An average home in Colorado requires 2.00 x 107 KJ of heat per month. How many grams of natural gas (methane) must be burned to supply this energy?CH4(g) + 2O2(g) → CO2(g) + 2H2O(l) ΔH°rxn= –890.4 kJ/mol

Answer:

3.6*105g CH4

Explanation:

The detailed solution is shown on the image. From the detailed chemical reaction, we calculate the mass of methane required in the standard combustion reaction of methane and use it to estimate the mass required to produce the quantity of heat required in the question.

Final answer:

To supply the energy needed for an average home in Colorado, approximately 3.58 x 10^8 grams of natural gas (methane) must be burned.

Explanation:

To calculate the amount of natural gas (methane) required to supply the energy needed for an average home in Colorado, we can use the balanced chemical equation for the combustion of methane:

CH4(g) + 2O2(g) → CO2(g) + 2H2O(l)

The molar enthalpy change for this reaction (ΔH°rxn) is -890.4 kJ/mol. First, we need to convert the energy requirement from kilojoules to joules:

2.00 x 107 kJ = 2.00 x 1010 J

Next, we can use the molar enthalpy change to calculate the number of moles of methane required:

moles of CH4 = energy requirement / mlar enthalpy change

moles of CH4 = 2.00 x 1010 J / (-890.4 kJ/mol)

Finally, we can convert the number of moles of methane to grams using the molar mass of methane:

molar mass of CH4 = 12.01 g/mol + 4(1.008 g/mol) = 16.04 g/mol

grams of CH4 = moles of CH4 * molar mass of CH4

Therefore, the number of grams of natural gas (methane) that must be burned to supply this energy is approximately:

grams of CH4 = (2.00 x 1010 J / (-890.4 kJ/mol)) * 16.04 g/mol

Simplifying the calculation:

grams of CH4 ≈ 3.58 x 108 g

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