The highest ratio is -0.613kj/g which is for automobile lead-acid battery .
Given ,
Reaction-1 used in fuel cells
Reaction-2 used in automobile lead-acid battery
Reacttion-3 used in experimental high-temperature battery for powering electric vehicles .
1) Fuel cells :
2H2(g) + O2(g) ==> 2H20 (l) , E^0cell = 1.23V
We know ,
Free energy is the maximum work done .
delta G = Wmax
=> Wmax = delta G = -4.75*10^5j/mol e^- = -4.75*10^2 kj/ mol e^-
Molecular mass of 1 mole of H2 = 2 .016 g / mol e^-
Molecular mass of 2 mole of H2 = 4.032 g/mol e^-
Molecular mass of O2 = 32 g/mol e^-
Total mass of the reactants = (4.032+32)g/mol e^- = 36.032 g/mol e^-
Ratio of Wmax to the total mass of the reactants
=Wmax/ total mass of the reactants
=( -4.75*10^2 kj/mol e^-)/36.032 g/mol e^-
=-13.2kj/g
Therefore , the ratio of Wmax to total mass of the reactants is -13.2kj/g .
2) Automobile lead-acid battery :
Pb(s) + PbO2(s) + 2H2SO4(aq) ==> 2PbSO4 (s) + 2H2O (l) , E^0cell = 2.04V
We know ,
Wmax = delta G = -3.94*10^5j/mol e^- = -3.94*10^2kj/mol e^-
molecular mass of Pb = 207.2 g /mol e^-
molecular mass of Pbo2 = 239.2g/mol e^-
molecular mass of H2SO4 = 98.008g/mol e^-
molecular mass of 2 mole of H2SO4 = 196.016g/mol e^-
total mass of the reactants = (207.2+239.2+196.016)g/mol e^- = 642.416g/mol e^-
Ratio of Wmax to total mass of the reactants
= Wmax/total mass of reactants
=(-3.94*10^2kj/mol e^-)/642.416g/mol e^-
=-0.613kj/g
Hence ,the ratio of Wmax to the total mass of the reactants of automobile lead-acid battery is -0.613kj/g .
3) Experimental high temperature battery :
2Na(l) +FeCl2(s) ==> 2NaCl (s) + Fe(s) , E^0 cell = 2.35V
We know ,
Wmax = delta G = -4.53*10^5j/mol e^- = -4.53*10^2kj/mol e^-
molecular mass of Na = 22.99 g/mol e^-
molecular mass of 2 moles of Na = 45.98g/mol e^-
molecular mass of FeCl2 = 126.85 g/mol e^-
total mass of the reactants =( 45.98+ 126.85)g/mol e^- = 172.83 g/mol e^-
Ratio of Wmax to the total mass of the reactants
= Wmax / total mass of reactants
=(-4.53*10^2kj/mol e^-)/ 172.83g/mol e^-
=-2.62kj/g
Therefore , the ratio of Wmax to the total mass of the reactants in an experimental high temperature battery is -2.62kj/g .
Hence , the highest ratio is -0.613kj/g which is of lead -acid battery .
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