Methanol, CH3OH, a colorless, volatile liquid, was formerly known as wood alcohol. It boils at 65.0C and has a heat of vaporization of 37.4kj/mol. What is its vapor pressure at 39.0C?
Use the Clausius-Clapeyron equation. P at 65.0C = 760 torr. Post your work if you get stuck.
lnP1/P2=3.74X104/8.314(1/312.15-1/338.15)
Not sure what to do from here?
You didn't fill in P1 or P2. I gave you P at 65.0 C = 760 torr.
You have let 65 (338K) = T1 so P1 = 760. Solve for P2.
Remember in this type problem that the vapor pressure of ANYTHING at it's boiling point is the pressure of the atmosphere. So if the pressure on Monday is 700 mm Hg, water will boil when it's vapor pressure is 700 mm Hg (which will be well below 100 C, it's normal boiling point). When it appears the problem didn't give you enough information, this is one you pull out of air. P at normal boiling point is standard pressure which, of course, is 760 torr. Make sure P1 goes with T1 and P2 with T2.
To find the vapor pressure of methanol (CH3OH) at 39.0C, we can use the Clausius-Clapeyron equation. The Clausius-Clapeyron equation relates the vapor pressure of a substance to its boiling point and heat of vaporization.
The equation is as follows:
ln(P2/P1) = (ΔHvap/R) * (1/T1 - 1/T2)
Where:
P1 = initial vapor pressure (at boiling point)
P2 = final vapor pressure (at 39.0C)
ΔHvap = heat of vaporization
R = gas constant (8.314 J/(mol⋅K))
T1 = initial temperature (boiling point in Kelvin)
T2 = final temperature (39.0C in Kelvin)
First, we need to convert the temperatures from Celsius to Kelvin:
T1 = 65.0C + 273.15 = 338.15K
T2 = 39.0C + 273.15 = 312.15K
Now, let's plug the values into the equation:
ln(P2/P1) = (37.4 kJ/mol / (8.314 J/(mol⋅K))) * (1/338.15K - 1/312.15K)
Let's simplify the equation:
ln(P2/P1) = (37.4 kJ/mol / 8.314 J/(mol⋅K)) * (0.000002961 - 0.000003204)
Now, subtract the fractions:
ln(P2/P1) = (37.4 kJ/mol / 8.314 J/(mol⋅K)) * (-0.000000243)
Divide the fraction by -0.000000243:
ln(P2/P1) = -319.61196
To solve for P2/P1, take the exponential of both sides of the equation:
P2/P1 = e^-319.61196
Finally, solve for P2 by multiplying both sides of the equation by P1:
P2 = P1 * e^-319.61196
Since P1 is the vapor pressure at the boiling point (65.0C or 338.15K), you may need to consult a vapor pressure table or use an online resource to find the vapor pressure of methanol at its boiling point. Multiply that value by e^-319.61196 to find the vapor pressure of methanol at 39.0C.