To calculate the heat required to turn solid phenol at 25°C and pressure of 1 atm to vapor at 300°C at 3 atm.
Understand the Problem
The question is asking us to determine the total heat needed to convert phenol from a solid state at a specific temperature and pressure to a vapor state at a higher temperature and pressure. This involves calculating the heat required for melting (fusion), heating the liquid, and then vaporizing it.
Answer
The total heat required for this process can be calculated using the formulas for fusion, heating, and vaporization, summed together.
Answer for screen readers
The total heat required, $Q_{\text{total}}$, is the sum of the heats for melting, heating, and vaporization based on the calculations performed using the relevant properties of phenol.
Steps to Solve
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Identify the phases and temperatures involved
We'll be transitioning from solid phenol at its melting point (fusion) to liquid, then heating the liquid, and finally vaporizing it to gas. We need the specific heat capacities and the heat of fusion/vaporization. -
Calculate the heat required for melting
Use the formula: $$ q_{\text{fusion}} = m \cdot \Delta H_f $$
where $m$ is the mass of phenol and $\Delta H_f$ is the heat of fusion for phenol. -
Calculate the heat needed to heat the liquid
Use the formula: $$ q_{\text{heating}} = m \cdot C_p \cdot \Delta T $$
where $C_p$ is the specific heat capacity of liquid phenol, and $\Delta T$ is the change in temperature from the melting point to the boiling point. -
Calculate the heat required for vaporization
Use the formula: $$ q_{\text{vaporization}} = m \cdot \Delta H_v $$
where $\Delta H_v$ is the heat of vaporization for phenol. -
Sum the heat quantities
Finally, the total heat required is: $$ Q_{\text{total}} = q_{\text{fusion}} + q_{\text{heating}} + q_{\text{vaporization}} $$
The total heat required, $Q_{\text{total}}$, is the sum of the heats for melting, heating, and vaporization based on the calculations performed using the relevant properties of phenol.
More Information
Phenol has specific transition temperatures and heats associated with its phase changes. This process, involving fusion and vaporization, is common in thermodynamic calculations.
Tips
- Forgetting to convert units consistently (e.g., grams to kilograms).
- Not accounting for the specific state change temperatures (melting and boiling points) accurately.
- Mixing up the heat of fusion and heat of vaporization values.
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