Questions: Concentrated hydrochloric acid (HCl) is 11.65 M with a density of 1.18 g / mL. What is the concentration of this solution in molality? Hint: One gram of the solution contains 0.64 g water.

Solution Steps

• Use the density of the solution to find the mass of 1 liter of solution.
• Given: Density = \(1.18 \, \text{g/mL}\).
• Convert 1 liter to milliliters: \(1000 \, \text{mL}\).
• Calculate mass: \(1000 \, \text{mL} \times 1.18 \, \text{g/mL} = 1180 \, \text{g}\).

• Use the hint that 1 gram of solution contains 0.64 grams of water.
• Calculate the mass of water in 1180 grams of solution: \[ 1180 \, \text{g} \times 0.64 = 755.2 \, \text{g of water} \]

• Molarity (\(M\)) is given as \(11.65 \, \text{mol/L}\).
• Calculate moles of HCl in 1 liter of solution: \(11.65 \, \text{mol}\).
• Convert the mass of water to kilograms: \[ 755.2 \, \text{g} = 0.7552 \, \text{kg} \]
• Calculate molality (\(m\)) using the formula: \[ m = \frac{\text{moles of solute}}{\text{kilograms of solvent}} = \frac{11.65 \, \text{mol}}{0.7552 \, \text{kg}} \]

Final Answer