Concept explainers
Lysozyme is an enzyme that cleaves bacterial cell walls. A sample of lysozyme extracted from egg white has a molar mass of 13,930 g. A quantity of 0.100 g of this enzyme is dissolved in 150 g of water at
Interpretation:
The vapor pressure lowering, depression in freezing point, elevation in boiling point, and atmospheric pressure of the solution are to be calculated with given molar mass of enzyme.
Concept Introduction:
The property that depends on the concentration of solute molecules and not on the identity of solute is termed as colligative property.
The four colligative properties of solution are vapor-pressure lowering, boiling point elevation, freezing point depression, and osmotic pressure.
Vapor pressure lowering is directly proportional to the mole fraction of the solute.
The pressure exerted by a solvent is equal to the product of that solvent’s mole fraction and the pressure exerted by the pure solvent. It is expressed as
Here,
Freezing point depression occurs when a nonvolatile solute is added to a solvent.
Freezing point depression is calculated by using the expression given below:
Here,
Elevation in boiling point occurs when a nonvolatile solute is added to a pure solvent.
Boiling point elevation is calculated by using the expression given below:
Here,
Osmotic pressure is the pressure that has to be applied to prevent the pure solvent to pass to a solution by osmosis.
The osmotic pressure is calculated by using the expression given below:
Here,
The number of moles is calculated by dividing the given mass of the compound by the molar mass. It is expressed as
Here,
The mole fraction of compound can be calculated as
Answer to Problem 139AP
Solution:
Explanation of Solution
Given information: Molar mass of the enzyme is
Mass of enzyme is
Mass of water is
Temperature is
Vapor pressure of pure water is
Calculate the number of moles of lysozyme by dividing the given mass of enzyme with the molar mass of the enzyme. It is calculated as
Calculate the number of moles of water by dividing the given mass of water with the molar mass of water. It is calculated as
Calculate the mole fraction of lysozyme as
The lowering in vapor pressure is calculated as follows by using the expression given below:
Substitute the values of mole fraction and vapor pressure of water
Freezing point depression is calculated by using the expression given below:
Here,
Substitute the required values
Boiling point elevation is calculated by using the expression given below:
Here,
Substitute the required values
Calculate the osmotic pressure by using the expression given below:
Here,
Assuming the density of solution is
The vapor pressure lowering, depression in freezing point, elevation in boiling point, and atmospheric pressure of the solution are
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Chapter 13 Solutions
Chemistry
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