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Whenever organic matter is decomposed under oxygen-free
Chapter 5, Problem 69P(choose chapter or problem)
Whenever organic matter is decomposed under oxygen-free (anaerobic) conditions, methane is one of the products. Thus, enormous deposits of natural gas, which is almost entirely methane, exist as a major source of fuel for home and industry.
(a) It is estimated that known sources of natural gas can produce \(5600 \mathrm{EJ}\) of energy \(\left(1 \mathrm{EJ}=10^{18} \mathrm{~J}\right)\). Current total global energy usage is \(4.0 \times 10^{2}\) EJ per year. Find the mass (in \(\mathrm{kg}\) ) of known sources of natural gas \(\left(\Delta H_{\mathrm{rxn}}^{\circ}\right\). for the combustion of \(\mathrm{CH}_{4}=-802 \mathrm{~kJ} / \mathrm{mol}\) ).
(b) For how many years could these sources supply the world's total energy needs?
(c) What volume \(in \mathrm{ft}^{3}\right)\) of natural gas, measured at STP, is required to heat \(1.00 \mathrm{qt}\) of water from \(25.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C}\) (\(d\) of \(\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{~g} / \mathrm{mL} ; d\) of \(\mathrm{CH}_{4}\) at \(\mathrm{STP}=0.72 \mathrm{~g} / \mathrm{L}\))?
(d) The fission of \(1 \mathrm{~mol}\) of uranium (about \(4 \times 10^{-4} \mathrm{ft}^{3}\) ) in a nuclear reactor produces \(2 \times 10^{13} \mathrm{~J}\). What volume \(in \mathrm{ft}^{3}\) of natural gas would produce the same amount of energy?
Equation Transcription:
Text Transcription:
5600EJ
(1EJ=10^18 J)
4.0 x10^2
kg
Delta H_rxn
CH_4= −802 kJ/mol
ft^3
1.00qt
25.0^circ C
100.0^circ C
d
H_2 O=1.00 g/mL;d
CH_4
STP=0.72 g/L
1 mol
4x10^−4 ft^3
2x10^13 J
Questions & Answers
QUESTION:
Whenever organic matter is decomposed under oxygen-free (anaerobic) conditions, methane is one of the products. Thus, enormous deposits of natural gas, which is almost entirely methane, exist as a major source of fuel for home and industry.
(a) It is estimated that known sources of natural gas can produce \(5600 \mathrm{EJ}\) of energy \(\left(1 \mathrm{EJ}=10^{18} \mathrm{~J}\right)\). Current total global energy usage is \(4.0 \times 10^{2}\) EJ per year. Find the mass (in \(\mathrm{kg}\) ) of known sources of natural gas \(\left(\Delta H_{\mathrm{rxn}}^{\circ}\right\). for the combustion of \(\mathrm{CH}_{4}=-802 \mathrm{~kJ} / \mathrm{mol}\) ).
(b) For how many years could these sources supply the world's total energy needs?
(c) What volume \(in \mathrm{ft}^{3}\right)\) of natural gas, measured at STP, is required to heat \(1.00 \mathrm{qt}\) of water from \(25.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C}\) (\(d\) of \(\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{~g} / \mathrm{mL} ; d\) of \(\mathrm{CH}_{4}\) at \(\mathrm{STP}=0.72 \mathrm{~g} / \mathrm{L}\))?
(d) The fission of \(1 \mathrm{~mol}\) of uranium (about \(4 \times 10^{-4} \mathrm{ft}^{3}\) ) in a nuclear reactor produces \(2 \times 10^{13} \mathrm{~J}\). What volume \(in \mathrm{ft}^{3}\) of natural gas would produce the same amount of energy?
Equation Transcription:
Text Transcription:
5600EJ
(1EJ=10^18 J)
4.0 x10^2
kg
Delta H_rxn
CH_4= −802 kJ/mol
ft^3
1.00qt
25.0^circ C
100.0^circ C
d
H_2 O=1.00 g/mL;d
CH_4
STP=0.72 g/L
1 mol
4x10^−4 ft^3
2x10^13 J
ANSWER:
Solution 69P:Step 1: (a)Here, we have to calculate the the mass (in kg) of known sources of natural gas.Given that,The combustion of CH4 = -802 kJ/molEnergy produced by natural gas = 5600 EJTherefore, the amount of natural gas required to produce 5600EJ energy is 18 1.0 mol CH 16.01 g CH5600EJ × 10 J × 4 × 1 kJ × 4 × 1 kg 1 EJ 802 kJ 1000 J 1.0 mol C4 1000 g 14= 1.12 × 10 kgHence, the mass (in kg) of known sources of natural gas is 1.12 × 10 kg 14