Interpretation:
The freezing point of the given glucose solution is to be calculated.
Concept introduction:
The osmotic pressure (π) of a solution is the product of the molarity, gas constant, and temperature. It is expressed as follows:
Here,
Molality is defined as the ratio of number of moles of the solute to the mass of the solvent (in kilograms). It is expressed as follows:
Here,
The temperature at which change of liquid state to solid state occurs is called freezing point.
The freezing point depression is as follows:
Here,
Density is defined as the ratio of mass to volume. It is expressed as follows:
Here,
Answer to Problem 130AP
Solution:
Explanation of Solution
Given information:
The osmotic pressure is
The density is
The gas constant R is
The osmotic pressure is expressed as follows:
Here,
Rearrange the above equation for the calculation of molarity as follows:
Substitute
The density of the solution is expressed as follows:
Rearrange the above equation for the calculation of mass as follows:
Consider the volume of the solution to be
The mass of
Number of moles is calculated as follows:
Rearrange the above equation for the calculation of mass of glucose as follows:
Substitute,
The mass of the solvent is the difference between the mass of the solution and the mass of the solute. It is calculated as follows:
Substitute,
The molality of the solution is calculated by the expression given below:
Substitute
The freezing point depression is calculated by using the expression given below:
Here,
Substituting the required values:
The freezing point of the glucose solution is
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