A XX-g sample of methane, CH4, is mixed with YY atm of O2 (an excess) in a VV L combustion chamber at 125.0°C. The combustion reaction to CO2 and H2O is initiated and the vessel is cooled back to 125.0°C. What is the final pressure in the combustion chamber assuming the reaction goes to completion?

CH4 + 2O2 ==> CO2 + 2H2O
3 mols of gas on the left goes to 3 mols of gas on the right.
Final pressure = initial pressure.
Initial pressure = pO2 + pCH4:
O2 = YY atm
CH4 = XXg x (1 mol/16 g) x (RT)/VV L

Check my thinking.

Your thinking is mostly correct. Let's go through the steps together to find the final pressure in the combustion chamber assuming the reaction goes to completion.

1. Calculate the number of moles of CH4:
CH4 = XX g * (1 mol/16 g) = XX/16 mol

2. Calculate the initial pressure:
Initial pressure = pO2 + pCH4
pO2 = YY atm
pCH4 = (XX/16 mol) * (RT/VV L)

3. Calculate the final pressure:
Since the reaction goes to completion, the number of moles of gas on the left side of the reaction (CH4 + 2O2) is equal to the number of moles of gas on the right side (CO2 + 2H2O). In this case, there are 3 moles of gas on both sides.

Final pressure = Initial pressure = pO2 + pCH4

Plug in the values you have and calculate the answer.