In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $$CH3OH($$ℓ$$)+32O2(g)$$→$$CO2(g)+2H2O($$ℓ$$)$$ At $$298K$$ standard Gibb’s energies of formation for $$CH3OH($$ℓ$$)$$,$$H2O($$ℓ$$)$$ and $$CO2(g)$$ are −$$166.2$$,−$$237.2$$ and −$$394.4kJ$$ mol−$$1$$ Respectively. If standard enthalpy of combustion of methanol is −$$726kJ$$ mol−$$1$$ . Efficiency of the fuel cell will be

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In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $$CH3OH($$ℓ$$)+32O2(g)$$→$$CO2(g)+2H2O($$ℓ$$)$$ At $$298K$$ standard Gibb’s energies of formation for $$CH3OH($$ℓ$$)$$,$$H2O($$ℓ$$)$$ and $$CO2(g)$$ are −$$166.2$$,−$$237.2$$ and −$$394.4kJ$$ mol−$$1$$ Respectively. If standard enthalpy of combustion of methanol is −$$726kJ$$ mol−$$1$$ . Efficiency of the fuel cell will be

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$$CH3OH($$ℓ$$)+32O2(g)$$→$$CO2(g)+2H2O($$ℓ$$)$$Δ$$H=$$−$$726kJ$$ mol−$$1$$       Also Δ$$Gf0CH3OH($$ℓ$$)=$$−$$166.2kJ$$ mol−$$1$$     Δ$$Gf0H2O($$ℓ$$)=$$−$$237.2kJ$$ mol−$$1$$     Δ$$Gf0CO2($$ℓ$$)=$$−$$394.4kJ$$ mol−$$1$$     ∵Δ$$G=$$∑Δ$$Gf0$$     Products −∑Δ$$Gf0$$     reactants. $$=$$−$$394.4$$−$$2(237.2)+166.2$$     $$=$$−$$702.6kJ$$ mol−$$1$$     Now efficiency of fuel cell $$=$$ΔGΔH×$$100$$     $$=702.6726$$×$$100$$     $$=97$$%

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