Bromine is sometimes used as a solution in tetrachloro- methane, CCl4. What is the vapor pressure in mm Hg of a solution of 1.50 g of Br2 in 145.0 g of CCl4 at 300 K? The vapor pressure of pure bromine at 300 K is 30.5 kPa, and the vapor pressure of CCl4 is 16.5 kPa.
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Convert the given masses of Br2 and CCl4 to moles using their respective molar masses.
Calculate the mole fraction of CCl4 in the solution. The mole fraction is given by the formula: \( X_{CCl4} = \frac{\text{moles of CCl4}}{\text{moles of CCl4} + \text{moles of Br2}} \).
Use Raoult's Law to find the partial vapor pressure of CCl4 in the solution: \( P_{CCl4} = X_{CCl4} \times P^0_{CCl4} \), where \( P^0_{CCl4} \) is the vapor pressure of pure CCl4.
Calculate the mole fraction of Br2 in the solution using the formula: \( X_{Br2} = \frac{\text{moles of Br2}}{\text{moles of CCl4} + \text{moles of Br2}} \).
Use Raoult's Law to find the partial vapor pressure of Br2 in the solution: \( P_{Br2} = X_{Br2} \times P^0_{Br2} \), where \( P^0_{Br2} \) is the vapor pressure of pure Br2.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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. This principle is essential for calculating the vapor pressure of a solution, as it allows us to determine how the presence of a solute (in this case, bromine) affects the overall vapor pressure of the solvent (CCl4).
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 fractions of bromine and CCl4 is crucial for applying Raoult's Law to find the vapor pressure of the solution.
Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. Understanding the vapor pressures of pure substances (bromine and CCl4) is necessary to determine how the addition of bromine alters the vapor pressure of the CCl4 solution, which is the main goal of the question.
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