Amount Of Energy Produced When Methane Is Combusted To Form Water

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Amount Of Energy Produced When Methane Is Combusted To Form Water

The combustion of 1 molecule of methane gas has water as a product:

(a) Calculate the amount of energy produced during this reaction.

(b) A typical X-ray photon has an energy of 8eV. How does the energy produced in(a) compare to the energy of the X-ray photon?

**The strings**:
S_{7}P_{6}A_{66} (grouping/interaction - chemical).
**The math**:

Pj Problem of Interest is of type *grouping/interaction* (chemical).
**(a)** The balanced chemical equation is:

CH_{4}(g) + 2O_{2}(g) -------> CO_{2}(g) + 2H_{2}O(l)

ΔH^{0}_{reaction} = ΣnΔH^{0}_{f(products)} - ΣmΔH^{0}_{f(reactants)}

Where ΔH^{0} = standard enthalpy change at standard pressure (1 atm) and temperature 25^{0}C (298 K).

ΔH_{f} = enthalpy of formation

n is coefficients of products and m is coefficients of reactants.
**Enthalpy Of Formation From Enthalpy Table**:

ΔH^{0}_{f} of CH_{4} = -74.80 kJ

ΔH^{0}_{f} of O_{2} = 0 (since this is the most stble state of oxygen)

ΔH^{0}_{f} of CO_{2} = -393.5 kJ

ΔH^{0}_{f} of H_{2}O = -285.8 kJ

From Equation:

ΔH^{0}_{reaction} = -393.5 -2(285.8) - (-74.8) = -965.1 + 74.8 = -890.4 kJ.

So 890.4 kJ of energy is released when 1 mole of CH_{4} is combusted

1 mole contains 6.022 x 10^{23} molecules (Avogadro's number)

So, energy released from combustion of 1 molecule of CH_{4}(g) = (890.4)/(6.022 x 10^{23}) = 1.479 x 10^{-18} J/molecule.
**(b)** 1eV = 1.602 x 10^{-19} J

So, 8eV = 8(1.602 x 10^{-19}) = 1.2 x 10^{-15} J/photon

So, the energy from a photon of X-ray is 1000 times more than that produced from the combustion of 1 molecule of CH_{4}(g).

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