Question

Commercial concentrated aqueous ammonia is \(28 \% \mathrm{NH}_{3}\) by mass and has a density of \(0.90 \mathrm{~g} / \mathrm{mL}\). What is the molarity of this solution?

Short answer

The molarity of the commercial concentrated aqueous ammonia solution is \(14.79 M\).

Step-by-step solution

Calculate the mass of NH3 in 1 L of solution

To calculate the mass of NH3 in 1 L of the solution, we need to use the given percentage and density of the solution. First, we find the mass of 1 L of the solution: Mass of 1 L of solution = Density × Volume Mass of 1 L of solution = 0.90 g/mL × 1000 mL Mass of 1 L of solution = 900 g Next, we find the mass of NH3 in 1 L of the solution: Mass of NH3 = (Percentage of NH3 × Mass of 1 L of the solution) / 100 Mass of NH3 = (28% × 900 g) / 100 Mass of NH3 = 252 g So, 1 L of the solution contains 252 g of NH3.

Convert mass of NH3 to moles

To convert the mass of NH3 to moles, we need the molar mass of NH3. The molar mass of NH3 can be calculated as follows: Molar mass of NH3 = (1 × Nitrogen's atomic mass) + (3 × Hydrogen's atomic mass) Molar mass of NH3 = (1 × 14.01 g/mol) + (3 × 1.01 g/mol) Molar mass of NH3 = 14.01 g/mol + 3.03 g/mol Molar mass of NH3 = 17.04 g/mol Now, we can calculate the moles of NH3: Moles of NH3 = Mass of NH3 / Molar mass of NH3 Moles of NH3 = 252 g / 17.04 g/mol Moles of NH3 = 14.79 mol

Calculate the molarity

Molarity is defined as the moles of solute (NH3) per liter of solution. Since we calculated the moles of NH3 in 1 L of the solution, the molarity of the solution is: Molarity = Moles of NH3 / Volume of the solution in liters Molarity = 14.79 mol / 1 L Molarity = 14.79 M Therefore, the molarity of the commercial concentrated aqueous ammonia solution is 14.79 M.