At 20◦C the vapor pressure of pure methanol
(CH3OH) is 89.0 torr and of pure water (H2O)
is 17.5 torr. A solution of methanol and water
has a total vapor pressure of 35.5 torr at
20◦C. Calculate the mole fraction of methanol
in this solution. Assume the solution obeys
Raoult’s Law
I missed the first day of class of the new unit due to blood donation and I honestly hardly even know where to start with the question this time. Any help would be appreciated
AY, someone put up an answer for this.
this site sux, no one gives legit answers.
this DrBob222 on this site doesnt do jack. people ask for answers, if ur gonna explain the process u might as well give an answer
every day i come to this site for chem answers, and everytime DrBob222 gives a stupid formula and then leaves.
No problem! I can help you understand how to approach this problem step by step.
To solve this question, we will use Raoult's law, which states that the vapor pressure of a liquid mixture is equal to the sum of the vapor pressures of each component multiplied by their respective mole fractions.
Let's break down the problem:
1. Identify the given information:
- Vapor pressure of pure methanol (CH3OH) = 89.0 torr
- Vapor pressure of pure water (H2O) = 17.5 torr
- Total vapor pressure of the methanol-water solution = 35.5 torr
2. Define the variables:
- Let x represent the mole fraction of methanol in the solution.
3. Apply Raoult's law:
According to Raoult's law, the total vapor pressure (PTotal) of the solution is given by:
PTotal = P1 * X1 + P2 * X2
where P1 and P2 are the vapor pressures of the pure components, and X1 and X2 are their respective mole fractions in the mixture.
In this case, P1 represents the vapor pressure of methanol (89.0 torr), and X1 represents the mole fraction of methanol (x).
P2 represents the vapor pressure of water (17.5 torr), and X2 represents the mole fraction of water (1 - x), since the sum of the mole fractions must be 1.
Plugging in the given values, we have:
35.5 torr = 89.0 torr * x + 17.5 torr * (1 - x)
4. Solve for x:
Simplify the equation using algebra:
35.5 torr = 89.0 torr * x + 17.5 torr - 17.5 torr * x
Combine like terms:
35.5 torr - 17.5 torr = 89.0 torr * x - 17.5 torr * x
18.0 torr = 71.5 torr * x
Divide both sides by 71.5 torr:
x = 18.0 torr / 71.5 torr
x ≈ 0.2521
5. Calculate the mole fraction of methanol:
The mole fraction of methanol (CH3OH) in the solution is approximately 0.2521.
So, the mole fraction of methanol in this solution is approximately 0.2521.