Household bleach is a 5.0 mass % aqueous solution of sodium hypochlorite, NaOCl, with a density of 1.08 g/mL. The molar mass of NaOCl is 74.44 g/mol. a. Calculate the molality of bleach: b. Calculate the molarity of bleach: c. What is the boiling point of bleach? Given Kb = 0.51 °C kg/mol, Kf = 1.86 °C kg/mol.
The Correct Answer and Explanation is:
To solve the problem step by step, let’s first extract the given information:
- Mass percent of NaOCl = 5.0%
- Density of solution = 1.08 g/mL
- Molar mass of NaOCl = 74.44 g/mol
- Kb = 0.51 °C kg/mol
- Kf = 1.86 °C kg/mol
Let’s assume we have 1000 g of solution to simplify calculations.
a. Molality (mol/kg solvent)
5.0% mass means 5.0 g of NaOCl in 100 g of solution. For 1000 g of solution:
- Mass of NaOCl = 5.0% of 1000 g = 50.0 g
- Mass of water (solvent) = 1000 g – 50.0 g = 950.0 g = 0.950 kg
Moles of NaOCl = 50.0 g / 74.44 g/mol = 0.6716 mol
Molality = moles of solute / kg of solvent = 0.6716 mol / 0.950 kg = 0.707 mol/kg
b. Molarity (mol/L solution)
Total mass = 1000 g
Volume = mass / density = 1000 g / 1.08 g/mL = 925.93 mL = 0.92593 L
Moles of NaOCl = 0.6716 mol (as before)
Molarity = moles of solute / L of solution = 0.6716 mol / 0.92593 L = 0.725 mol/L
c. Boiling point elevation
ΔTb = Kb × molality = 0.51 °C·kg/mol × 0.707 mol/kg = 0.3606 °C
Normal boiling point of water = 100.00 °C
Boiling point of bleach = 100.00 + 0.3606 = 100.36 °C
Explanation
Household bleach is commonly used as a disinfectant and cleaner. It typically contains sodium hypochlorite dissolved in water. Understanding its concentration is important both for safe use and for chemical calculations. We began by analyzing a bleach solution that is 5.0 percent sodium hypochlorite by mass with a given density of 1.08 g/mL. This allows us to calculate important concentration units like molality and molarity, as well as physical properties such as boiling point.
To calculate molality, we assume a fixed amount of total solution—1000 grams in this case. Since 5 percent of it is sodium hypochlorite, we find there are 50 grams of solute. The mass of water, the solvent, is then 950 grams. Using the molar mass of sodium hypochlorite, we convert the mass into moles. Dividing by the mass of the solvent in kilograms gives us the molality: 0.707 mol/kg.
For molarity, we need the volume of the solution. Knowing the mass and density, we calculate the volume in liters. Using the moles of sodium hypochlorite from earlier and dividing by this volume gives a molarity of 0.725 mol/L.
Finally, to find the boiling point, we apply the boiling point elevation formula. It states that the boiling point increases based on the molality and the ebullioscopic constant (Kb) for the solvent, which in this case is water. Multiplying molality by Kb gives the temperature increase above the normal boiling point. Adding this to 100 degrees Celsius results in a final boiling point of approximately 100.36 °C.
This step-by-step approach illustrates the usefulness of basic chemical principles in understanding everyday products.
