Final answer:
To emit 276 kJ of heat, you need to burn approximately 4.97 grams of methane (CH4), based on the enthalpy of combustion for methane which is 890.4 kJ/mol.
Step-by-step explanation:
To determine the mass of natural gas (CH4) you must burn to emit 276 kJ of heat, you can use the stoichiometry of the combustion reaction along with the known enthalpy change. The thermochemical equation for the combustion of methane is CH₄(g) + 2O₂(g) → CO₂(g) + 2H₂O(l) + 890.4 kJ, meaning that the combustion of 1 mole of methane releases 890.4 kJ of heat. You can set up a proportion since the relationship between the mass of methane burned and the heat released is linear.
First, convert 276 kJ to the number of moles of methane by using the enthalpy change per mole:
$$ \frac{276 \text{ kJ}}{890.4 \text{ kJ/mol}} = 0.31 \text{ moles of CH4} $$
Since the molar mass of methane (CH₄) is approximately 16.04 g/mol, you can find the mass needed:
$$ 0.31 \text{ moles} \times 16.04 \text{ g/mol} = 4.97 \text{ g of CH4} $$
Thus, approximately 4.97 grams of methane is required to emit 276 kJ of heat.