Question

When organic matter decomposes under oxygen-free (anaerobic) conditions, methane is one of the products. Thus, enormous deposits of natural gas, which is almost entirely methane, serve as a major source of fuel for home and industry.
(a) Known deposits of natural gas can produce 5600 EJ of energy (1 EJ = 10¹⁸ J). Current total global energy usage is 4.0X10² EJ per year. Find the mass (in kg) of known deposits of natural gas (ΔH°rxn for the combustion of CH₄ = -802 kJ/mol).

Answer 1

The mass of methane is 1.117×10^17 g.

Given,

∆H°rxn =-802kj/mol

1Ej = 10^18 j =10^-3×10^18 kj

802kj of energy is released by 1 mol of CH4.

1kj of energy is released by 1/802 mol of CH4.

5600Ej of energy is released= 5600/802 mol of CH4

5600×10^18×10^-3 kj of energy is released

=5600 × 10^18 × 10^-3 /802 mol

=6.982 ×10^15 mol of CH4

We know,

the molecular mass of CH4 = 16 g

1 mol of CH4 = 16g

6.982×10^15 mol = 16 × 6.982 × 10^15 = 1.117×10^17 g

Hence, the mass of methane is 1.117×10^17 g.

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