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General Mechanism of Electrophilic Aromatic Substitution

Consider an i...

Question

Consider an isothermal reversible compression of 1 mole of an ideal gas in which pressure of the system increased from 5 atm to 30 atm at 300 K. The entropy change (in kJ) of the surrounding is:
( $R = 8.314 J m o l^{- 1} K^{- 1}$ )

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Solution

We know, $d W = - p d V$
Then
$W = - \int_{V_{1}}^{V_{2}} P d V = - \int_{V_{1}}^{V_{2}} \frac{n R T}{V} d V = - n R T l n (\frac{V_{1}}{V_{2}})$

or, $W = - n R T l n (\frac{P_{1}}{P_{2}})$ [ $∵ \frac{P_{1}}{P_{2}} = \frac{V_{1}}{V_{2}}$ ]

or, $W = - 1 \times 8.314 \times 300 \times l n (\frac{5}{30}) = - 8.314 \times 300 \times 1.79$

or, $W = - 4.46 k J$
Therefore, $Q = - W = 4.46 k J$ [ $∵ Δ U = 0$ ]

$Δ S = \frac{Q}{T} = \frac{4.46 \times 10^{3}}{3 \times 10^{2}} = 15 k J / m o l$

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R = 8.314 J m o l^{- 1} K^{- 1}

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[R = 0.082 L a t m m o l^{- 1} K^{- 1} = 8.3 J m o l^{- 1} K^{- 1}]

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