Coal can be used to generate hydrogen gas by this endothermic reaction:

C(s) + H2O(g) CO(g) + H2(g)

If this reaction is at equilibrium, which of these stresses would increase the formation of hydrogen gas? (choose ALL of the possible answers - there may be more than one.)

a. Adding more C to the reaction mixture.
b. Adding more H2O to the reaction mixture.
c. Raising the temperature of the reaction mixture.
d. Increasing the volume of the reaction mixture.
e. Adding a catalyst to the reaction mixture.
f. Adding an inert gas to the reaction mixture.

To determine which stresses would increase the formation of hydrogen gas in the given equilibrium reaction, we need to understand Le Chatelier's principle. This principle states that if a system at equilibrium is subjected to a stress, the system will adjust itself in a way that minimizes the effect of the stress.

Let's consider each stress option one by one:

a. Adding more C to the reaction mixture:
According to Le Chatelier's principle, if we increase the concentration of reactant C, the system will try to consume more of it to restore equilibrium. Since the formation of hydrogen gas involves the consumption of C, adding more C would indeed increase the formation of hydrogen gas. Therefore, option a is correct.

b. Adding more H2O to the reaction mixture:
Similarly, increasing the concentration of reactant H2O would cause the system to consume more of it. However, the formation of hydrogen gas does not involve the consumption of H2O. Therefore, adding more H2O would not directly affect the formation of hydrogen gas. Hence, option b is not correct.

c. Raising the temperature of the reaction mixture:
In an endothermic reaction, an increase in temperature shifts the reaction in the forward direction, towards the products, to absorb the excess heat. Since the formation of hydrogen gas is a product, increasing the temperature would increase the formation of hydrogen gas. Thus, option c is correct.

d. Increasing the volume of the reaction mixture:
Changing the volume of a gaseous reaction mixture affects the partial pressures of reactants and products. According to Le Chatelier's principle, when the volume is increased, the system will shift in the direction that reduces the number of gas molecules. Since the formation of hydrogen gas generates two moles of gas (H2), increasing the volume would favor the formation of hydrogen gas. Therefore, option d is correct.

e. Adding a catalyst to the reaction mixture:
A catalyst speeds up the rate of a reaction but does not affect the equilibrium position. It provides an alternative pathway for the reaction with lower activation energy, but the equilibrium concentrations remain the same. Hence, the addition of a catalyst would not affect the formation of hydrogen gas. Therefore, option e is not correct.

f. Adding an inert gas to the reaction mixture:
Adding an inert gas does not change the concentrations of the reactants or products. Since an inert gas does not participate in the reaction, it has no effect on the formation of hydrogen gas. Thus, option f is not correct.

In summary, the stresses that would increase the formation of hydrogen gas in the given equilibrium reaction are:
a. Adding more C to the reaction mixture.
c. Raising the temperature of the reaction mixture.
d. Increasing the volume of the reaction mixture.