Consider a $$70$$% efficient $$hydrogen-oxygen$$ fuel cell working under standard conditions at $$1$$ bar and $$298$$ K. Its cell reaction is $$H2(g)+12O2(g)$$→$$H2O($$ℓ$$)The$$ work derived from the cell on the consumption of $$1.0$$ × $$10$$–$$3mol$$ of $$H2(g)$$ is used to compress $$1.00$$ mol of a monoatomic ideal gas in a thermally insulted container. What is the change in the temperature (in$$ $$K) of the ideal gas ?The standard reduction potentials for the two $$half-cells$$ are given below. $$O2(g)+4H+(aq$$.$$)+4e$$−→$$2H2O($$ℓ$$)$$,$$Eo=1.23V2H+(aq$$.$$)+2e$$−→$$H2(g)$$,$$Eo=0.00VUse$$ F $$=$$ $$96500$$ C mol–$$1$$ , R $$=$$ $$8.314$$ J mol–$$1K$$–$$1$$

Question

Consider a $$70$$% efficient $$hydrogen-oxygen$$ fuel cell working under standard conditions at $$1$$ bar and $$298$$ K. Its cell reaction is $$H2(g)+12O2(g)$$→$$H2O($$ℓ$$)The$$ work derived from the cell on the consumption of $$1.0$$ × $$10$$–$$3mol$$ of $$H2(g)$$ is used to compress $$1.00$$ mol of a monoatomic ideal gas in a thermally insulted container. What is the change in the temperature (in$$ $$K) of the ideal gas ?The standard reduction potentials for the two $$half-cells$$ are given below. $$O2(g)+4H+(aq$$.$$)+4e$$−→$$2H2O($$ℓ$$)$$,$$Eo=1.23V2H+(aq$$.$$)+2e$$−→$$H2(g)$$,$$Eo=0.00VUse$$ F $$=$$ $$96500$$ C mol–$$1$$ , R $$=$$ $$8.314$$ J mol–$$1K$$–$$1$$

Infinity Learn · Accepted Answer

Ecell $$0=1.23$$−$$0.00=1.23V$$ΔGcell $$0=$$−nFEcell $$0=$$−$$2$$×$$96500$$×$$1.23J$$∴ Work derived from this fuel $$cell=70100$$×−Δ$$Gcell0$$×$$10$$−$$3=xJSince$$ insulated vessel, hence q $$=$$ $$0From$$ equation, for monoatomic gas, $$w=$$ΔU ⇒ $$x=nCV$$,mΔTCv,$$m=3R2$$ or,  $$70100$$×(2$$×$$96500$$×$$1.23)×$$10$$−$$3=1$$×$$32$$×$$8.314$$×ΔT∴ Δ$$T=13.32$$

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