Methanol has a normal boiling point of 64.6 °C and a heat of vaporization (∆Hvap) of 35.2 kJ/mol. What is the vapor pressure of methanol at 12.0 °C?

Question

Methanol has a normal boiling point of 64.6 °C and a heat of vaporization (∆H[latex]_{vap}[/latex]) of 35.2 kJ/mol. What is the vapor pressure of methanol at 12.0 °C?

SORT The problem gives you the normal boiling point of methanol (the temperature at which the vapor pressure is 760 mmHg) and the heat of vaporization. You are asked to find the vapor pressure at a specified temperature, which is also given.

GIVEN T[latex]_{1}[/latex](°C) = 64.6 °C
P[latex]_{1}[/latex] = 760 torr
∆H[latex]_{vap}[/latex] = 35.2 kJ/mol
T[latex]_{2}[/latex](°C) = 12.0 °C
FIND P[latex]_{2}[/latex]

STRATEGIZE The conceptual plan is essentially the Clausius–Clapeyron equation, which relates the given and find quantities.

CONCEPTUAL PLAN

ln[latex]\frac{ P_{2}}{P_{1}}=\frac{-ΔH_{vap}}{R}(\frac{1}{T_{2}}-\frac{1}{T_{1}})[/latex]

(Clausius–Clapeyron equation, two-point form)

SOLVE First, convert T[latex]_{1}[/latex] and T[latex]_{2}[/latex] from °C to K.

Accepted Answer

T[latex]_{1}[/latex](K) = T[latex]_{1}[/latex](°C) + 273.15
= 64.6 + 273.15
= 337.8 K
T[latex]_{2}[/latex](K) = T[latex]_{2}[/latex](°C) + 273.15
= 12.0 + 273.15
= 285.2 K

Then, substitute the required values into the Clausius–Clapeyron equation and solve for P[latex]_{2}[/latex].
In order to isolate P[latex]_{2}[/latex], you must take the inverse natural log (or inv ln) of ln(P[latex]_{2}[/latex]/P[latex]_{1}[/latex]). Remember that inv ln (ln x) = x.

ln[latex]\frac{ P_{2}}{P_{1}}=\frac{-ΔH_{vap}}{R}(\frac{1}{T_{2}}-\frac{1}{T_{1}})[/latex]

ln[latex]\frac{ P_{2}}{P_{1}}=\frac{-35.2 imes10^{3}\frac{\cancel{J}}{\cancel{mol}}}{8.314\frac{\cancel{J}}{\cancel{mol}.\cancel{K}}}(\frac{1}{2.85.2\cancel{K}}-\frac{1}{337.8\cancel{K}})[/latex]

= -2.31
[latex]\frac{P_{2}}{P_{1}}= e^{-2.31}[/latex]
P[latex]_{2}= P_{1}(e^{-2.31}[/latex])
= 760 torr10.09932
= 75.4 torr

CHECK The units of the answer are correct. The magnitude of the answer makes sense because vapor pressure should be significantly lower at the lower temperature.

Question 11.5: Methanol has a normal boiling point of 64.6 °C and a heat of...

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