Question

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

Short answer

The concentration (molarity) of the original solution of calcium hydroxide is approximately \(0.3272 M\).

Step-by-step solution

Write the balanced chemical equation for the reaction between calcium hydroxide and nitric acid

Write the balanced equation for the reaction between aqueous calcium hydroxide and nitric acid: \[ Ca(OH)_2(aq) + 2HNO_{3}(aq) \rightarrow Ca(NO_{3})_{2}(aq) + 2H_{2}O(l) \] Notice that the ratio between the moles of Ca(OH)2 and HNO3 is 1:2.

Find the moles of nitric acid HNO3

To find the moles of HNO3, use the formula: Moles of HNO3 = Molarity × Volume(L) Moles of HNO3 = 0.944 M × (34.66 mL × (1L / 1000mL)) Moles of HNO3 = 0.944 M × 0.03466 L Moles of HNO3 ≈ 0.03273

Find the moles of calcium hydroxide Ca(OH)2

Now, we need to find the moles of Ca(OH)2. We know the ratio between the moles of Ca(OH)2 and HNO3 is 1:2. Therefore, divide the moles of HNO3 by 2: Moles of Ca(OH)2 = Moles of HNO3 / 2 Moles of Ca(OH)2 = 0.03273 / 2 Moles of Ca(OH)2 ≈ 0.01636

Calculate the molarity of calcium hydroxide Ca(OH)2

Now that we have the moles of Ca(OH)2 and the volume of the solution (given 50.00 mL), we can find the molarity of Ca(OH)2 using the formula: Molarity = Moles of Ca(OH)2 / Volume(L) Molarity = 0.01636 / (50.00 mL × (1L / 1000 mL)) Molarity ≈ 0.01636 / 0.05000 L Molarity ≈ 0.3272 M Thus, the concentration (molarity) of the original solution of calcium hydroxide is approximately 0.3272 M.

Key concepts

Chemical Equation Balancing

Balancing chemical equations is a fundamental skill in chemistry. It's like creating a recipe that describes how substances interact. In our context, we are looking at the neutralization reaction between calcium hydroxide, Ca(OH)_2, and nitric acid, HNO_3.
To balance this reaction, we must ensure that there is the same number of each type of atom on both sides of the equation.
This makes sure that the law of conservation of mass, which states mass cannot be created or destroyed in a chemical reaction, is followed.
For the reaction in our problem, the balanced chemical equation is:

• Ca(OH)_2(aq) + 2HNO_3(aq) -> Ca(NO_3)_2(aq) + 2H_2O(l)

This shows that one mole of calcium hydroxide reacts with two moles of nitric acid to produce one mole of calcium nitrate and two moles of water. By getting the coefficients right, you ensure the atoms are balanced on both sides.
Remember:

• Always start by balancing the atoms that appear in only one compound on each side of the equation.
• Leave hydrogen and oxygen to be balanced last, as they often appear in multiple compounds.

Acid-Base Titration

Acid-base titration is a technique used to determine the concentration of an unknown acid or base using a reaction with a base or acid of known concentration. In the problem, we perform a titration to find the concentration of calcium hydroxide ( Ca(OH)_2 ).
Titration is all about measuring the precise volume of a titrant (a solution of known concentration) needed to react completely with the analyte (a solution of unknown concentration). In this example, the titrant is nitric acid ( HNO_3 ) and the analyte is calcium hydroxide.
Essential steps in an acid-base titration:

• Start by filling a burette with the titrant and recording the initial volume.
• Transfer a measured volume of the analyte (here, Ca(OH)_2 ) into a flask.
• Slowly add titrant to the analyte while continuously stirring until the reaction reaches the equivalence point, where the acid and base have completely reacted.
• Use an indicator to identify the equivalence point, typically when you observe a permanent color change.
• The final volume reading on the burette helps you calculate the volume of titrant added, which is used for further calculations to find the concentration of the analyte.

Stoichiometry

Stoichiometry involves using balanced chemical equations to calculate relationships between reactants and products. In this exercise, stoichiometry helps us link the amounts of reactants, Ca(OH)_2, and HNO_3, in a neutralization reaction.
First, recognize that stoichiometry relies heavily on molar relationships. In our balanced equation, the ratio of Ca(OH)_2 to HNO_3 is 1:2, meaning one mole of calcium hydroxide reacts with two moles of nitric acid.
Steps in stoichiometry:

• Start by calculating the moles of a substance, using its volume and molarity, as we do for HNO_3.
• Use the stoichiometric ratio from the balanced equation to find moles of another reactant, in this case, Ca(OH)_2.
• Apply the formula: \[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \] to find the concentration of the solution.

This way, stoichiometry provides a bridge between the balanced equation and the calculation of unknown concentrations in reactions. Always ensure your measurements in titration and your balanced chemical equation are accurate for stoichiometry to work effectively.