The equilibrium conversion of synthesis gas (CO + H₂) to methane (CH₄) is favored at higher pressures. Here's why:

The Reaction:

CO + 3H₂ ⇌ CH₄ + H₂O

Le Chatelier's Principle:

Le Chatelier's Principle states that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress. In this case, increasing pressure is the stress.

Shifting the Equilibrium:

The synthesis gas to methane reaction has 4 moles of reactants (1 CO + 3 H₂) and 2 moles of products (1 CH₄ + 1 H₂O). Therefore, increasing the pressure will favor the side with fewer moles of gas, which is the product side.

Conclusion:

By increasing the pressure, you force the equilibrium to shift towards the formation of methane, thereby increasing the equilibrium conversion of synthesis gas to methane.