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

Two liquids, $A$ and $B$, have vapor pressures at a given temperature of $24 \mathrm{mmHg}$ 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: $$ \begin{aligned} &\begin{array}{cccc} \text { Solution } & \text { Amt A (mol) } & \text { Amt B (mol) } & \text { P (mmHg) } \\ \hline 1 & 1 & 1 & 30 \\ \hline 2 & 2 & 1 & 28 \\ \hline 3 & 1 & 2 & 32 \\ \hline 4 & 1 & 3 & 33 \\ \hline \end{array}\\ &\text { Predict the total pressure above a solution of } 5 \mathrm{~mol} \mathrm{~A} \text { and } 1 \mathrm{~mol} \mathrm{~B} \text { . } \end{aligned} $$

Two liquids, $A$ and $B$, have vapor pressures at a given temperature of $24 \mathrm{mmHg}$ 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:
$$
\begin{aligned}
&\begin{array}{cccc}
\text { Solution } & \text { Amt A (mol) } & \text { Amt B (mol) } & \text { P (mmHg) } \\
\hline 1 & 1 & 1 & 30 \\
\hline 2 & 2 & 1 & 28 \\
\hline 3 & 1 & 2 & 32 \\
\hline 4 & 1 & 3 & 33 \\
\hline
\end{array}\\
&\text { Predict the total pressure above a solution of } 5 \mathrm{~mol} \mathrm{~A} \text { and } 1 \mathrm{~mol} \mathrm{~B} \text { . }
\end{aligned}
$$

Key Concepts

Raoult's Law

Raoult's Law states that in an ideal solution, the vapor pressure of each component is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. This relationship allows one to predict the total vapor pressure of a mixture by summing the contributions from each component according to their respective mole fractions.

Mole Fraction

The mole fraction is a way to express the composition of a solution, defined as the number of moles of a component divided by the total number of moles in the solution. It is a key variable in applying Raoult's Law, as it directly scales the contribution of each pure component's vapor pressure to the overall vapor pressure of the solution.

Ideal Solutions

An ideal solution is one in which the interactions between unlike molecules are similar to those between like molecules, resulting in behavior that can be accurately described by Raoult's Law. This concept simplifies the calculation of properties such as vapor pressure since deviations from ideality, often due to strong intermolecular forces, are negligible.

Partial Pressure

Partial pressure refers to the pressure exerted by each individual component in a mixture when it behaves independently according to its concentration. In the context of vapor pressures, each component’s partial pressure is determined by multiplying its mole fraction by its pure component vapor pressure, and the total vapor pressure is the sum of these partial pressures.

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