JEE MAIN - Chemistry (2022 - 26th June Evening Shift - No. 20)
40% of HI undergoes decomposition to H2 and I2 at 300 K. $$\Delta$$G$$^\Theta $$ for this decomposition reaction at one atmosphere pressure is __________ J mol$$-$$1. [nearest integer]
(Use R = 8.31 J K$$-$$1 mol$$-$$1 ; log 2 = 0.3010, ln 10 = 2.3, log 3 = 0.477)
Explanation
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$$\therefore$$ $$K = {{{{\left( {{\alpha \over 2}} \right)}^{1/2}} \times {{\left( {{\alpha \over 2}} \right)}^{1/2}}} \over {(1 - \alpha )}}$$
Given $$\alpha = {{40} \over {100}} = 0.4$$
$$\therefore$$ $$K = {{{{\left( {{{0.4} \over 2}} \right)}^{1/2}} \times {{\left( {{{0.4} \over 2}} \right)}^{1/2}}} \over {(1 - 0.4)}}$$
$$ = {1 \over 3}$$
We know,
$$\Delta G^\circ = - RT\ln K$$
$$ = - RT\ln \left( {{1 \over 3}} \right)$$
$$ = + RT\ln 3$$
$$ = + 8.314 \times 300 \times \ln 3$$
= 2735 J/mol
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