Phosphorus(V) chloride decomposes into phosphorus(III) chloride and chlorine at a temperature of 500 K according to the following balanced equation. $$\text{PCl}_5 (g) \rightleftharpoons \text{PCl}_3 (g) + \text{Cl}_2 (g)$$ (a) This is a reversible reaction and a dynamic equilibrium is reached. Explain the underlined terms. Why is the equilibrium described as dynamic? (b) State Le Chatelier's principle. Write the equilibrium constant $(K_c)$ expression for the above reaction. (c) When 208.50 g of phosphorus(V) chloride is heated in a 100 liter container at a temperature of 500 K equilibrium is established with 53.25 g of chlorine gas present in the container. Calculate the value of the equilibrium constant $(K_c)$ for the reaction at 500 K. (d) When the temperature of the equilibrium mixture is increased, the phosphorus(V) chloride decomposes further. Is the reaction endothermic or exothermic? Justify your answer. (e) What change, if any, would an increase in pressure have on the value of $K_c$? Explain.

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Phosphorus(V) chloride decomposes into phosphorus(III) chloride and chlorine at a temperature of 500 K according to the following balanced equation - Leaving Cert Chemistry - Question 7 - 2010

Question 7

Phosphorus(V) chloride decomposes into phosphorus(III) chloride and chlorine at a temperature of 500 K according to the following balanced equation. $$\text{PCl}_5 ... show full transcript

Worked Solution & Example Answer:Phosphorus(V) chloride decomposes into phosphorus(III) chloride and chlorine at a temperature of 500 K according to the following balanced equation - Leaving Cert Chemistry - Question 7 - 2010

Step 1

Explain the underlined terms. Why is the equilibrium described as dynamic?

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Answer

A reversible reaction is one where products can react to form the original reactants, allowing the reaction to proceed in both directions. An equilibrium reaction achieves a state where the rates of the forward and reverse reactions are equal, creating a balanced system. The term 'dynamic' indicates that while the concentrations of reactants and products remain constant, the reactions of formation and decomposition continue to occur simultaneously, meaning that the system has not completely ceased.

Step 2

State Le Chatelier's principle.

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Answer

Le Chatelier's principle states that if a system at equilibrium is disturbed by a change in concentration, temperature, or pressure, the system will adjust to counteract that disturbance and re-establish equilibrium.

Step 3

Write the equilibrium constant (Kc) expression for the above reaction.

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The equilibrium constant expression for the reaction is given by:

$K_c = \frac{[\text{PCl}_3][\text{Cl}_2]}{[\text{PCl}_5]}$

where the square brackets denote the concentration of each species at equilibrium.

Step 4

Calculate the value of the equilibrium constant (Kc) for the reaction at 500 K.

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First, we need to convert the mass of PCl5 to moles:

$\text{Molar mass of PCl}_5 = 208.24 \text{ g/mol}$

$\text{Moles of PCl}_5 = \frac{208.50}{208.24} = 1.000 \text{ moles}$

The moles of Cl2 can be calculated from its given mass:

$\text{Molar mass of Cl}_2 = 70.90 \text{ g/mol}$

$\text{Moles of Cl}_2 = \frac{53.25}{70.90} = 0.751 \text{ moles}$

At equilibrium, assuming x moles of PCl3 is formed and using stoichiometry:

Initially: 1.000 moles of PCl5, 0 moles of PCl3, and 0 moles of Cl2
Change: x moles of PCl3 produced and 0.751 moles of Cl2 produced gives:

$K_c = \frac{(0.75)(0.75)}{(1-x)}$

Plugging in the values yields:

$K_c = \frac{(0.751)(0.751)}{(1 - 0.75)} = 0.0225 \, \text{mol}^{-1}$

Step 5

Is the reaction endothermic or exothermic? Justify your answer.

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Answer

The reaction is endothermic. According to Le Chatelier's principle, when the temperature of the reaction system is increased, the equilibrium will shift to favor the endothermic direction to absorb some of that added heat. Since the decomposition of PCl5 into PCl3 and Cl2 requires energy, the reaction absorbs heat, indicating it is endothermic.

Step 6

What change, if any, would an increase in pressure have on the value of Kc? Explain.

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Answer

The value of $K_c$ will not change with a change in pressure, as $K_c$ is a constant at a given temperature. However, increasing pressure generally shifts the equilibrium towards the side with fewer gas moles. In this case, since there are 2 moles of products (1 PCl3 + 1 Cl2) and 1 mole of reactant (PCl5), the shift, if any, would favor the PCl5 formation but does not affect the numerical value of $K_c$ itself.

Phosphorus(V) chloride decomposes into phosphorus(III) chloride and chlorine at a temperature of 500 K according to the following balanced equation - Leaving Cert Chemistry - Question 7 - 2010

Worked Solution & Example Answer:Phosphorus(V) chloride decomposes into phosphorus(III) chloride and chlorine at a temperature of 500 K according to the following balanced equation - Leaving Cert Chemistry - Question 7 - 2010

Explain the underlined terms. Why is the equilibrium described as dynamic?

State Le Chatelier's principle.

Write the equilibrium constant (Kc) expression for the above reaction.

Calculate the value of the equilibrium constant (Kc) for the reaction at 500 K.

Is the reaction endothermic or exothermic? Justify your answer.

What change, if any, would an increase in pressure have on the value of Kc? Explain.

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