From data below, calculate the total heat (J) needed to convert 0.298 mol of gaseous ethanol (C2H6O) at 401°C and 1 atm to liquid ethanol at 25.0°C and 1 atm.
To calculate the total heat needed to convert the given amount of gaseous ethanol to liquid ethanol, we need to consider the heat required for two steps: (1) heating the gaseous ethanol to its boiling point and (2) condensing the gaseous ethanol to liquid ethanol.
Step 1: Heating the gaseous ethanol to its boiling point (401°C)
To calculate the heat required to raise the temperature of the gaseous ethanol from its initial temperature to its boiling point, we'll use the formula:
q1 = n * C * deltaT
where:
q1 = heat required (Joules)
n = number of moles of ethanol (0.298 mol, as given in the question)
C = molar heat capacity of ethanol at constant pressure (calculated as the sum of the heat capacities for each element in the compound; in this case, 2.16 J/(mol°C) for C2H6O)
deltaT = change in temperature (401°C - initial temperature, in °C)
Substituting the values into the formula, we get:
q1 = 0.298 mol * 2.16 J/(mol°C) * (401°C - initial temperature)
Step 2: Condensing the gaseous ethanol to liquid ethanol at its boiling point (25.0°C)
To calculate the heat required for condensing the gaseous ethanol at its boiling point, we'll use the formula:
q2 = n * deltaHvap
where:
q2 = heat required for condensation (Joules)
n = number of moles of ethanol (0.298 mol, as given in the question)
deltaHvap = molar enthalpy of vaporization of ethanol (-38.6 kJ/mol, which is equivalent to -38.6 * 10^3 J/mol)
Substituting the values into the formula, we get:
q2 = 0.298 mol * (-38.6 * 10^3 J/mol)
Finally, the total heat required (q_total) to convert the gaseous ethanol to liquid ethanol is the sum of q1 and q2:
q_total = q1 + q2
Note: It's important to convert all the units to the same system (e.g., Joules and Kelvin) before performing the calculations.