Gas A is in equilibrium with gases B and C according to the following equation. $$A_g \rightleftharpoons B_g + C_g$$ The equilibrium constant (Kc) value at 15 °C for the dissociation reaction is 4.0. A rigid 10 litre container was filled with 30 moles of gas A and stored at 15 °C. Calculate the number of gaseous moles at equilibrium in the container. The graph shows the relationship between temperature (T) and Kc for this equilibrium. Deduce whether the dissociation of gas A is exothermic or endothermic. Explain your reasoning. Explain how an increase in the storage temperature would affect the pressure of the equilibrium mixture.

Photo AI

Gas A is in equilibrium with gases B and C according to the following equation - Leaving Cert Chemistry - Question b - 2015

Question b

Gas A is in equilibrium with gases B and C according to the following equation. $$A_g \rightleftharpoons B_g + C_g$$ The equilibrium constant (Kc) value at 15 °C f... show full transcript

Worked Solution & Example Answer:Gas A is in equilibrium with gases B and C according to the following equation - Leaving Cert Chemistry - Question b - 2015

Step 1

Calculate the number of gaseous moles at equilibrium in the container.

96%

114 rated

Answer

To find the number of gaseous moles at equilibrium, we start with the initial concentration of gas A. We have 30 moles of gas A in a 10-litre container:

Initial concentration of A: $C_A = \frac{30 \text{ moles}}{10 \text{ litres}} = 3.0 \text{ mol/L}$

Let the change in concentration of A at equilibrium be denoted as 'x'. The equilibrium expression is:

$K_c = \frac{[B][C]}{[A]} \Rightarrow K_c = \frac{(x)(x)}{(3.0 - x)} = 4$

This can be rearranged into:

$4(3.0 - x) = x^2 \Rightarrow 12 - 4x = x^2 \Rightarrow x^2 + 4x - 12 = 0$

Using the quadratic formula:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} = \frac{-4 \pm \sqrt{16 + 48}}{2} = \frac{-4 \pm 8}{2}$

This gives us: $x = 2 ext{ or } x = -6$

Since x must be positive, we have x = 2. Thus, at equilibrium:

Moles of gas A = 3.0 - 2 = 1.0 moles.
Moles of gas B = 2.
Moles of gas C = 2.

Total moles at equilibrium = 1.0 + 2 + 2 = 5.0 moles.

Step 2

Deduce whether the dissociation of gas A is exothermic or endothermic.

99%

104 rated

Answer

From the given graph of Kc versus temperature, we observe that Kc increases with an increase in temperature. This behavior indicates that the forward reaction (the dissociation of gas A) produces more products (B and C) at higher temperatures.

This suggests that the reaction is endothermic because, according to Le Chatelier's principle, increasing the temperature favors the direction that absorbs heat. Therefore, the dissociation of gas A is endothermic.

Step 3

Explain how an increase in the storage temperature would affect the pressure of the equilibrium mixture.

96%

101 rated

Answer

An increase in temperature will shift the equilibrium position to the right, favoring the formation of more gaseous products (B and C) due to the endothermic nature of the reaction. As the number of gaseous molecules increases, the total pressure in the container will also rise due to the increase in particle collisions with the walls of the container.

Thus, an increase in storage temperature increases the pressure of the equilibrium mixture.

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

Gas A is in equilibrium with gases B and C according to the following equation - Leaving Cert Chemistry - Question b - 2015

Worked Solution & Example Answer:Gas A is in equilibrium with gases B and C according to the following equation - Leaving Cert Chemistry - Question b - 2015

Calculate the number of gaseous moles at equilibrium in the container.

Deduce whether the dissociation of gas A is exothermic or endothermic.

Explain how an increase in the storage temperature would affect the pressure of the equilibrium mixture.

Join the Leaving Cert students using SimpleStudy...

Other Leaving Cert Chemistry topics to explore