Question

The rubbing alcohol used to clean test tubes is 70% isopropanol, C3H8O, by volume. 100 mL of solution contains 54.95 g of isopropanol and 29.95 g of water. The vapor pressure of water is 20 degrees celsius is .0230 atm and the vapor pressure...?

of isopropanol is .0419 atm. What is the vapor pressure of the solution at 20 degrees celsius? How would the vapor pressure change if the temperature was increased?

Answer 1

The vapour pressure of the solution is 0.0297 atm. The vapour pressure will increase if the temperature increases.

Explanation:

To solve this problem, we use Raoult's Law:

`color(blue)("The partial vapour pressure of a component in a mixture is equal"`
`color(blue)("to the vapour pressure of the pure component multiplied by its")`
`color(blue)("mole fraction in the mixture.")`

In symbols, the partial vapour pressure `p_text(A)` of component A is given by

`color(blue)(bar(ul(|color(white)(a/a)p_text(A) = chi_text(A)p_text(A)^@color(white)(a/a)|)))" "`

where

`chi_text(A) =` the mole fraction of A
`p_text(A)^@ =` the vapour pressure of pure A

If we have two volatile components A and B, the total pressure `p_text(tot)` over the solution is

`p_text(tot) = chi_text(A)p_text(A)^@ + chi_text(B)p_text(B)^@`

Step 1. Calculate the moles of `bb"A"` and `bb"B"`

Let A = isopropyl alcohol (IPA) and B = water. Then

`n_text(A) = 54.95 color(red)(cancel(color(black)("g A"))) × "1 mol A"/(60.09 color(red)(cancel(color(black)("g A")))) = "0.9145 mol A"`

`n_text(B) = 29.95 color(red)(cancel(color(black)("g B"))) × "1 mol B"/(18.02 color(red)(cancel(color(black)("g B")))) = "1.662 mol B"`

Step 2. Calculate the mole fractions of `bb"A"` and `bb"B"`

`chi_text(A) = n_text(A)/(n_text(A) + n_text(B)) = 0.9145/(0.9145 + 1.662) = 0.9145/2.577 = 0.3549`

`chi_text(B) = n_text(B)/(n_text(A) + n_text(B)) = 1.662/2.577 = 0.6451`

Step 2. Calculate the total pressure

`p_text(tot) = "0.3549 × 0.0419 atm + 0.6451 × 0.0230 atm"`

`= "(0.014 87 + 0.014 84) atm = 0.0297 atm"`

In the diagram above, you are at the position of the red dot.