A solution contains 50.0 g of heptane(C7H16) and 50.0 g of octane(C8H18) at 25 C. The vapor pressures of pure heptane and pure octane at 25 C are 45.8 torr and 10.9 torr, respectively. Assuming ideal behavior, answer each question. a. What is the vapor pressure of each solution component in the mixture? b. What is the total pressure above the solution? c. What is the composition of the vapor in mass percent? d. Why is the composition of the vapor different from the composition of the solution?

Determining molar mass is crucial for many chemistry calculations, including those involving Raoult's Law. Molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). To calculate the molar mass of a compound, you sum the masses of all atoms in its molecular formula. For example, heptane (C7H16) has a molar mass calculated by multiplying the number of carbon atoms (7) by the atomic mass of carbon (approximately 12.01 g/mol), and the number of hydrogen atoms (16) by the atomic mass of hydrogen (approximately 1.008 g/mol) and adding the two products together.

The formula looks like this:
\[ M_{\text{heptane}} = 7(12.01 \text{ g/mol}) + 16(1.008 \text{ g/mol}) = 100.204 \text{ g/mol} \].
Using this approach ensures accurate measurements of substances involved in chemical reactions and is the first step toward understanding the vapor pressures in mixtures.

The 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 particular substance to the total number of moles in the mixture. You calculate it using this formula:
\( X_i = \frac{n_i}{n_{\text{total}}} \)
where \( X_i \) is the mole fraction of substance \( i \), and \( n_i \) is the number of moles of the substance. In the context of our exercise, you would find the mole fraction of heptane and octane in the solution by dividing the moles of each component by the total moles present. Mole fraction is a dimensionless quantity, helping us in determining the partial vapor pressures of each component in a solution.

Partial vapor pressure is the pressure exerted by a single component in a mixture when the substance is in its gaseous form. According to Raoult's Law, the partial pressure of a component in a solution is directly proportional to its mole fraction. This can be represented by the formula:
\( P_i = X_i \cdot P^0_i \)
where \( P_i \) is the partial vapor pressure, \( X_i \) is the mole fraction of the component in the liquid phase, and \( P^0_i \) is the pure component's vapor pressure at the same temperature. This principle is key to understanding how different substances contribute to the total vapor pressure of a solution.

Dalton's Law of Partial Pressures states that the total pressure exerted by a gaseous mixture is the sum of the partial pressures of each individual component in the gas mixture. The formula to express this law is:
\( P_{\text{total}} = P_1 + P_2 + \ldots + P_n \)
where \( P_{\text{total}} \) is the total pressure, and \( P_1, P_2, \ldots, P_n \) are the partial pressures of the components. By understanding Dalton's Law, students can better grasp how to calculate the total vapor pressure above a solution from its individual vapor pressures, which is especially relevant in the given exercise.

The ideal gas law is a fundamental principle in chemistry and physics, providing a clear relationship between pressure, volume, temperature, and the number of moles of a gas. Represented by the equation
\( PV = nRT \)
the law states that the pressure (\( P \)) multiplied by the volume (\( V \)) of an ideal gas equals the number of moles (\( n \)) times the ideal gas constant (\( R \)), times the temperature in Kelvin (\( T \)). In the context of our problem, this law allows us to relate the mass percent composition of a vapor in a mixture to the physical properties of the gas.

Volatility refers to how readily a substance vaporizes. In a solution, substances with higher vapor pressures have greater volatility and will contribute more to the vapor phase. This is why the composition of vapor above a solution often differs from the liquid mixture; the more volatile substance will be overrepresented. Understanding this concept is essential for responding to why the vapor composition differs from the solution's composition, a common question in chemistry exercises that involve mixtures and solutions.