Calculate the total entropy change, _total and state if the proce… - Vidyadip

Question

Calculate the total entropy change, $\Delta\text{S}_\text{total}$ and state if the process is spontaneous, when one mole of liquid mercury Hg(l) changes to mercury vapour, Hg(g) at 298K. The molar entropy of vapourisation of Hg is 99JK^-1mol^-1 and molar enthalpy of vapourisation is 59.1k J mol^-1.

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Answer

$\Delta\text{S}_\text{surr}=\frac{-\Delta\text{H}_\text{sys}}{\text{T}}=\frac{-59100\text{J mol}^{-1}}{298\text{K}}$

$=-198\text{JK}^{-1}\text{mol}^{-1}$

$\Delta\text{S}_\text{total}=\Delta\text{S}_\text{sys}+\Delta\text{S}_\text{surr}$

$=99\text{J}-198\text{J}=-99\text{JK}^{-1}\text{mol}^{-1}$

Since $\Delta\text{S}_\text{total}=-\text{ve},$ therefore, process is non-spontaneous at 298K.

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