A \(1.37-M\) solution of citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) in water has a density of \(1.10 \mathrm{~g} / \mathrm{cm}^{3}\). Calculate the mass percent, molality, mole fraction, and normality of the citric acid. Citric acid has three acidic protons.

The density of the solution is given as 1.10 g/cm³, so the mass of one liter of solution can be calculated as follows: Mass of 1 L solution = Density × Volume Mass of 1 L solution = 1.10 g/cm³ × 1000 cm³ = 1100 g Since the solution is a 1.37-M solution, we can find the mass of citric acid in one liter of solution by multiplying the molarity by the molar mass of citric acid and the volume: Molar mass of citric acid (H3C6H5O7) = 3(1.01) + 6(12.01) + 5(1.01) + 7(16.00) = 192.12 g/mol Mass of citric acid = Molarity × Molar mass of citric acid × Volume Mass of citric acid = 1.37 mol/L × 192.12 g/mol × 1 L = 263.2 g Now, we can find the mass of water in the solution: Mass of water = Mass of 1 L solution - Mass of citric acid Mass of water = 1100 g - 263.2 g = 836.8 g

The mass percent of citric acid in the solution can be calculated as follows: Mass percent of citric acid = (Mass of citric acid / Mass of 1 L solution) × 100% Mass percent of citric acid = (263.2 g / 1100 g) × 100% = 23.93 %

Molality is the number of moles of solute per kilogram of solvent. We already calculated the mass of citric acid and mass of water, so we can find the molality as follows: Molality of citric acid = Moles of citric acid / Mass of water (in kg) Molality of citric acid = (1.37 mol) / (0.8368 kg) = 1.636 mol/kg

To calculate the mole fraction of citric acid, we first need to find the moles of water. We can then use the moles of citric acid and water to find the mole fraction: Moles of water = Mass of water / Molar mass of water Moles of water = 836.8 g / 18.02 g/mol = 46.42 mol Mole fraction of citric acid = Moles of citric acid / (Moles of citric acid + Moles of water) Mole fraction of citric acid = 1.37 / (1.37 + 46.42) = 0.0286

Normality is the number of gram-equivalent masses of solute per liter of solution. Since citric acid has three acidic protons, the equivalent mass is one-third of the molar mass: Equivalent mass of citric acid = Molar mass of citric acid / 3 Equivalent mass of citric acid = 192.12 g/mol / 3 = 64.04 g/mol Normality is equal to molarity multiplied by the number of acidic protons: Normality of citric acid = Molarity × Number of acidic protons Normality of citric acid = 1.37 mol/L × 3 = 4.11 N In summary, the properties of the citric acid solution are: 1. Mass percent: 23.93% 2. Molality: 1.636 mol/kg 3. Mole fraction: 0.0286 4. Normality: 4.11 N