The problem describes an endothermic reaction where methane ($CH_4$) reacts with water vapor ($H_2O$) to produce hydrogen gas ($H_2$) and carbon monoxide ($CO$):

$CH_4(g) + H_2O(g) \rightleftharpoons 3H_2(g) + CO(g)$

The task is to predict the effect of temperature changes on the equilibrium, specifically how it affects the pressures of $CH_4$ and $CO$, and to indicate whether the equilibrium will shift to the left or right.

General Analysis:

1. Endothermic Reaction: Since the reaction is endothermic, increasing the temperature favors the forward reaction (shifting equilibrium to the right), while lowering the temperature favors the reverse reaction (shifting equilibrium to the left). This follows Le Chatelier's principle, which states that the system will adjust to counteract any changes applied to it.

2. Raising the Temperature:

   • Effect on $CH_4$: Raising the temperature will favor the forward reaction, so the concentration of reactants ($CH_4$) will decrease.
   • Shift in Equilibrium: The equilibrium will shift to the right, favoring the production of more $H_2$ and $CO$.

3. Lowering the Temperature:

   • Effect on $CO$: Lowering the temperature will favor the reverse reaction, increasing the concentration of reactants ($CH_4$) and decreasing the products ($CO$).
   • Shift in Equilibrium: The equilibrium will shift to the left.

Specific Answers for the Table:

1. If the temperature is raised:

   • The pressure of $CH_4$ will decrease.
   • The equilibrium will shift to the right.

2. If the temperature is lowered:

   • The pressure of $CO$ will decrease.
   • The equilibrium will shift to the left.

Would you like further clarification or more details?

Here are some related questions to explore:

1. How does pressure influence equilibrium in gas-phase reactions?
2. How does Le Chatelier's principle apply to changes in pressure and volume?
3. What happens to the equilibrium if a catalyst is added?
4. How does the concept of Gibbs free energy relate to equilibrium shifts?
5. What are the effects of adding more $H_2O$ to the system at equilibrium?

Tip: Remember, in an endothermic reaction, adding heat acts like adding a reactant, shifting equilibrium toward the products.