Question

A solution is formed by mixing \(50.0 \mathrm{~mL}\) of \(0.015 \mathrm{M} \mathrm{NaOH}(a q)\) with \(50.0 \mathrm{~mL}\) of \(0.010 \mathrm{M}\) \(\mathrm{HNO}_{3}(a q)\) (a) Is the solution acidic or basic? (b) Draw a beaker and show all species present in the solution. (c) What is the pH of the solution?

Short answer

(a) The solution is basic as there is excess sodium hydroxide (NaOH) after the reaction between NaOH and nitric acid (HNO3). (b) The species present in the solution are sodium ions (Na+), nitrate ions (NO3-), water molecules (H2O), and hydroxide ions (OH-). (c) The pH of the solution is 11.40. This was calculated by firstly determining the concentration of the excess NaOH which was found to be 0.0025 M. This gave a pOH of 2.60 which was then subtracted from 14 to find the pH.

Step-by-step solution

(Recognize the nature of NaOH and HNO3)

(In this step, it's essential to understand the nature of the given compounds. Sodium hydroxide, NaOH, is a strong base whereas nitric acid, HNO3, is a strong acid.)

(Calculate the final concentration of NaOH and HNO3 in the solution)

(To calculate the final concentrations of NaOH and HNO3, we must first find the initial moles of each compound: Moles of NaOH = Volume x Molarity Moles of NaOH = (50.0 mL) x (0.015 M) Moles of NaOH = 0.75 mmol Moles of HNO3 = Volume x Molarity Moles of HNO3 = (50.0 mL) x (0.010 M) Moles of HNO3 = 0.50 mmol Since both volumes are equal, we can find the final concentration by dividing moles by the total volume (100.0 mL).)

(Determine the pH of the solution)

(Since NaOH and HNO3 react with each other to form water and a salt (sodium nitrate), we must determine which substance remains in excess and calculate the excess concentration. The mole ratio of NaOH to HNO3 is 1:1. Excess NaOH moles = Initial moles of NaOH - Initial moles of HNO3 Excess NaOH moles = 0.75 mmol - 0.50 mmol Excess NaOH moles = 0.25 mmol The concentration of the excess NaOH = Excess moles / Total volume The concentration of excess NaOH = (0.25 mmol) / (100 mL) The concentration of excess NaOH = 0.0025 M Since we have excess NaOH in the solution, the solution is basic and has a pOH value. To find the pH, we must first determine the pOH: pOH = - log [OH^-] pOH = - log [0.0025] pOH = 2.60 Now we can calculate the pH using the relationship, pH + pOH = 14: pH = 14 - pOH pH = 14 - 2.60 pH = 11.40) So the solution is basic with a pH of 11.40.

(Represent species present in the beaker)

(In the beaker, we have the following species present in the solution: sodium ions (Na+), nitrate ions (NO3-), hydroxide ions (OH-), and water molecules (H2O), which are the products of the reaction between NaOH and HNO3.)

Key concepts

Chemical Solution Preparation

Understanding chemical solution preparation is pivotal when dealing with any laboratory work involving solutions. It's the process of mixing various substances in precise proportions to create a homogeneous mixture with the desired concentration of components. In our exercise, we prepared a solution by mixing equal volumes of two different solutions: one containing sodium hydroxide (NaOH), a strong base, and the other containing nitric acid (HNO3), a strong acid.

When combining chemical solutions, it’s crucial to consider the nature and strength of the reactants. Strong acids and bases, like HNO3 and NaOH respectively, fully dissociate in water, which means their ions (protons for acids and hydroxide ions for bases) are completely released into the solution. The volume and molarity (concentration) of the reactants determine the total number of moles of each substance in the sample, which then allows you to predict the outcome of the reaction and the concentration of ions in the resulting solution.

Acid-Base Reaction

The heart of our textbook exercise lies in the acid-base reaction, which occurs when an acid and a base mix together. Specifically, this is a type of neutralization reaction where hydronium ions (H3O+) from the acid combine with hydroxide ions (OH-) from the base to form water. This process can be generalized with the reaction: acid + base → salt + water.

In our example, NaOH and HNO3 react to create water (H2O) and a salt, sodium nitrate (NaNO3). A 1:1 mole ratio means that the reaction proceeds until one of the reactants is completely used up—known as the limiting reagent. Any remaining excess reactant will determine the pH of the final solution. If you start with more moles of NaOH than HNO3, as in our exercise, the solution will ultimately be basic because excess hydroxide ions remain in solution after all the HNO3 has reacted.

Molarity

Molarity, symbolized by an uppercase 'M', is a measure of the concentration of a solute in a solution, or the number of moles of solute per liter of solution. Molarity plays a crucial role in quantitative aspects of chemical reactions in solution, as seen with our acid-base reacting couple, NaOH and HNO3.

To find the molarity of each substance after they have been mixed, you must consider the total volume of the new combined solution. The initial moles of each substance (found by multiplying initial volume by its molarity) allow you to determine the amount of each reactant in the mix. Post-reaction, the molarity of any excess reactant gives us valuable information to calculate the pH, which is reliant on the concentration of hydrogen or hydroxide ions in the solution. This quantitative measurement is essential not just for balancing chemical reactions but also for understanding properties of the solution, like its acidity or basicity.