# Question 885c3

Jan 5, 2018

This problem demands a fairly deep understanding of thermodynamic relationships.

The universe in this problem is but the system and the surroundings.

$C a O \left(s\right) + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s C a {\left(O H\right)}_{2} \left(s\right)$

Consider,

$\Delta {S}_{\text{univ") = DeltaS_("sys") + DeltaS_("surr}}$,

The change in enthalpy or entropy of a system is the sum of the property for products less the sum of the property for reactants,

$\Delta S = \frac{\Delta H}{T}$, and,

$- \Delta {H}_{\text{sys") = DeltaH_("surr}}$
$\implies - \frac{\Delta {H}_{\text{sys"))/T = (DeltaH_("surr}}}{T}$
=> DeltaS_("surr") = -(DeltaH_("sys"))/T

Hence,

$\Delta {H}_{\text{sys}} = - 65.2 k J$
$\therefore \Delta {H}_{\text{surr}} = 65.2 k J$, and $\Delta {S}_{\text{surr}} = \frac{6.52 \cdot {10}^{4} J}{298 K} \approx \frac{218.7 J}{K}$

Moreover,

$\Delta {S}_{\text{sys}} = \frac{- 26.4 J}{K}$

DeltaS_("univ") = DeltaS_"surr" + DeltaS_"sys" approx (192.3J)/K#

I'm open to feedback if I made a mistake!