Question

A chemist needs to prepare the compound \(\mathrm{PH}_{3} \mathrm{BCl}_{3}\) by using the reaction \(\mathrm{PH}_{3}(\mathrm{~g})+\mathrm{BCl}_{3}(\mathrm{~g}) \longrightarrow \mathrm{PH}_{3} \mathrm{BCl}_{3}(\mathrm{~s})\) for which \(K=19.2\) at \(60 .{ }^{\circ} \mathrm{C}\). (a) Write the expression for \(K\). (b) What is the value of \(K_{c}\) for this reaction? (c) Some solid \(\mathrm{PH}_{3} \mathrm{BCl}_{3}\) was added to a closed \(500 .-\mathrm{mL}\) vessel at \(60 .{ }^{\circ} \mathrm{C}\) that already contains \(0.0128 \mathrm{~mol}\) \(\mathrm{PH}_{3}\). What is the equilibrium concentration of \(\mathrm{PH}_{3}\) ? (d) At \(70 .{ }^{\circ} \mathrm{C}\), \(K=26.2\). Is the reaction endothermic or exothermic? Explain your reasoning. (e) What is the new value of \(K_{c}\) ? (f) Can the reactants in the preceding reaction be classified as acids or bases? Explain your answer.

Short answer

a) K expression: \(\frac{1}{[\mathrm{PH}_3][\mathrm{BCl}_3]}\). b) Value of Kc: 19.2. c) Equilibrium concentration of \(\mathrm{PH}_3\): 0.0128 mol/L. d) The reaction is endothermic as K increases with temperature. e) Value of Kc at 70°C: 26.2. f) \(\mathrm{PH}_3\) is a Lewis base, and \(\mathrm{BCl}_3\) is a Lewis acid.

Step-by-step solution

Write the expression for K

The expression for the equilibrium constant (K) for the reaction is written using the concentrations of the products over the reactants, each raised to the power of their stoichiometric coefficients. Since the reaction produces a solid, and solids do not appear in the expression for K, only gaseous substances are included. The expression for K is given by the formula: \[K = \frac{1}{[\mathrm{PH}_3][\mathrm{BCl}_3]}\]. Note that since the stoichiometric coefficients are all 1, the concentrations are not raised to any power.

Determine the value of Kc

For the given reaction, K is already provided and does not require the determination of individual concentrations of reactants and products. Therefore, the value of Kc for this reaction is 19.2, as given in the problem.

Calculate the equilibrium concentration of PH3

Since \(\mathrm{PH_{3}BCl_{3}}\) is a solid, adding it does not affect the equilibrium concentrations of the gaseous reactants. Therefore, the equilibrium concentration of PH3 remains as initially present, which is \(0.0128 mol/L\) (since it's in a 500 mL vessel, and we assume ideal behavior and that no PH3 has reacted yet).

Determine whether the reaction is endothermic or exothermic

Since the value of K increases with an increase in temperature (from 19.2 at 60°C to 26.2 at 70°C), the reaction is endothermic. This is because an increase in temperature shifts the equilibrium to the right for an endothermic reaction, resulting in a larger K value.

Calculate the new value of Kc at 70°C

The new value of Kc at 70°C is already given as 26.2. Note that Kc and K are used interchangeably here, as the units of concentration are not specified or changed.

Classification of reactants as acids or bases

According to Lewis definitions, a base is an electron-pair donor, and an acid is an electron-pair acceptor. \(\mathrm{PH}_3\) can act as an electron-pair donor (Lewis base), while \(\mathrm{BCl}_3\) can act as an electron-pair acceptor (Lewis acid) due to the presence of a vacant p-orbital on the boron atom.

Key concepts

Equilibrium Constant (K)

In chemistry, the equilibrium constant (K) is paramount in understanding the dynamics of a reversible reaction. It's a measure of the relative concentrations of the products to reactants at equilibrium. For the reaction \[\mathrm{PH}_{3}(\mathrm{g}) + \mathrm{BCl}_{3}(\mathrm{g}) \longrightarrow \mathrm{PH}_{3} \mathrm{BCl}_{3}(\mathrm{s})\]the equilibrium constant expression excludes solids, resulting in \[K = \frac{1}{[\mathrm{PH}_3][\mathrm{BCl}_3]}\].The absence of powers in the expression indicates that the stoichiometric coefficients for each component are one. Knowing the value of K, which is 19.2 at 60°C, allows chemists to predict the direction of the reaction and the concentrations of reactants and products at equilibrium.

Understanding and calculating K is crucial for students, especially in assessing how the reaction behaves under various conditions. For instance, when additional solid \(\mathrm{PH}_{3} \mathrm{BCl}_{3}\) is introduced, the equilibrium concentration of \(\mathrm{PH}_{3}\) remains unaltered at \(0.0128 \, \text{mol/L}\), assuming that the reaction has not yet proceeded.

Endothermic and Exothermic Reactions

A critical aspect of chemical reactions is understanding the energy changes that occur. Endothermic reactions absorb heat from their surroundings, while exothermic reactions release heat. Given the reaction's equilibrium constant (K) increasing from 19.2 at 60°C to 26.2 at 70°C, the process is endothermic. Here's why: an increase in temperature provides more energy for reactants to overcome activation energy barriers, shifting the equilibrium towards product formation in an endothermic reaction.

For students grappling with the temperature dependence of chemical reactions, it's beneficial to invoke Le Chatelier's principle. This principle states that a system at equilibrium will adjust to counteract any imposed change. Thus, in this case, as temperature increases, the system adjusts by favoring the endothermic reaction, consuming heat and increasing the K value. This upward shift in K with rising temperature is a classic signal of an endothermic process.

Lewis Acids and Bases

Moving from the traditional Brønsted-Lowry concept, Lewis definitions provide a broader outlook on acids and bases. A Lewis acid is an electron-pair acceptor, while a Lewis base is an electron-pair donor. This perspective focuses on the exchange of electron pairs rather than protons. In our reaction, \(\mathrm{PH}_3\) is a Lewis base as it can donate a pair of electrons, whereas \(\mathrm{BCl}_3\), with an electron-deficient boron atom, functions as a Lewis acid.

• \(\mathrm{PH}_3\): Lewis base due to its ability to donate electron pairs.
• \(\mathrm{BCl}_3\): Lewis acid due to its electron-deficient boron atom, ready to accept electron pairs.

For students, recognizing Lewis acids and bases paves the way for predicting reaction partners in a vast array of chemical reactions, beyond those involving mere proton transfer. This broader understanding can unveil a myriad of interactions in organic chemistry, coordination chemistry, and various biochemical processes.