Problem 26 - Chemistry: Principles and Reactions

Question

WEB When boron trifluoride reacts with ammonia, the following \(T\) reaction occurs: for $$\mathrm{BF}_{3}(g)+\mathrm{NH}_{3}(g) \longrightarrow \mathrm{BF}_{3} \mathrm{NH}_{3}(g)$$ The following data are obtained at a particular temperature: $$\begin{array}{cccc}\hline \text { Expt. } & {\left[\mathrm{BF}_{3}\right]} & {\left[\mathrm{NH}_{3}\right]} & \text { Initial Rate }(\mathrm{mol} / \mathrm{L} \cdot \mathrm{s}) \\\\\hline 1 & 0.100 & 0.100 & 0.0341 \\ 2 & 0.200 & 0.233 & 0.159 \\ 3 & 0.200 & 0.0750 & 0.0512 \\ 4 & 0.300 & 0.100 & 0.102 \\\\\hline\end{array}$$

Step-by-Step Solution

Answer

Based on the given experimental data, the rate law for the reaction between boron trifluoride (BF3) and ammonia (NH3) is: $$Rate = (3.41 \ \mathrm{L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1})([\mathrm{BF}_{3}])([\mathrm{NH}_{3}])$$ with both reactants having a reaction order of 1 and the rate constant (k) being 3.41 L·mol⁻¹·s⁻¹.

Step 1: Find the reaction order with respect to the reactants

Compare Experiments 1 and 3 to find the reaction order for BF3: Initial rate exp. 3 = \(\frac {1}{2}\) (Initial rate exp. 1) \(\frac{0.0512}{0.0341} = \frac{2^x}{1^x} \implies 1.5 = 2^x \implies x = 0.58496\) We can approximate this value as the reaction order for BF3 to 1. Now, let's find the reaction order for NH3 by comparing Experiments 1 and 4: Initial rate exp. 4 = \(3\) (Initial rate exp. 1) \(\frac{0.102}{0.0341} = \frac{1^x}{3^y} \implies 2.99 \approx 3^y\) We can approximate the reaction order for NH3 to 1 as well.

Step 2: Calculate the Rate Constant

Now that we have both reaction orders, let's use any of the given experiment data to determine the rate constant (k): Using Experiment 1 data to calculate the rate constant: $$Rate = k[\mathrm{BF}_{3}]^1[\mathrm{NH}_{3}]^1$$ $$0.0341 = k(0.100)(0.100) \implies k = 3.41 \ \mathrm{L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1}$$

Step 3: Write the Rate Law based on Reaction Orders and Rate Constant

We will now write the rate law using the reaction orders for both reactants and the rate constant k: $$Rate = (3.41 \ \mathrm{L} \cdot \mathrm{mol}^{-1} \cdot \mathrm{s}^{-1})([\mathrm{BF}_{3}])([\mathrm{NH}_{3}])$$ This expression represents the rate law for the given reaction.

Key Concepts

Reaction Rate

The reaction rate in a chemical process refers to how fast or slow a reaction takes place. It is typically measured by the change in concentration of a reactant or product over time. For the reaction between boron trifluoride and ammonia, the table provided shows the initial reaction rates for different concentrations of the reactants. A higher reaction rate indicates that the reactants are converting to products more quickly.

Factors affecting reaction rates include the concentration of reactants, temperature, and presence of catalysts. In this particular example, by examining how the initial rate changes with different concentrations, one can infer how sensitive the rate is to the concentrations of the involved chemicals.

Reaction Order

The reaction order provides insight into how the reaction rate depends on the concentration of each reactant. In other words, it helps us understand the power to which the concentration of a reactant is raised in the rate law.

For the reaction between boron trifluoride and ammonia, the analysis of the data through experiments indicated a reaction order of approximately 1 for both BF extsubscript{3} and NH extsubscript{3}. This means that the rate of reaction is directly proportional to the concentration of each reactant.

Calculating the reaction order involves observing changes in concentration and how those changes influence the reaction rate. If doubling the concentration of a reactant approximately doubles the rate, the reaction is first order in that reactant.

Rate Law

The rate law is a mathematical expression that describes the rate of a chemical reaction in terms of the concentration of its reactants. It effectively links the reaction rate to these concentrations using the determined reaction orders. For our reaction with boron trifluoride and ammonia, the rate law was determined to be: \[ Rate = k[\mathrm{BF}_3]^1[\mathrm{NH}_3]^1 \]where \( k \) is the rate constant.

With a rate law, you can predict how changes in concentration affect the reaction speed. It is highly useful in understanding and controlling chemical processes.

Rate Constant

The rate constant (\( k \)) is a crucial factor in the rate law. It quantifies the rate of reaction when the concentrations of all reactants are unity. In essence, it provides a measure of how fast a reaction happens aside from the concentrations.

For the given reaction, using experiment data, the rate constant was found to be 3.41 L mol\(^{-1}\) s\(^{-1}\). This value was calculated by substituting known concentrations and the rate into the rate law equation.

The rate constant is specific to the reaction and conditions like temperature. As such, changing the temperature would alter \( k \). It's an essential component for accurately utilizing the rate law in chemical kinetics.