Question

the heat of fusion $\delta h_f$ of toluene $(\ce{c6h5ch3})$ is 6.6 kj/mol. calculate the change in entropy $\delta s$ when 2.6 g of toluene melts at $-95.0\\ ^\circ\text{c}$. be sure your answer contains a unit symbol. round your answer to 2 significant digits.

Explanation:

Step1: Calculate moles of toluene

Molar mass of toluene ($\ce{C6H5CH3}$) is $92.14\ \text{g/mol}$. Moles ($n$) = $\frac{\text{mass}}{\text{molar mass}}$ = $\frac{2.6\ \text{g}}{92.14\ \text{g/mol}}$ ≈ $0.0282\ \text{mol}$.

Step2: Find heat of fusion for 2.6 g

$\Delta H = n \times \Delta H_f$ = $0.0282\ \text{mol} \times 6.6\ \text{kJ/mol}$ ≈ $0.1861\ \text{kJ}$ = $186.1\ \text{J}$.

Step3: Convert temperature to Kelvin

$T = -95.0 + 273.15 = 178.15\ \text{K}$.

Step4: Calculate entropy change

$\Delta S = \frac{\Delta H}{T}$ = $\frac{186.1\ \text{J}}{178.15\ \text{K}}$ ≈ $1.04\ \text{J/K}$. Round to 2 sig figs: $1.0\ \text{J/K}$ (or $1.0\ \text{J·K}^{-1}$).

Answer:

$1.0\ \text{J/K}$ (or $1.0\ \text{J·K}^{-1}$)