Question

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

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

Step-by-step solution

Convert the temperature to Kelvin#

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

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: \(M = 0.0506\ \frac{\text{mol}}{\text{L}}\)

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 = \(0.0506\ \frac{\text{mol}}{\text{L}} × 0.100\ \text{L} = 0.00506\ \text{mol}\)

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.

Key concepts

Understanding Molar Mass Calculation

The molar mass of a compound is a crucial piece of information when dealing with chemical solutions. It represents the mass of one mole of that compound, expressed in grams per mole (\[\frac{\text{g}}{\text{mol}}\]).To find molar mass, you need the mass of the solute and the number of moles of the solute. Once you've measured the sample mass and determined the moles present in a solution, molar mass is calculated as follows:- **Formula**: Molar mass \(= \frac{\text{mass of solute (g)}}{\text{moles of solute}}\)- This requires knowing the mass in grams and the moles calculated from concentration and volume.To use this information, ensure you have accurate values for both mass and moles to determine the precise molar mass of a solute in any solution.

Dissociation In Solution Explained

In some solutions, compounds dissociate into more than one particle per molecule. This affects the properties of the solution significantly. The term "dissociation" refers to the formation of two or more ions or molecules from a single compound. Dissociation impacts the calculation of properties like osmotic pressure, as it influences the number of particles in the solution. - **Impact**: It alters the effective concentration of solute particles. - **Example**: A compound dissolving into two particles will double the particle count used in osmotic pressure calculations. Understanding how solutes dissociate helps accurately predict and calculate solution behaviors such as boiling point elevation, freezing point depression, and osmotic pressure.

Molarity and Its Role in Solutions

Molarity is a key measurement in chemistry that shows the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution, and is denoted as \(\text{M}\).To find molarity, you use the following formula:- **Formula**: Molarity (\(\text{M}\)) = \(\frac{\text{moles of solute}}{\text{liters of solution}}\)This unit is essential for preparing solutions with precise concentrations for various chemical reactions and experiments. Molarity helps in:

• Predicting how solutions will behave under different conditions
• Determining reactant and product quantities in reactions
• Calculating other solution properties connected to concentration, like osmotic pressure

Grasping the concept of molarity is fundamental to understanding solution composition and its practical applications in scientific studies.