Question

A 50.00 -mL sample of aqueous \(\mathrm{Ca}(\mathrm{OH})_{2}\) requires \(34.66 \mathrm{mL}\) of a 0.944-M nitric acid for neutralization. Calculate the concentration (molarity) of the original solution of calcium hydroxide.

Short answer

The concentration (molarity) of the original calcium hydroxide solution is 0.3268 M.

Step-by-step solution

Write the balanced chemical equation

We first need to identify the chemical equation for the neutralization reaction between nitric acid (HNO₃) and calcium hydroxide (Ca(OH)₂). The balanced equation is given by: \[2\,\text{HNO}_3 + \text{Ca}(\text{OH})_2 \longrightarrow \text{Ca}(\text{NO}_3)_2 + 2\,\text{H}_2\text{O}\]

Calculate moles of nitric acid

Next, we need to calculate the moles of nitric acid used in the reaction. We are given the volume (34.66 mL) and the molarity (0.944 M) of nitric acid. To find the moles of nitric acid, we use the formula: moles of nitric acid = molarity × volume (in L) So, moles of nitric acid = 0.944 M × 34.66 mL × \(\frac{1\,\text{L}}{1000\,\text{mL}}\) = 0.03268 mol

Calculate moles of calcium hydroxide

Now, using the balanced chemical equation, we can determine the moles of calcium hydroxide. From the equation, we have: 2 moles of HNO₃ → 1 mole of Ca(OH)₂ So, we can set up a proportion to calculate the moles of calcium hydroxide that reacted with the given moles of nitric acid: \(\frac{1\,\text{mole}\,\text{Ca}(\text{OH})_{2}}{2\,\text{moles}\,\text{HNO}_3}\) = \(\frac{\text{moles of Ca(OH)}_2}{0.03268\,\text{mol}\,\text{HNO}_3}\) Solving for moles of Ca(OH)₂, we get: moles of Ca(OH)₂ = (0.03268 mol) × \(\frac{1\,\text{mole}\,\text{Ca}(\text{OH})_{2}}{2\,\text{moles}\,\text{HNO}_3}\) = 0.01634 mol

Calculate the molarity of calcium hydroxide

Now that we have the moles of calcium hydroxide, we can calculate the molarity of the original calcium hydroxide solution using the given volume (50.00 mL): Molarity of Ca(OH)₂ = \(\frac{\text{moles of Ca(OH)}_2}{\text{volume in L}}\) Molarity of Ca(OH)₂ = \(\frac{0.01634\,\text{mol}}{50.00\,\text{mL}\times\frac{1\,\text{L}}{1000\,\text{mL}}}\) = 0.3268 M The concentration (molarity) of the original calcium hydroxide solution is 0.3268 M.

Key concepts

Stoichiometry Calculations

Stoichiometry is a section of chemistry that involves calculating the amounts of reactants and products in a chemical reaction. It's an essential concept for understanding how to measure substances in reactions accurately. In the case of our calcium hydroxide neutralization problem, we used stoichiometry to find out how many moles of calcium hydroxide, \( \text{Ca}(\text{OH})_2 \), react with nitric acid, \( \text{HNO}_3 \).The balanced chemical equation gives us the ratio of reactants to products needed. For instance, it indicates that two moles of \( \text{HNO}_3 \) react with one mole of \( \text{Ca}(\text{OH})_2 \). Understanding these ratios allows us to convert between moles of acid and moles of base, crucial for finding the molarity of our unknown \( \text{Ca}(\text{OH})_2 \) solution. When working on such calculations, always ensure that your chemical equation is balanced and use it as your 'recipe' to relate different substances in the reaction.

Molarity Concentration

Molarity is a way to express the concentration of a solution, commonly denoted as \( M \). It is defined as the number of moles of a solute divided by the volume of the solution in liters. In our example with calcium hydroxide, calculating the molarity tells us how 'strong' or 'concentrated' the base is. This measurement is critical in chemistry because reactions depend on the concentration of the substances involved. After finding the number of moles of \( \text{Ca}(\text{OH})_2 \) that reacted, we divided by the volume of the solution that was titrated to find its molarity.The ability to calculate molarity is especially useful in preparing solutions for various experiments and understanding the progress of chemical reactions. It's also integral to the process of titration, where a solution of known concentration is used to determine the concentration of an unknown solution.

Acid-Base Titration

Acid-base titration is an analytical technique used to determine the concentration of an unknown acid or base solution by adding a measured volume of a standard solution of known concentration until neutralization occurs. The point at which neutralization occurs is called the equivalence point and can often be identified by a color change with an indicator or by measuring pH.In the practice problem, we conducted a titration of a \( \text{Ca}(\text{OH})_2 \) solution using \( \text{HNO}_3 \) with a known molarity. By carefully measuring the volume of \( \text{HNO}_3 \) needed to reach neutralization, we were able to perform stoichiometry calculations to determine the molarity of the unknown \( \text{Ca}(\text{OH})_2 \) solution. It's crucial to add the titrant slowly near the end point and observe the reaction carefully for the most accurate results.

Chemical Reaction Equation

The chemical reaction equation is a symbolic representation showing the reactants and products in a chemical reaction. It's crucial to balance the equation because it respects the conservation of mass - matter can neither be created nor destroyed.In the example concerning calcium hydroxide neutralization, the balanced reaction equation allowed us to understand the proportional relationship between nitric acid and calcium hydroxide. It also indicated the products of the reaction, calcium nitrate, and water, and their quantities. The coefficients in the balanced equation provided the mole ratio needed to carry out the stoichiometry calculations. Whenever you're faced with a chemical problem, writing out and balancing the chemical equation is one of the first and most important steps you should take to understand what the reaction entails and how to calculate the quantities of interest.