To determine the amount of heat required to convert solid benzene (C6H6) at 5.5°C into benzene vapor at 100°C, we need to consider the following steps:
1. Calculate the heat required to raise the temperature of solid benzene from its melting point (5.5°C) to the boiling point (80.1°C).
- This can be calculated using the specific heat capacity (mhc) of benzene in its liquid state:
- mhc C6H6(l) = 136 J/mol°C
- First, calculate the heat required to raise the temperature from 5.5°C to the melting point of benzene (80.1°C):
- q1 = m * mhc * (T2 - T1)
- q1 = 234.3 g * (1 mol/78.11 g) * 136 J/mol°C * (80.1°C - 5.5°C)
2. Calculate the heat required for the phase change from solid benzene to liquid benzene.
- This can be calculated using the heat of fusion (mhfusion) of benzene at 5.5°C:
- mhfusion at 5.5°C = 9.92 kJ/mol = 9.92 * 10^3 J/mol
- Calculate the heat required for the phase change from solid to liquid:
- q2 = m * (mhfusion at 5.5°C)
- q2 = 234.3 g * (1 mol/78.11 g) * (9.92 * 10^3 J/mol)
3. Calculate the heat required to raise the temperature of liquid benzene from its boiling point (80.1°C) to the desired final temperature (100°C).
- This can be calculated using the specific heat capacity (mhc) of benzene in its gaseous state:
- mhc C6H6(g) = 81.6 J/mol°C
- Calculate the heat required to raise the temperature from the boiling point to the final temperature:
- q3 = m * (mhc C6H6(g)) * (T_final - T_boiling)
- q3 = 234.3 g * (1 mol/78.11 g) * (81.6 J/mol°C) * (100°C - 80.1°C)
4. Calculate the heat required for the phase change from liquid benzene to benzene vapor.
- This can be calculated using the heat of vaporization (mhvaporization) of benzene at its boiling point (80.1°C):
- mhvaporization at 80.1°C = 30.8 kJ/mol = 30.8 * 10^3 J/mol
- Calculate the heat required for the phase change from liquid to vapor:
- q4 = m * (mhvaporization at 80.1°C)
- q4 = 234.3 g * (1 mol/78.11 g) * (30.8 * 10^3 J/mol)
5. Add up all the calculated heats to get the total heat required:
- total heat = q1 + q2 + q3 + q4
Now, you can substitute the given values into the equations to calculate the specific amounts of heat required at each step and finally find the total heat required to convert the given mass of solid benzene at 5.5°C into benzene vapor at 100°C.