initial Rate be if [a] is halved and [b] is tripled? This can be determined by understanding how changes in the concentrations of reactants A and B impact the reaction rate. We can calculate the new initial Rate after these changes using the rate law and considering the reaction orders m and n. This approach is a fundamental concept in chemical kinetics, allowing scientists and researchers to predict the outcome of reactions under different conditions.

When interpreting reaction rates and concentrations, always remember that the impact of concentration changes depends heavily on the order of the reaction concerning each reactant. This ensures accurate calculations and predictions about the reaction rate and behavior under varying conditions.