Final answer:
Calculating the enthalpy change for the given mass of CH3OH involved finding the moles of methanol and then using the proportional enthalpy change from the balanced equation. The correct enthalpy change for 3.24 g CH3OH is approximately 13 kJ.
Step-by-step explanation:
The problem requires calculation of the change in enthalpy when a certain mass of CH3OH is reacted. The balanced equation for the reaction given is 2 CH3OH (g) → 2 CH4 (g) + O2 (g) with a ΔH of 252.8 kJ. To solve the problem, we need to find the moles of CH3OH and use the molar ratio from the balanced equation.
The molar mass of CH3OH (methanol) is 32.04 g/mol. We calculate the moles of CH3OH by:
Moles of CH3OH = Mass of CH3OH / Molar Mass of CH3OH
Moles of CH3OH = 3.24 g / 32.04 g/mol = 0.101 mol
Since the above reaction describes the enthalpy change for 2 moles of CH3OH, we adjust for our specific amount:
ΔH for 3.24 g CH3OH = (252.8 kJ / 2 mol) × 0.101 mol = 12.7954 kJ
The enthalpy change, rounded to proper significant figures and converted to correct units, gives us the answer B. 13 kJ (226 kJ is for 2 moles, so none of the originally suggested options were correct).