Respuesta :
Answer : The change in molar entropy of the sample is 10.651 J/K.mol
Explanation :
To calculate the change in molar entropy we use the formula:
[tex]\Delta S=n\int\limits^{T_f}_{T_i}{\frac{C_{p,m}dT}{T}[/tex]
where,
[tex]\Delta S[/tex] = change in molar entropy
n = number of moles = 1.0 mol
[tex]T_f[/tex] = final temperature = 300 K
[tex]T_i[/tex] = initial temperature = 273 K
[tex]C_{p,m}[/tex] = heat capacity of chloroform = [tex]91.47+7.5\times 10^{-2}(T/K)[/tex]
Now put all the given values in the above formula, we get:
[tex]\Delta S=1.0\int\limits^{300}_{273}{\frac{(91.47+7.5\times 10^{-2}(T/K))dT}{T}[/tex]
[tex]\Delta S=1.0\times [91.47\ln T+7.5\times 10^{-2}T]^{300}_{273}[/tex]
[tex]\Delta S=1.0\times 91.47\ln (\frac{T_f}{T_i})+7.5\times 10^{-2}(T_f-T_i)[/tex]
[tex]\Delta S=1.0\times 91.47\ln (\frac{300}{273})+7.5\times 10^{-2}(300-273)[/tex]
[tex]\Delta S=8.626+2.025[/tex]
[tex]\Delta S=10.651J/K.mol[/tex]
Therefore, the change in molar entropy of the sample is 10.651 J/K.mol
