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Chapter 11: Problem 96

A 0.500 -g sample of a compound is dissolved in enough water to form 100.0 mL of solution. This solution has an osmotic pressure of 2.50 atm at $25^{\circ} \mathrm{C}$ . If each molecule of the solute dissociates into two particles (in this solvent), what is the molar mass of this solute?

Short Answer

Expert verified
The molar mass of the solute is approximately 98.82 g/mol.

Step by step solution

01

Convert the temperature to Kelvin#

To convert the temperature from Celsius to Kelvin, add 273.15 to the given temperature in Celsius. \(T_K = 25 + 273.15 = 298.15 K\)
02

Calculate the molarity (M) using the osmotic pressure formula#

Rearrange the osmotic pressure formula to solve for M: \(M = \frac{Π}{R T i}\) Substitute the given values into the formula: \(M = \frac{2.50 \ \text{atm}}{(0.0821 \ \frac{\text{L}\ \text{atm}}{\text{mol}\ \text{K}})(298.15\ \text{K})(2)}\) Calculate the molarity: \(M = 0.0506\ \frac{\text{mol}}{\text{L}}\)
03

Calculate the moles of solute#

Since we know the molarity and the volume of the solution, we can find the moles of solute using the formula: Moles of solute = Molarity × Volume of solution Convert the volume of the solution to liters: \(100.0\ \text{mL} = 0.100\ \text{L}\) Calculate the moles of solute: Moles of solute = \(0.0506\ \frac{\text{mol}}{\text{L}} × 0.100\ \text{L} = 0.00506\ \text{mol}\)
04

Calculate the molar mass of the solute#

Finally, use the moles of solute and the mass of the sample to find the molar mass of the solute using the formula: Molar mass = \(\frac{\text{mass of the solute}}{\text{moles of solute}}\) Calculate the molar mass: Molar mass = \(\frac{0.500\ \text{g}}{0.00506\ \text{mol}} = 98.82\ \frac{\text{g}}{\text{mol}}\) Thus, the molar mass of the solute is approximately 98.82 g/mol.

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Most popular questions from this chapter

The weak electrolyte \(\mathrm{NH}_{3}(g)\) does not obey Henry's law. Why? \(\mathrm{O}_{2}(g)\) obeys Henry's law in water but not in blood (an aqueous solution). Why?

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