What is the composition of a methanol () – propanol () solution that has a vapor pressure of 121 torr at 40°C? At 40°C, the vapor pressures of pure methanol and pure propanol are 303 and 44.6 torr, respectively. Assume the solution is ideal.

Mole fraction of methanol =

Mole fraction of propanol =

why are you posting all these under different names? Do you think we are stupid?

We will be happy to critique your work. Keep the same name, so we can figure out exactly what you are having difficulty with.

To find the mole fraction of methanol and propanol in the solution, we can first use Raoult's law, which states that the vapor pressure of a component in a solution is directly proportional to its mole fraction.

Let's denote the mole fraction of methanol as x and the mole fraction of propanol as y.

According to Raoult's law, the vapor pressure of the solution can be expressed as the sum of the individual vapor pressures of methanol and propanol multiplied by their respective mole fractions:

P_solution = P_methanol * x + P_propanol * y

Given:
P_solution = 121 torr
P_methanol = 303 torr
P_propanol = 44.6 torr

Substituting the values into the equation, we can solve for x and y:

121 torr = 303 torr * x + 44.6 torr * y

Since we want to find the mole fractions, we need to normalize the equation by dividing both sides by the total pressure:

121 torr / (303 torr + 44.6 torr) = (303 torr * x + 44.6 torr * y) / (303 torr + 44.6 torr)

Simplifying the equation further:

0.3539 = 0.8507x + 0.1249y

Now, we need an additional equation to solve for x and y. Since the sum of mole fractions must be equal to 1, we have:

x + y = 1

Now we have a system of two equations:

0.3539 = 0.8507x + 0.1249y
x + y = 1

We can solve this system of equations using substitution or elimination method. Let's solve it using substitution:

Rearranging the second equation:
y = 1 - x

Substituting this into the first equation:

0.3539 = 0.8507x + 0.1249(1 - x)
0.3539 = 0.8507x + 0.1249 - 0.1249x
0.3539 - 0.1249 = 0.8507x - 0.1249x
0.229 = 0.7258x

Dividing both sides by 0.7258:
x = 0.229 / 0.7258
x = 0.3157

Now, substitute this value back into the equation for y:

y = 1 - x
y = 1 - 0.3157
y = 0.6843

Therefore, the mole fraction of methanol is approximately 0.3157, and the mole fraction of propanol is approximately 0.6843.

To find the mole fraction of methanol and propanol in the solution, we need to use Raoult's Law. According to Raoult's Law, the vapor pressure of a component in a solution is equal to the mole fraction of that component multiplied by its vapor pressure in the pure state.

Let's calculate the mole fraction of methanol first. We know that the vapor pressure of methanol in the solution is 121 torr and the vapor pressure of pure methanol at the same temperature is 303 torr.

Using Raoult's Law:

P_methanol_solution = X_methanol * P_methanol_pure

Solving for X_methanol:
X_methanol = P_methanol_solution / P_methanol_pure

Substituting the given values:
X_methanol = 121 torr / 303 torr

Now, let's calculate the mole fraction of propanol. We know that the vapor pressure of propanol in the solution is 121 torr and the vapor pressure of pure propanol at the same temperature is 44.6 torr.

Using Raoult's Law:

P_propanol_solution = X_propanol * P_propanol_pure

Solving for X_propanol:
X_propanol = P_propanol_solution / P_propanol_pure

Substituting the given values:
X_propanol = 121 torr / 44.6 torr

Therefore, the mole fraction of methanol in the solution is 0.399 (or 39.9%) and the mole fraction of propanol is 2.717 (or 27.17%).