Question

What mass of natural gas (CH₄) must burn to emit 267 kJ of heat? CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H2_O(g) ∆H°rxn = -802.3 kJ

a) 10.6 g
b) 15.9 g
c) 21.2 g
d) 25.5 g

Answer 1

The mass of methane required to emit 267 kJ of heat is calculated to be approximately 4.812 grams, based on the energy released per mole of methane during combustion.

Step-by-step explanation:

The question asks to calculate the mass of methane, CH4, that must burn to emit 267 kJ of heat. The reaction is exothermic, meaning it releases heat. Given that the combustion of 1 mol of methane releases 890.4 kJ, we can set up a proportional relationship to find the required mass:

Step 1: Write down the given thermochemical equation with its ΔH:

CH4(g) + 2 O2(g) → CO2(g) + 2 H2O(l) ΔH°rxn = -890.4 kJ

Step 2: Calculate moles of CH4 needed for 267 kJ of heat:
(1 mol CH4 / 890.4 kJ) × 267 kJ = 0.3 mol CH4

Step 3: Convert moles to mass using molar mass of methane:
0.3 mol × 16.04 g/mol = 4.812 g

The mass of methane that must burn to emit 267 kJ of heat is approximately 4.812 g.