Two liquids, A and B, have vapor pressures at a given...

Two liquids, $\mathrm{A}$ and $\mathrm{B},$ have vapor pressures at a given temperature of 24 $\mathrm{mm} \mathrm{Hg}$ and 36 $\mathrm{mmHg}$ , respectively. We prepare solutions of $\mathrm{A}$ and $\mathrm{B}$ at a given temperature and measure the total pressures above the solutions. We obtain this data:

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a specific temperature. It indicates the tendency of particles to escape from the liquid phase into the gas phase and is a crucial property in describing the volatility of a liquid.

Raoult's Law

Raoult's Law is a principle that states the partial vapor pressure of each component in an ideal solution is directly proportional to its mole fraction in the solution and the vapor pressure of the pure component. This law is fundamental for analyzing how the composition of a solution affects its total vapor pressure.

Partial Pressure

The concept of partial pressure refers to the pressure that a single component of a mixture would exert if it were alone in the container at the same temperature. In the context of vapor-liquid equilibria, the total pressure is the sum of the partial pressures of all components, as described by Dalton's Law.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a given component to the total number of moles in the solution. This concept is essential for applying Raoult's Law in determining the partial contributions to the overall vapor pressure.

Transcript

00:01 So for this question, we want to find the total pressure of a solution that contains vapor a and vapor b.

00:11 Now, vapor a is known to have a pressure of 24 millimeters mercury, and we have solution b, which has a pressure of 36 millimeters mercury.

00:28 So we want to find the total vapor pressure.

00:32 But what is vapor pressure? basically, it is the amount of pressure exerted by a vapor when it's at thermodynamic equilibrium.

00:42 So when they're in a container of a constant volume, pressure, and temperature.

00:50 So you have a chart that tells you the amount of pressure exerted per mole of a and b.

00:59 And we know that in our solution, there are 5 moles of a, and there is one mole of b.

01:13 So in order to get the total vapor pressure, we want to find the ratio of the amount of a and b in this solution.

01:23 So we're going to do this thing called a mole fraction, and we want to find the mole fractions of both of these substances.

01:30 Now, a mole fraction is written as x1, so the first substance, divided by x1 plus x.

01:50 So to find the mole fraction of a, it's going to be xa over xa plus xb.

02:08 And so we know that there are five moles of a, so we're going to write five.

02:12 We're going to just plug in the numbers.

02:14 So we have 5 divided by 5 plus 1.

02:18 And so that's 5 divided by 6.

02:22 And we get 0 .83.

02:29 Solution a or vapor a takes up 83 % or makes up of 83 % of the total vapor pressure.

02:39 And for the mole fraction of b, we're just going to subtract 1...

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