From data below, calculate the total heat (J) needed to convert 0.172 mol of gaseous ethanol (C2H6O) at 451° C and 1 atm to liquid ethanol at 25.0° C and 1 atm.
Boiling point at 1 atm 78.5°C
cgas 1.43 J/g · °C
cliquid 2.45 J/g · °C
ΔH°vap 40.5 kJ/mol
When no phase change is involved, use this equation.
q = mass x specific heat x (Tfinal-Tinitial).
When a phase change is involved (at the melting point or boiling point) use this one.
q = mass x heat fusion or heat vap
Total q = sum of individual qs.
To calculate the total heat (J) needed to convert the given amount of gaseous ethanol to liquid ethanol, we need to consider the following steps:
Step 1: Calculate the heat required to cool the gaseous ethanol from 451°C to its boiling point, using the specific heat of the gas (cgas).
Step 2: Calculate the heat required to convert the gaseous ethanol at its boiling point to liquid ethanol at the same temperature, using the molar enthalpy of vaporization (ΔH°vap).
Step 3: Calculate the heat required to cool the liquid ethanol from its boiling point to 25.0°C, using the specific heat of the liquid (cliquid).
Let's calculate step by step:
Step 1:
We need to calculate the heat required to cool the gaseous ethanol from 451°C to its boiling point, 78.5°C.
ΔT1 = 451°C - 78.5°C = 372.5°C
Mass of ethanol (g): We know that there are 0.172 moles of ethanol present. To calculate the mass, we need to multiply the number of moles by the molar mass.
Molar mass of C2H6O = (2 * 12.01 g/mol) + (6 * 1.01 g/mol) + (1 * 16.00 g/mol) = 46.08 g/mol
Mass = 0.172 mol * 46.08 g/mol = 7.92 g
Now, we can calculate the heat using the specific heat of the gas (cgas):
Heat1 = Mass * cgas * ΔT1
Step 2:
Next, we need to calculate the heat required to convert the gaseous ethanol at its boiling point to liquid ethanol at the same temperature.
The heat of vaporization (ΔH°vap) is given in kJ/mol. To calculate the heat required, we need to multiply it by the number of moles.
Heat2 = ΔH°vap * 0.172 mol
Since ΔH°vap is given in kJ/mol, we need to convert it to J/mol by multiplying it by 1000:
Heat2 = (40.5 kJ/mol) * (1000 J/kJ) * 0.172 mol
Step 3:
Lastly, we need to calculate the heat required to cool the liquid ethanol from its boiling point to 25.0°C.
ΔT3 = 78.5°C - 25.0°C = 53.5°C
Mass of ethanol (g) remains the same as in Step 1, which is 7.92 g.
Now, we can calculate the heat using the specific heat of the liquid (cliquid):
Heat3 = Mass * cliquid * ΔT3
Finally, we can calculate the total heat required by adding up the values from Step 1, Step 2, and Step 3:
Total heat (J) = Heat1 + Heat2 + Heat3
Calculate the values using the given data and plug them into the equations to find the total heat required.