When 4.33g of a nonelectrolyte solute is dissolved in water to make 205 mL of solution at 21 C, the solution exerts an osmotic pressure of 891 torr.
What is the molar concentration of the solution?
How many moles of solute are in the solution?
What is the molar mass of the solute?
The concepts used to solve this problem are osmotic pressure and molarity.
The osmotic pressure is a colligative property as it is directly proportional to the concentration of solute. The number of moles of solute can be calculated by multiplying the molarity and volume of solution in liters. The molar mass of solute is obtained by dividing the mass of solute by the number of moles of solute.
The osmotic pressure is calculated as:
Here, is the molar concentration of solute, is the universal gas constant which is equal to and is the temperature in Kelvin.
The number of moles of solute is calculated as:
Here, is the molarity in and is the volume of solution in .
The molar mass of solute is calculated as:
Here, is the mass of solute and is the number of moles of solute.
(1)
The osmotic pressure of the solution is
Since,
Therefore,
The temperature is .
Since,
Therefore,
The expression of osmotic pressure is:
On rearranging the above expression,
Substitute for , for and for in the above expression.
The molar concentration of the solution is .
(2)
The volume of the solution is .
Since,
Therefore,
Thus, the volume of solution in liters is .
The number of moles of solute is calculated as:
Substitute for and for .
Thus, the number of moles of nonelectrolyte solute is .
(3)
The mass of nonelectrolyte solute dissolved in water .
The molar mass of solute is calculated as:
Substitute for and for .
Therefore, the molar mass of solute is .
Ans:The molar concentration of the solution is .
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