In the system A(g) + 2B(g) ⇔ 2C(g) + 2D(g) ΔH=21 kJ/mol, it is possible to increase the quantity of C by:

a) adding a catalyst
b) decreasing the [B]
c) increasing the pressure
d) increasing the temperature

Le Chatelier's Principle.

To determine how to increase the quantity of C in the given chemical system, we need to analyze the factors that affect the equilibrium position of the reaction. Let's go through each option:

a) Adding a catalyst: A catalyst does not affect the equilibrium position of a reaction. It only increases the rate of the forward and backward reactions, thereby reaching equilibrium more quickly. Therefore, adding a catalyst would not increase the quantity of C.

b) Decreasing the [B]: According to Le Chatelier's principle, when the concentration of a reactant is decreased, the equilibrium shifts in the direction that produces more of that reactant. In this case, if we decrease the concentration of B, the equilibrium will shift to the right, resulting in an increase in the quantity of C. Therefore, decreasing the [B] is a valid option to increase the quantity of C.

c) Increasing the pressure: The given reaction involves only gases. According to Le Chatelier's principle, when the pressure of a system is increased, the equilibrium shifts in the direction that reduces the total number of gas molecules. In this case, increasing the pressure would shift the equilibrium to the left, reducing the quantity of C. So increasing the pressure is not a valid option to increase the quantity of C.

d) Increasing the temperature: For an exothermic reaction like the one given (ΔH < 0), according to Le Chatelier's principle, increasing the temperature shifts the equilibrium position in the direction that consumes heat. In this case, the forward reaction is exothermic (as ΔH is negative), so increasing the temperature would shift the equilibrium to the left and therefore decrease the quantity of C. Hence, increasing the temperature is not a valid option to increase the quantity of C.

From the options given, the only valid choice to increase the quantity of C is to decrease the [B].