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 of the original solution of calcium hydroxide is approximately \(0.327 M\).

Step-by-step solution

Write the balanced chemical equation

The balanced chemical equation between calcium hydroxide and nitric acid is: \[Ca(OH)_2 + 2HNO_3 \rightarrow Ca(NO_3)_2 + 2H_2O\]

Find the moles of nitric acid used

The volume and concentration of nitric acid used for neutralization are given. We can find the moles of nitric acid using the formula: moles = volume (in L) × concentration (M) volume of nitric acid = 34.66 mL = 0.03466 L concentration of nitric acid = 0.944 M moles of nitric acid = 0.03466 L × 0.944 M = 0.03272104 mol

Determine the moles of calcium hydroxide

Now, we'll use the stoichiometry from the balanced chemical equation to find the moles of calcium hydroxide present in the original solution. According to the balanced equation, 1 mole of calcium hydroxide reacts with 2 moles of nitric acid. moles of Ca(OH)_2 = (moles of HNO_3) / 2 moles of Ca(OH)_2 = 0.03272104 mol / 2 = 0.01636052 mol

Calculate the concentration of calcium hydroxide

Now that we know the moles of calcium hydroxide and the volume of the original solution (50.00 mL), we can calculate the concentration using the formula: concentration (M) = moles / volume (in L) volume of Ca(OH)_2 = 50.00 mL = 0.0500 L concentration of Ca(OH)_2 = 0.01636052 mol / 0.0500 L = 0.3272104 M The concentration of the original solution of calcium hydroxide is approximately \(0.327 M\).

Key concepts

Stoichiometry

Stoichiometry is a core concept in chemistry that involves the calculation of reactants and products in chemical reactions. It relies heavily on the concept of the mole, allowing us to predict the amounts of substances consumed and produced in reactions. In this exercise, stoichiometry helps us determine the relationship between calcium hydroxide and nitric acid in the neutralization reaction. We start by identifying the balanced equation: 1 mole of calcium hydroxide reacts with 2 moles of nitric acid. This ratio is essential for converting between moles of different substances in the reaction. Understanding stoichiometry allows you to make these conversions accurately, ensuring you can calculate the concentration of a reactant or product when given the appropriate data.

Molarity

Molarity, often denoted as M, is a measure of concentration that reflects the number of moles of solute per liter of solution. In chemical reaction calculations, molarity helps determine how concentrated a solution is, allowing for precise measurements in laboratory settings. In our example, we use molarity to represent nitric acid's concentration (0.944 M) and eventually find the calcium hydroxide concentration.

• To find the concentration of a solution, divide the moles of solute by the volume of the solution in liters.
• This calculation helps understand how much solute is present in a fixed volume, which is crucial for reactions requiring precise quantities.

By calculating molarity, students develop insight into how substances dissolve and interact in solutions.

Neutralization

Neutralization is a chemical reaction where an acid and a base react to form water and a salt. It's the core principle behind titrations, used to determine unknown concentrations in solutions. In this exercise,

• calcium hydroxide (a base) reacts with nitric acid (an acid),
• resulting in the formation of calcium nitrate and water.

This reaction occurs until all the hydrogen ions from the acid and hydroxide ions from the base have combined to form water, indicating complete neutralization. This concept is crucial when calculating unknown molarities as it provides a clear endpoint, evidenced by the balanced equation, where the stoichiometric point is reached when the moles of acid equal the moles of base.

Balanced Chemical Equation

A balanced chemical equation is fundamental in showing the exact proportions of reactants and products in a chemical reaction. It follows the law of conservation of mass, meaning the number of atoms for each element must be the same on both sides of the equation. In our exercise's equation:\[Ca(OH)_2 + 2HNO_3 \rightarrow Ca(NO_3)_2 + 2H_2O\]

• Every atom is accounted for, and the stoichiometry (mole ratio) is established.
• This ratio guides you in predicting the amounts needed or produced during a chemical reaction.

Balancing equations is a critical skill as it lays the groundwork for accurately calculating reactant and product quantities, ensuring experiments or reactions are consistent and predictive.