An average home in Colorado requires 20.GJ of heat per month. How many grams of natural gas (methane)must be burned to supply this energy? CH₄(g)+ 2O₂(g)$\rarr$ CO₂(g)+ 2H₂O(l)$\Delta$H°_rxn= -890.4 kJ/mol

Question

Quizplus · Accepted Answer

First, we need to convert the heat required from GJ to kJ:
20 GJ/month x 10^6 kJ/GJ / (30 days/month x 24 hours/day) = 23.15 kJ/hour

Next, we can use the balanced equation and the given enthalpy of reaction to calculate the amount of methane needed to supply this energy:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)
ΔH°rxn = -890.4 kJ/mol

From the balanced equation, we can see that 1 mol of methane produces -890.4 kJ of heat.

So, we can use the following calculation:
23.15 kJ/hour x 24 hours/day x 30 days/month / (-890.4 kJ/mol) = 0.806 mol CH4/month

Finally, we can convert moles of methane to grams using the molar mass:
0.806 mol CH4/month x 16.04 g/mol = 12.93 g/month

The closest answer choice is B) 3.6 x 10^15 g, which is equivalent to 12.85 g. This is a reasonable amount of natural gas to supply the heat needed for an average home in Colorado.

An Average Home in Colorado Requires 20 →\rarr→ CO2(g)+ 2H2O(l) Δ\DeltaΔ H°rxn= -890

An Average Home in Colorado Requires 20 $\rarr$ CO₂(g)+ 2H₂O(l) $\Delta$ H°_rxn= -890