Question

Carbon Emissions from Natural Gas: Worldwide combustion of methane, CH₄ (natural gas), provides about 10.9 × 10¹⁶ kJ of energy per year. If methane has an energy content of 39 × 10³ kJ/m3 (at STP: Standard Temperature and Pressure), what mass of CO₂ is emitted into the atmosphere each year? Also express that emission rate as metric tons of carbon (not CO₂) per year. A metric ton, which is 1,000 kg is usually written as tonne to distinguish it from the 2,000-lb American, or short, ton.

Answer 1

Solution :-

CH4 +2O2 --- > CO2 + 2H2O

Total energy given by the methane combustion is 10.9*10^16 kJ/year

Energy content of methane is 39*10^3 kJ/m3

So lets first calculate the volume of the methane in cubic meter

[10.9*10^16 kJ per year] / [39*10^3 kJ per m3 ]= 2.795*10^12 m3

Now using the volume in cubic meter we can find the moles of methane CH4 burned each year

At STP conditions 1 mol gas = 22.4 L

(2.795*10^12 m^3 * 1000 L / 1 m^3)*( 1 mol / 22.4 L) =1.248*10^14 mol CH4

Now using the moles of CH4 we can find the mass of CO2

(1.248*10^14 molCH4 * 1 mol CO2/1 molCH4)*(44.01 g / 1 mol CO2) = 5.49*10^15 g CO2

Lets convert mass of CO2 from grams to metric ton

(5.49*10^15 g CO2 *1 kg / 1000 g)*(1 metric ton/1000 kg) = 5.49*10^9 metric ton CO2

Now lets write the rate of emission as the metric tone of carbon

Using the mass of CO2 we can find the mass of carbon as follows

(5.49*10^9 metric ton CO2 * 12.01 ton C / 44.01 ton CO2) = 1.50*10^9 metric ton C

So the answers are

Mass of CO2 produced = 5.49*10^9 metric ton /year

Rate of emission of carbon is 1.50*10^9 metric ton/year