A 'canned heat' product used to warm buffet dishes consists of a homogeneous mixture of ethanol 1C2H5OH2 and paraffin, which has an average formula of C24H50. What mass of C2H5OH should be added to 620 kg of the paraffin to produce 8 torr of ethanol vapor pressure at 35 °C? The vapor pressure of pure ethanol at 35 °C is 100 torr.

Verified step by step guidance

1. Identify the components of the mixture: ethanol (\(C_2H_5OH\)) and paraffin (\(C_{24}H_{50}\)).
2. Use Raoult's Law to relate the vapor pressure of the solution to the mole fraction of ethanol: \(P_{solution} = X_{ethanol} \times P^0_{ethanol}\), where \(P_{solution}\) is the vapor pressure of ethanol in the mixture (8 torr), \(X_{ethanol}\) is the mole fraction of ethanol, and \(P^0_{ethanol}\) is the vapor pressure of pure ethanol (100 torr).
3. Rearrange Raoult's Law to solve for the mole fraction of ethanol: \(X_{ethanol} = \frac{P_{solution}}{P^0_{ethanol}}\).
4. Calculate the moles of paraffin using its molar mass (\(C_{24}H_{50}\)) and the given mass (620 kg).
5. Use the mole fraction equation \(X_{ethanol} = \frac{n_{ethanol}}{n_{ethanol} + n_{paraffin}}\) to solve for the moles of ethanol needed, and then convert this to mass using the molar mass of ethanol.

Key Concepts

Raoult's Law

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent present. In this case, it helps determine how the addition of ethanol affects the overall vapor pressure of the mixture with paraffin. Understanding this law is crucial for calculating the required mass of ethanol to achieve a specific vapor pressure.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components. In this problem, calculating the mole fraction of ethanol in the mixture is essential to apply Raoult's Law and find the mass of ethanol needed to reach the desired vapor pressure.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It is a key concept in understanding how substances behave in mixtures. In this scenario, knowing the vapor pressure of pure ethanol and how it changes when mixed with paraffin is vital for determining how much ethanol is needed to achieve the target vapor pressure of 8 torr.