How much energy is required to heat 87.1 g acetone (molar mass = 58.08 g/mol) from a solid at -154.0°C to a liquid at -42.0°C? The following physical data may be useful. ΔH_fus = 7.27 kJ/mol
C_liq = 2.16 J/g°C
C_gas= 1.29 J/g°C
C_sol = 1.65 J/g°C
T_melting= -95.0°C

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Quizplus · Accepted Answer

To calculate the total energy required, we need to consider three phases of heating: solid phase from -154.0°C to -95.0°C (melting point), phase change from solid to liquid at -95.0°C, and liquid phase from -95.0°C to -42.0°C. 1. Heating in solid phase: $q_1 = m \cdot C_{\text{solid}} \cdot \Delta T = 87.1 \, \text{g} \cdot 1.65 \, \text{J/g°C} \cdot ( -95.0 - (-154.0)) \, \text{°C}$2. Phase change (melting): First, calculate moles of acetone $n = \frac{87.1 \, \text{g}}{58.08 \, \text{g/mol}}$. Then, $q_2 = n \cdot \Delta H_{\text{fus}}$3. Heating in liquid phase: $q_3 = m \cdot C_{\text{liquid}} \cdot \Delta T = 87.1 \, \text{g} \cdot 2.16 \, \text{J/g°C} \cdot (-42.0 - (-95.0)) \, \text{°C}$Summing $q_1$, $q_2$, and $q_3$ gives the total energy required. Calculating each part:1. $q_1 = 87.1 \cdot 1.65 \cdot 59 = 8464.635 \, \text{J} = 8.465 \, \text{kJ}$2. $n = \frac{87.1}{58.08} = 1.5 \, \text{mol}$, $q_2 = 1.5 \cdot 7.27 = 10.905 \, \text{kJ}$3. $q_3 = 87.1 \cdot 2.16 \cdot 53 = 9933.48 \, \text{J} = 9.933 \, \text{kJ}$Total energy required = $8.465 \, \text{kJ} + 10.905 \, \text{kJ} + 9.933 \, \text{kJ} = 29.303 \, \text{kJ}$, which rounds to approximately 29.4 kJ.

How Much Energy Is Required to Heat 87