A lithium salt used in lubricating grease has the formula LiC nH2n + 1O2. The salt is soluble in water to the extent of 0.036 g per 100 g of water at 25 °C. The osmotic pressure of this solution is found to be 57.1 torr. Assuming that molality and molarity in such a dilute solution are the same and that the lithium salt is completely dissociated in the solution, determine an appropriate value of n in the formula for the salt.

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Calculate the molarity of the solution using the osmotic pressure formula: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor, \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.

Convert the osmotic pressure from torr to atm by using the conversion factor: 1 atm = 760 torr.

Assume the van't Hoff factor \( i \) is 2, since the lithium salt dissociates into two ions (Li^+ and C_nH_{2n+1}O_2^-).

Use the given solubility to find the molality of the solution: 0.036 g of salt per 100 g of water. Convert grams of salt to moles using the molar mass of the salt, which is \( 7 + 12n + 2n + 16 \) g/mol.

Set the molarity equal to the molality (since they are assumed to be the same in this dilute solution) and solve for \( n \) using the calculated molarity and the expression for the molar mass.

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 molarity of the solute and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor (number of particles the solute dissociates into), C is the molarity, R is the ideal gas constant, and T is the temperature in Kelvin.

Dissociation of Ionic Compounds

When ionic compounds dissolve in water, they dissociate into their constituent ions. For the lithium salt in the question, it is assumed to completely dissociate into lithium ions (Li⁺) and the corresponding anion. This dissociation affects the colligative properties of the solution, such as osmotic pressure, since the total number of particles in solution increases, impacting calculations involving concentration.

Molality and Molarity

Molality (m) and molarity (M) are both measures of concentration, but they differ in their definitions. Molality is defined as the number of moles of solute per kilogram of solvent, while molarity is defined as the number of moles of solute per liter of solution. In dilute solutions, molality and molarity can be approximated as equal, which simplifies calculations involving osmotic pressure and other colligative properties.

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Carbon disulfide (CS₂) boils at 46.30 °C and has a density of 1.261 g/mL. (a) When 0.250 mol of a nondissociating solute is dissolved in 400.0 mL of CS₂, the solution boils at 47.46 °C. What is the molal boiling-point-elevation constant for CS₂?

Textbook Question

Carbon disulfide (CS₂) boils at 46.30 °C and has a density of 1.261 g/mL. (b) When 5.39 g of a nondissociating unknown is dissolved in 50.0 mL of CS₂, the solution boils at 47.08 °C. What is the molar mass of the unknown?

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