How much heat would be required to convert 234.3 g of solid benzene, C6H6(s), at 5.5 c into benzene vapor, C6H6, at 100 c?

mp of C6H6=5.5c bp of C6H6=80.1 c
mhc C6H6(l)=136J/mol*c
mhc C6H6(g)=81.6J/mol*c
mhfusion at 5.5 c=9.92kJ/mol
mhvaporization at 80.1 c= 30.8kJ/mol

To calculate the amount of heat required to convert solid benzene to benzene vapor, we need to consider the following steps:

1. Calculate the heat required to heat the solid benzene from 5.5°C to its melting point at 80.1°C.
Heat required = mass × specific heat capacity (mp to temp of fusion)
Heat required = 234.3 g × (80.1°C - 5.5°C) × 136 J/mol·°C

2. Calculate the heat required to melt the solid benzene at its melting point.
Heat required = mass × heat of fusion (temp of fusion)
Heat required = 234.3 g × 9.92 kJ/mol

3. Calculate the heat required to heat the liquid benzene from its melting point to its boiling point at 100°C.
Heat required = mass × specific heat capacity (temp of fusion to bp)
Heat required = 234.3 g × (100°C - 80.1°C) × 136 J/mol·°C

4. Calculate the heat required to vaporize the liquid benzene at its boiling point.
Heat required = mass × heat of vaporization (bp)
Heat required = 234.3 g × 30.8 kJ/mol

5. Calculate the total heat required by summing up the above values.
Total heat required = Heat for step 1 + Heat for step 2 + Heat for step 3 + Heat for step 4

Note: The molar mass of C6H6 is 78.11 g/mol.

Let's calculate the values:

1. Heat required to heat solid benzene from 5.5°C to its melting point at 80.1°C:
Heat required = 234.3 g × (80.1°C - 5.5°C) × 136 J/mol·°C

2. Heat required to melt the solid benzene at its melting point:
Heat required = 234.3 g × 9.92 kJ/mol

3. Heat required to heat the liquid benzene from its melting point to its boiling point at 100°C:
Heat required = 234.3 g × (100°C - 80.1°C) × 136 J/mol·°C

4. Heat required to vaporize the liquid benzene at its boiling point:
Heat required = 234.3 g × 30.8 kJ/mol

5. Total heat required:
Total heat required = Heat for step 1 + Heat for step 2 + Heat for step 3 + Heat for step 4

Calculating the values will give you the final answer for the amount of heat required.

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.

Benzene must be melted, heat to boiling point, converted to vapor.

mass bz x heat fusion to melt it.
mass bz x specific heat x delta T to move it to the boiling point.
mass bz x heat vaporization to turn it into vapor.
mass bz x specific heat vapor x delta T to move vapor to 100.
Add the four steps together to obtain the total.