Question

A bottle of concentrated aqueous ammonia is labelled " \(29.8 \% \mathrm{NH}_{3}\) by mass; density \(=0.8960 \mathrm{~g} / \mathrm{mL}\)." (a) What is the molarity of the ammonia solution? (b) If \(300.0 \mathrm{~mL}\) of the commercial ammonia is diluted with water to make \(2.50 \mathrm{~L}\) of solution, what is the molarity of the diluted solution?

Short answer

Question: Calculate the molarities of (a) a concentrated ammonia solution with a density of 0.8960 g/mL and a mass percentage of 29.8% ammonia, and (b) a diluted solution made by taking 300 mL of the concentrated solution and diluting it to 2.50 L. Answer: (a) The molarity of the concentrated ammonia solution is 15.704 M. (b) The molarity of the diluted solution is 1.8845 M.

Step-by-step solution

(a) Calculating the molarity of the ammonia solution

To calculate the molarity of the ammonia solution, first, we need to find the moles of ammonia present in 1 L of the concentrated solution. To do this, use the given density and mass percentage of ammonia: $$ 0.8960 \frac{\text g}{\text{mL}} \cdot 1000\,\text{mL} = 896\,\text g \;\text{solution} $$ $$ 0.298 \times 896\,\text g = 267.488\,\text g \;\mathrm{NH}_3 $$ Now we can find the moles of ammonia: $$ \frac{267.488\,\text g \;\mathrm{NH}_3}{17.03\,\text g \frac{\text{mole}}{\text g}} = 15.704\,\text{moles} $$ Finally, the molarity of the solution is: $$ \frac{15.704\,\text{moles}}{1\,\text L} = 15.704\,\text M $$

(b) Calculating the molarity of the diluted solution

To determine the molarity of the diluted solution, first, calculate the moles of ammonia in the 300 mL of the concentrated solution: $$ 15.704\,\text M \cdot 0.3\,\text L = 4.7112\,\text{moles} $$ The moles of ammonia remain constant after dilution, so to find the new molarity of the solution after diluting the concentrated ammonia solution to 2.50 L, use the following formula: $$ \frac{4.7112\,\text{moles}}{2.5\,\text L} = 1.8845\,\text M $$ The molarity of the diluted solution is 1.8845 M.