Calculate \(\Delta S_{\text { surr }}\) for the following reactions at \(25^{\circ} \mathrm{C}\) and 1 \(\mathrm{atm}\) . a. $\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(l)\Delta H^{\circ}=-2221 \mathrm{kJ}$ b. $2 \mathrm{NO}_{2}(g) \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \qquad \Delta H^{\rho}=112 \mathrm{kJ}$

To convert the given temperature from Celsius to Kelvin, we add 273.15 to it. \(T_\text{K} = 25^\circ\text{C} + 273.15 = 298.15\,\text{K}\) #Step 2: Calculate \(\Delta S_{\text{surr}}\) for Reaction a#

Using the formula for \(\Delta S_{\text{surr}}\) and the provided values, we can calculate the change in entropy for reaction a: \(\Delta S_{\text{surr}}^\text{(a)} = -\frac{\Delta H^{\circ}_\text{(a)}}{T} = -\frac{-2221\,\text{kJ}\,\mathrm{mol^{-1}}}{298.15\,\text{K}}\) First, we need to convert \(\Delta H^{\circ}\) from kJ/mol to J/mol: \(\Delta H^{\circ}_\text{(a)} \times 1000 = -2221000\,\text{J}\,\mathrm{mol^{-1}}\) Now, we can plug in the values: \(\Delta S_{\text{surr}}^\text{(a)} = -\frac{-2221000\,\text{J}\,\mathrm{mol^{-1}}}{298.15\,\text{K}} = 7454\,\text{J}\,\mathrm{K^{-1}\,mol^{-1}}\) Therefore, the change in entropy of the surroundings for reaction a is: \(\Delta S_{\text{surr}}^\text{(a)} = 7454\,\text{J}\,\mathrm{K^{-1}\,mol^{-1}}\) #Step 3: Calculate \(\Delta S_{\text{surr}}\) for Reaction b#

Using the formula for \(\Delta S_{\text{surr}}\) and the provided values, we can calculate the change in entropy for reaction b: \(\Delta S_{\text{surr}}^\text{(b)} = -\frac{\Delta H^{\circ}_\text{(b)}}{T} = -\frac{112\,\text{kJ}\,\mathrm{mol^{-1}}}{298.15\,\text{K}}\) First, we need to convert \(\Delta H^{\circ}\) from kJ/mol to J/mol: \(\Delta H^{\circ}_\text{(b)} \times 1000 = 112000\,\text{J}\,\mathrm{mol^{-1}}\) Now, we can plug in the values: \(\Delta S_{\text{surr}}^\text{(b)} = -\frac{112000\,\text{J}\,\mathrm{mol^{-1}}}{298.15\,\text{K}} = -376\,\text{J}\,\mathrm{K^{-1}\,mol^{-1}}\) Therefore, the change in entropy of the surroundings for reaction b is: \(\Delta S_{\text{surr}}^\text{(b)} = -376\,\text{J}\,\mathrm{K^{-1}\,mol^{-1}}\)