Answer:
Q = 7.7 KJ
Explanation:
The complete question carries the following data:
Specific Heat Capacity of Liquid State = C(l) = 1.45 J/mol.°C
Specific Heat Capacity of Gaseous State = C(g) = 0.65 J/mol.°C
Boiling Temperature = Tb = 88.5°C
Heat of Vaporization = ΔH(vap) = 1.23 KJ/mol
Now, first we calculate the heat required (Q₁) to raise he temperature to boiling point:
Q₁ = n*C(l)*ΔT₁
where,
n = no. of moles = 5.31 mol
ΔT₁ = Temperature difference from 40°C to Tb = 88.5°C - 40°C = 48.5°C
Therefore,
Q₁ = (5.31 mol)(1.45 J/mol.°C)(48.5°C)
Q₁ = 373.4 J = 0.37 KJ
Now, we calculate the heat required (Q₂) to change its phase:
Q₂ = nΔH(vap)
Q₂ = (5.31 mol)(1.23 KJ/mol)
Q₂ = 6.53 KJ
Now, we calculate the heat required (Q₃) to raise he temperature to boiling point:
Q₃ = n*C(g)*ΔT₃
where,
n = no. of moles = 5.31 mol
ΔT₃ = Temperature difference from Tb to 113°C = 113°C - 88.5°C = 24.5°C
Therefore,
Q₃ = (5.31 mol)(0.65 J/mol.°C)(24.5°C)
Q₃ = 84.5 J = 0.08 KJ
So, the total heat required to convert 5.31 mol of this pure substance from a liquid at 40°C to a gas at 113°C is:
Q = Q₁ + Q₂ + Q₃
Q = 0.37 KJ + 6.53 KJ + 0.08 KJ
Q = 7.7 KJ
The total heat required to convert the pure substance from liquid to gas at the given temperature is 814 J.
The given parameters;
The total heat required to convert the pure substance from liquid to gas at the given temperature is calculated as follows;
[tex]Q = nc_l \Delta \theta + nc_g \Delta \theta \\\\ \Delta \theta = (113 - 40) = 73^0 C \\\\Q = (5.31 \ mol \times 1.45 \frac{J}{mol .\ ^0C} \times 73\ ^0C) + (5.31 \ mol \times 0.65 \frac{J}{mol .\ ^0C} \times 73 \ ^0C)\\\\Q = 814 \ J[/tex]
Thus, the total heat required to convert the pure substance from liquid to gas at the given temperature is 814 J.
"Your question is not complete, it seems to be missing the following information;"
How much heat would be required to convert 5.31 mol of a pure substance from a liquid at 40.0°C to a gas at 113.0°C? (molar heat capacity of liquid, C(l) is 1.45 J/mol.⁰C and molar heat capacity of gas, C(g) is 0.65 J/mol.⁰C).
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