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 \(14.8~\text{M}\).

Step-by-step solution

Identify the Formula

We will use the formula for molarity, which is: Molarity (M) = \(\frac{\text{moles of solute}}{\text{liters of solution}}\) Since we are given the mass of ammonia in the solution and its density, we need to convert this information into moles and volume.

Calculate the Moles of Ammonia

First, let's find the mass of ammonia in \(1~mL\) of solution. If the solution is \(28\% \mathrm{NH}_3\) by mass, we have: Mass of NH3 in \(1~mL\) of solution = \(0.28 \times 0.9 ~\frac{g}{mL}\) = \(0.252 ~g\) Now, we need to convert this mass into moles of ammonia. We will use the molar mass of ammonia (\(\mathrm{NH}_3\)), which is: Molar Mass of ammonia = \(14.01 + (3 \times 1.008) = 17.03~g/mol\) Thus, moles of ammonia in \(1~mL\) of solution = \(\frac{0.252~g}{17.03~\frac{g}{mol}} = 0.0148~mol\)

Convert mL of Solution to Liters

Since molarity is measured in moles per liter of solution, we need to convert the volume of solution from mL to L. We know that, \(1~L = 1000~mL\). Therefore: Volume of solution = \(\frac{1~mL}{1000} = 0.001~L\)

Calculate Molarity

Now that we have the moles of ammonia and volume of the solution, we can calculate the molarity: Molarity (M) = \(\frac{0.0148~mol}{0.001~L}\) Molarity = \(\boxed{14.8~M}\) So, the commercial concentrated aqueous ammonia solution has a molarity of \(14.8~\text{M}\).