Ch.13 - Properties of Solutions

Brown - Chemistry: The Central Science 14th Edition

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Brown 14th Edition

Ch.13 - Properties of Solutions

Problem 82

Chapter 13, Problem 82

A dilute aqueous solution of an organic compound soluble in water is formed by dissolving 2.35 g of the compound in water to form 0.250 L of solution. The resulting solution has an osmotic pressure of 0.605 atm at 25 °C. Assuming that the organic compound is a nonelectrolyte, what is its molar mass?

Verified step by step guidance

Step 1: Understand the problem. We are given the mass of the solute, the volume of the solution, and the osmotic pressure. We are asked to find the molar mass of the solute. The formula for osmotic pressure is: \(\Pi = n/V * R * T\), where \(\Pi\) is the osmotic pressure, n is the number of moles of solute, V is the volume of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

Step 2: Convert the temperature from Celsius to Kelvin. The formula to convert Celsius to Kelvin is: \(K = °C + 273.15\).

Step 3: Rearrange the osmotic pressure formula to solve for n, the number of moles of solute: \(n = \Pi * V / (R * T)\).

Step 4: Calculate the number of moles of solute using the values given in the problem for osmotic pressure, volume, the ideal gas constant (0.0821 L*atm/K*mol), and the temperature in Kelvin.

Step 5: Calculate the molar mass of the solute. The formula for molar mass is: \(Molar Mass = mass of solute (g) / number of moles\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the concentration of solute particles in the solution and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor (which is 1 for nonelectrolytes), C is the molarity of the solution, R is the ideal gas constant, and T is the temperature in Kelvin.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is expressed in moles per liter (mol/L). To find the molarity of a solution, you can use the formula M = n/V, where n is the number of moles of solute and V is the volume of the solution in liters. This concept is essential for calculating the molar mass of the solute from the osmotic pressure.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It can be calculated by dividing the mass of the solute by the number of moles present in the solution. In this context, once the molarity is determined from the osmotic pressure, the molar mass can be derived by rearranging the formula to find the number of moles and using the mass of the solute provided.

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Textbook Question

The osmotic pressure of a 0.010 M aqueous solution of CaCl₂ is found to be 0.674 atm at 25 °C. Calculate the van't Hoff factor, i, for the solution.

Lysozyme is an enzyme that breaks bacterial cell walls. A solution containing 0.150 g of this enzyme in 210 mL of solution has an osmotic pressure of 0.953 torr at 25 °C. What is the molar mass of lysozyme?

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Textbook Question

Adrenaline is the hormone that triggers the release of extra glucose molecules in times of stress or emergency. A solution of 0.64 g of adrenaline in 36.0 g of CCl₄ elevates the boiling point by 0.49 °C. Calculate the approximate molar mass of adrenaline from this data.

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Textbook Question

Lauryl alcohol is obtained from coconut oil and is used to make detergents. A solution of 5.00 g of lauryl alcohol in 0.100 kg of benzene freezes at 4.1 °C. What is the molar mass of lauryl alcohol from this data?

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