An aqueous CaCl, solution has a vapor pressure of 81.6 mmHg at 50^∘ C . The vapor pressure of pu

step 1 Here we have the problem 98. In this question, we're going to calculate the concentration of cal

An aqueous CaCl, solution has a vapor pressure of 81.6 mmHg...

An aqueous CaCl, solution has a vapor pressure of 81.6 $\mathrm{mmHg}$ at $50^{\circ} \mathrm{C}$ . The vapor pressure of pure water at this temperature is 92.6 $\mathrm{mmHg.}$ What is the concentration of $\mathrm{CaCl}_{2}$ in mass percent? (Assume complete dissociation of the solute.)

Key Concepts

Complete Dissociation

Complete dissociation refers to the process by which an ionic compound splits into its constituent ions in solution. In the context of the problem, CaCl2 dissociates into three ions (one Ca²? and two Cl?), significantly increasing the total number of particles and thereby amplifying the colligative effect on vapor pressure.

Mole Fraction

The mole fraction is the ratio of the number of moles of one component in a mixture to the total number of moles of all components. It is a fundamental concept in solution chemistry and is essential for applying Raoult's Law to determine how solute particles affect the vapor pressure of the solvent.

Mass Percent Concentration

Mass percent concentration is a measure of the concentration of a component in a solution expressed as the mass of the component divided by the total mass of the solution, multiplied by 100. This concept is used to quantify the composition of a solution in terms of the solute's mass, which is particularly useful in practical and laboratory settings.

Raoult's Law

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to its mole fraction. This principle is used to relate the decrease in vapor pressure to the amount of solute dissolved in the solvent, making it a key concept for solving problems involving vapor pressure lowering in solutions.

Colligative Properties

Colligative properties are properties of solutions that depend only on the number of solute particles present, not their identity. Vapor pressure lowering is one such property, and it allows us to calculate solute concentration from changes in vapor pressure, especially in cases where the solute dissociates into multiple particles.

Transcript

00:01 Here we have the problem 98.

00:02 In this question, we're going to calculate the concentration of calcium chloride in mass percent.

00:09 So at 50 degree, the pure water has a vapor pressure equal to 92 .6.

00:25 And the calcium chloride solution has a vapor pressure equal to 81 .6.

00:37 So now we need to calculate the mole fraction of the solvent water, from the following equation p solution is equal to more fraction of the solvent times p zero of the solvent p solution is the vapor pressure of the solution and p zero solution solvent is the vapor pressure of the pure water so rearrange the equation and find the more fraction of the solvent is equal to p solution divided by p0 of the solvent.

01:31 This is equal to 81 .6 divided by 92 .6.

01:43 And this will give us equal to 0 .881.

01:48 So this is the more fraction of the solvent.

01:51 So we know that the more fraction of solvent, we can calculate the more fraction of the solvent.

01:57 Is equal to 1 minus the mole fraction of the solvent, 1 minus 0 .881 is equal to 0 .119.

02:13 So assume a sample of 100 moles of solution.

02:29 The calcium chloride dissociate completely given one mole of calcium ion and 2 modes of chloride ion.

02:36 So the value of vanhoff factor is equal to 3.

02:47 So the mole fraction of chloride would be one -third of that of the solute.

02:55 So the moles of solute is equal to one -third times 0 .119 times 100 moles.

03:13 This is equal to 3 .97 moles.

03:19 And the moles of solvent will be 100...

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