
Concept explainers
(a)
Interpretation:
The molar mass of the fragment is to be calculated.
Concept introduction:
The osmotic pressure is defined as the measure of the tendency of a solution to take in pure solvent via osmosis. It is defined as the minimum pressure that is to be applied to the solution to prevent the inward flow of the pure solvent across the semipermeable membrane. Osmosis occurs when two solutions have different concentrations of solute and are separated by a semipermeable membrane.
The formula to calculate the osmotic pressure of the solution is as follows:
Here,
Molarity is defined as the number of moles of solute that are dissolved in one litre of solution. It is represented by
The formula to calculate the molarity of the solution is as follows:
The conversion factor to convert
(a)

Answer to Problem 13.139P
The molar mass of the fragment is
Explanation of Solution
Rearrange equation (1) to calculate the molarity of the solution as follows:
Substitute
Rearrange equation (2) to calculate the amount of solute as follows:
Substitute
The molar mass of the compound is calculated as follows:
Substitute
The molar mass of the fragment is
(b)
Interpretation:
The depression in freezing point is to be calculated.
Concept introduction:
The freezing point is the temperature at which both the solid and liquid phases coexist in equilibrium. It is the temperature at which the vapor pressure of the substance in the liquid state becomes equal to the vapor pressure in a solid state.
The formula to calculate the change in freezing point is as follows:
Here,
Molality is the measure of the concentration of solute in the solution. It is the amount of solute that is dissolved in one kilogram of the solvent. It is represented by
The formula to calculate the density of the solution is as follows:
(b)

Answer to Problem 13.139P
The freezing point of the solution is
Explanation of Solution
Rearrange equation (7) to calculate the mass of the solution as follows:
Substitute
The formula to calculate the mass of the solution is as follows:
Rearrange equation (9) to calculate the mass of the solvent as follows:
Substitute
The formula to calculate the molality of the solution is as follows:
Substitute
Substitute
But this is the change in freezing point of the solution.
The freezing point of the solution is calculated as follows:
Substitute
The freezing point of the solution is
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Chapter 13 Solutions
Loose Leaf for Chemistry: The Molecular Nature of Matter and Change
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