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.