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NEET CHEMISTRYEasy

If enthalpies of formation of C2H4(g)C_{2}H_{4}(g), CO2(g)CO_{2}(g) and H2O(l)H_{2}O(l) at 25C25^{\circ}C and 1 atm pressure be 52, –394 and –286 kJ mol⁻¹ respectively, the enthalpy of combustion of C2H4(g)C_{2}H_{4}(g) will be [CBSE PMT 1995; AIIMS 1998; Pb. PMT 1999]:

A

+1412 kJ mol⁻¹

B

–1412 kJ mol⁻¹

C

+141.2 kJ mol⁻¹

D

–141.2 kJ mol⁻¹

Step-by-Step Solution

The enthalpy of combustion (ΔcH\Delta_{c}H^{\circ}) is calculated using the standard molar enthalpies of formation (ΔfH\Delta_{f}H^{\circ}) of the products and reactants . First, we write the balanced thermochemical equation for the complete combustion of ethene (C2H4C_{2}H_{4}): C2H4(g)+3O2(g)2CO2(g)+2H2O(l)C_{2}H_{4}(g) + 3O_{2}(g) \rightarrow 2CO_{2}(g) + 2H_{2}O(l) .

According to thermodynamics, the reaction enthalpy is the sum of the enthalpies of the products minus the sum of the enthalpies of the reactants: ΔrH=[2×ΔfH(CO2,g)+2×ΔfH(H2O,l)][ΔfH(C2H4,g)+3×ΔfH(O2,g)]\Delta_{r}H^{\circ} = [2 \times \Delta_{f}H^{\circ}(CO_{2}, g) + 2 \times \Delta_{f}H^{\circ}(H_{2}O, l)] - [\Delta_{f}H^{\circ}(C_{2}H_{4}, g) + 3 \times \Delta_{f}H^{\circ}(O_{2}, g)] .

By convention, the standard enthalpy of formation for an element in its reference state, such as O2(g)O_{2}(g), is taken as zero .

Substituting the values provided in the problem: ΔcH=[2(394 kJ mol1)+2(286 kJ mol1)][52 kJ mol1+3(0)]\Delta_{c}H^{\circ} = [2(-394 \text{ kJ mol}^{-1}) + 2(-286 \text{ kJ mol}^{-1})] - [52 \text{ kJ mol}^{-1} + 3(0)] ΔcH=[788572]52\Delta_{c}H^{\circ} = [-788 - 572] - 52 ΔcH=136052=1412 kJ mol1\Delta_{c}H^{\circ} = -1360 - 52 = -1412 \text{ kJ mol}^{-1}.

The negative sign confirms that combustion is an exothermic process . This result matches Option B.

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