What amount of heat (in kJ) is required to convert 10.7 g of an unknown liquid (MM = 83.21 g/mol) at 19.2 °C to a gas at 93.5 °C? (specific heat capacity of liquid = 1.58 J/g•°C; specific heat capacity
What amount of heat (in kJ) is required to convert 10.7 g of an unknown liquid (MM = 83.21 g/mol) at 19.2 °C to a gas at 93.5 °C? (specific heat capacity of liquid = 1.58 J/g•°C; specific heat capacity
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![### Heat Calculation for Phase Transition of an Unknown Liquid
**Problem Statement:**
Determine the amount of heat (in kJ) required to convert 10.7 g of an unknown liquid (Molar Mass = 83.21 g/mol) at 19.2 °C to a gas at 93.5 °C. The following data is provided:
- Specific heat capacity of the liquid: 1.58 J/g·°C
- Specific heat capacity of the gas: 0.932 J/g·°C
- Enthalpy of vaporization (ΔHvap): 22.5 kJ/mol
- Normal boiling point (Tb): 57.3 °C
**Calculation:**
To find the total heat required for this process, we must consider three steps:
1. Heating the liquid from its initial temperature to its boiling point.
2. Vaporizing the liquid at its boiling point.
3. Heating the vapor from the boiling point to the final temperature.
### Step 1: Heating the Liquid
\[ q_1 = mass \times C_{liquid} \times \Delta T_1 \]
Where:
- \( mass = 10.7 \, g \)
- \( C_{liquid} = 1.58 \, J/g·°C \)
- \( \Delta T_1 = Tb - T_{initial} = 57.3 - 19.2 = 38.1 \, °C \)
\[ q_1 = 10.7 \, g \times 1.58 \, J/g·°C \times 38.1 \, °C = 643.206 \, J = 0.643206 \, kJ \]
### Step 2: Vaporizing the Liquid
\[ q_2 = n \times \Delta Hvap \]
Where:
- \( n = \frac{10.7 \, g}{83.21 \, g/mol} \approx 0.1286 \, mol \)
- \( \Delta Hvap = 22.5 \, kJ/mol \)
\[ q_2 = 0.1286 \, mol \times 22.5 \, kJ/mol = 2.8935 \, kJ \]
### Step 3: Heating the Vapor
\[ q_3 = mass \times C_{gas} \times \Delta T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2d924445-39e4-4bb2-9286-0ab6470dbf21%2Fa4caf052-286d-4fa6-bd25-3b904328cdee%2Fnfdyya_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Heat Calculation for Phase Transition of an Unknown Liquid
**Problem Statement:**
Determine the amount of heat (in kJ) required to convert 10.7 g of an unknown liquid (Molar Mass = 83.21 g/mol) at 19.2 °C to a gas at 93.5 °C. The following data is provided:
- Specific heat capacity of the liquid: 1.58 J/g·°C
- Specific heat capacity of the gas: 0.932 J/g·°C
- Enthalpy of vaporization (ΔHvap): 22.5 kJ/mol
- Normal boiling point (Tb): 57.3 °C
**Calculation:**
To find the total heat required for this process, we must consider three steps:
1. Heating the liquid from its initial temperature to its boiling point.
2. Vaporizing the liquid at its boiling point.
3. Heating the vapor from the boiling point to the final temperature.
### Step 1: Heating the Liquid
\[ q_1 = mass \times C_{liquid} \times \Delta T_1 \]
Where:
- \( mass = 10.7 \, g \)
- \( C_{liquid} = 1.58 \, J/g·°C \)
- \( \Delta T_1 = Tb - T_{initial} = 57.3 - 19.2 = 38.1 \, °C \)
\[ q_1 = 10.7 \, g \times 1.58 \, J/g·°C \times 38.1 \, °C = 643.206 \, J = 0.643206 \, kJ \]
### Step 2: Vaporizing the Liquid
\[ q_2 = n \times \Delta Hvap \]
Where:
- \( n = \frac{10.7 \, g}{83.21 \, g/mol} \approx 0.1286 \, mol \)
- \( \Delta Hvap = 22.5 \, kJ/mol \)
\[ q_2 = 0.1286 \, mol \times 22.5 \, kJ/mol = 2.8935 \, kJ \]
### Step 3: Heating the Vapor
\[ q_3 = mass \times C_{gas} \times \Delta T
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