Answer
10.39 grams
Work Step by Step
From the balanced reaction we have that 2 moles of CH3OH produces 2 moles of CH4 and an enthalpy change of 252.8 kJ. Given that we have an enthalpy change of 82.1 kJ, we can use the ratio from the balanced reaction to find how many moles of methane are produced:
82.1 kJ * (2 moles CH4/ 252.8 kJ) = 0.6495 moles CH4
To find how many grams, we need to ind the molar mass of methane;
C has a mass of 12 g/mol
H has a mass of 1 g/mol, 4 * 1 = 4
CH4 has a mass of 16 g/mol
Since we have 0.6495 mole * (16 g /1 mole) = 10.39 grams