A synthetic chemist is modifying the combustion of a generic hydrocarbon fuel,

CHEMISTRY · Multi-part · AP · Chemistry · Thermochemistry · Thermochemistry

Problem

C_{n}H_{2n+2}(g)

, by partially substituting the fuel with an oxygenated additive,

C_{n}H_{2n}O(g)

, to attain a near-zero enthalpy change for the overall combustion mixture. Assume complete combustion to

CO_{2}(g)

and

H_{2}O(l)

and neglect any phase changes other than the formation of liquid water. Let the mole fraction of the oxygenated additive in the fuel blend be

f

(0 ≤

f

≤ 1). The blend composition is therefore

(1 - f)

mol

C_{n}H_{2n+2}

and

f

mol

C_{n}H_{2n}O

. Average bond enthalpies (representative, in

\text{kJ}\,\text{mol}^{-1}

): C–H 413 C–C 348 C–O 358 C=O (in

CO_{2}

) 799 O=O 498 O–H 463 Additional information: • Combustion of

C_{n}H_{2n+2}(g)

C_{n}H_{2n+2} + \left(3n + \frac{1}{2}\right) O_{2} \to n\,CO_{2} + (n + 1)\,H_{2}O(l)

\Delta H^\circ_{1}

(depends on

n

) • Combustion of

C_{n}H_{2n}O(g)

C_{n}H_{2n}O + \frac{3n}{2} O_{2} \to n\,CO_{2} + n\,H_{2}O(l)

\Delta H^\circ_{2}

(depends on

n

) • For this question, treat

\Delta H^\circ_{1}

and

\Delta H^\circ_{2}

as unknown expressions derived solely from average bond energies and show them symbolically in your work. (1) Part 1: a. Derive an expression for the overall standard enthalpy change,

\Delta H_{\text{blend}}(f)

, for complete combustion of 1 mole of the fuel blend as a function of the mole fraction

f

. (2) Part 2: b. Determine the value of

f

that makes

\Delta H_{\text{blend}}(f)

exactly zero. Express your answer algebraically in terms of

n

and any constants that appear in your expression. (3) Part 3: c. For the specific case

n = 8

(octane family), evaluate numerically the value of

f

using the average bond enthalpies supplied. Show all intermediate steps. (4) Part 4: d. Critically assess whether the calculated mole fraction

f

is practically achievable in a real combustion engine, citing at least two operational or chemical factors that could deviate from the idealized bond-enthalpy model used.

Related theory

Browse the problem library