In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is CH ₃ OH ( )+ 3 2 O ₂( ~g ) CO ₂( ~g )+2 H ₂ O ( ) At 298 ~K standard Gibb's energies of formation for CH ₃ OH ( ), H ₂ O ( ) and CO ₂( ~g ) are -166.2,-237.2 and -394.4 ~kJ ~mol ⁻¹ respectively. If standard enthalpy of combustion of methanol is -726 ~kJ ~mol ⁻¹ , efficiency of the fuel cell will be

Step-by-step solution

CH ₃ OH ( )+ 3 2 O ₂( ~g ) CO ₂( ~g )+2 H ₂ O ( ) H =-726 ~kJ ~mol ⁻¹ Also G _ f ^0 CH ₃ OH ( )=-166.2 ~kJ ~mol ⁻¹ aligned & G _ f ^0 H ₂ O ( )=-237.2 ~kJ ~mol ⁻¹ & G _ f ^0 CO ₂( )=-394.4 ~kJ ~mol ⁻¹ & G = G _ f ^0 products - G _ f ^0 reactants. & =-394.4-2(237.2)+166.2 & =-702.6 ~kJ ~mol ⁻¹ aligned aligned & now Efficiency of fuel cell = G H 100 & = 702.6 726 100 & =97 % aligned