Question

The following reactions are used in batteries:Reaction I is used in fuel cells, II in the automobile lead-acid battery, and III in an experimental high-temperature battery for powering electric vehicles. The aim is to obtain as much work as possible from a cell, while keeping its weight to a minimum.(b) Calculate the ratio, in kJ/g, of wmax to mass of reactants for each of the cells. Which has the highest ratio, which the lowest, and why? (Note: For simplicity, ignore the masses of cell components that do not appear in the cell as reactants, including electrode materials, electrolytes, separators, cell casing, wiring, etc.)

Answer 1

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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