Comparison Of Fuel Value Of Propyne, Propylene And Propane Combustion

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Comparison Of Fuel Value Of Propyne, Propylene And Propane Combustion

The standard enthalpies of formation of gaseous propyne (C_{3}H_{4}), propylene (C_{3}H_{6}), and propane (C_{3}H_{8}) are +185.4, +20.4, and -103.8 kJ/mol, respectively.

(a) Calculate the heat evolved per mole on combustion of each substance to yield carbon dioxide and water.

(b) Calculate the heat evolved on combustion of 1 kg of each substance.

(c) Which is the most efficient fuel in terms of heat evolved?

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

Pj Problem of Interest is of type *grouping/interaction* (chemical).
**(ai)** Balanced chemical equation of propyne combustion:

C_{3}H_{4}(g) + 4O_{2}(g) -------> 3CO_{2}(g) + 2H_{2}O(g)

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.
**Given Enthalpies Of Formation**:

ΔH^{0}_{f} of C_{3}H_{4} = +185.4 kJ/mol

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

ΔH^{0}_{f} of CO_{2}(g) = -393.5 kJ

ΔH^{0}_{f} of H_{2}O(g) = -241.8 kJ

From Equation for standard enthalpy of reaction:

ΔH^{0}_{reaction} = -3(393.5) -2(241.8) - (185.4) =-1180.5-483.6-185.4 = -1849.5 kJ/mol.
**(aii)** Balanced chemical equation of propylene combustion

2C_{3}H_{6}(g) + 9O_{2}(g) -------> 6CO_{2}(g) + 6H_{2}O(g)

Simplified equation

C_{3}H_{6}(g) + (9/2)O_{2}(g) -------> 3CO_{2}(g) + 3H_{2}O(g)

From Equation for standard enthalpy of reaction:

ΔH^{0}_{reaction} = -3(393.5) -3(241.8) - (20.4) = -1180.5-725.4-20.4 = -1926.3 kJ/mol.
**(aiii)** Balanced chemical equation of propane combustion

C_{3}H_{4}(g) + 5O_{2}(g) -------> 3CO_{2}(g) + 4H_{2}O(g)

From Equation for standard enthalpy of reaction:

ΔH^{0}_{reaction} = -3(393.5) -4(241.8) - (-103.8) = -1180.5-967.2+103.8 = -2043.9 kJ/mol
**(bi)** Divide by molar mass of each substance

Molar mass of C_{3}H_{4}(g) = 36 + 4 = 40 g = 0.040 kg

So, for C_{3}H_{4}(g), heat evolved per kg = -1849.5/0.040 = -4.62 x 10^{4} kJ/kg.
**(bii)**

Molar mass of C_{3}H_{6}(g) = 36 + 6 = 42 g = 0.042 kg

So, for C_{3}H_{4}(g), heat evolved per kg = -1926/0.042 = -4.59 x 10^{4} kJ/kg.
**(biii)**

Molar mass of C_{3}H_{8}(g) = 36 + 8 = 44 g = 0.044 kg

So, for C_{3}H_{8}(g), heat evolved per kg = -2043.9/0.044 = -4.65 x 10^{4} kJ/kg.
**(c)** Propyne, propylene and propane release approximately the same amount of heat per unit mass, however, heat released by propane is marginally the highest.

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