Question

It takes \(23.77 \mathrm{~mL}\) of \(0.1505 \mathrm{M} \mathrm{HCl}\) to titrate with \(15.00 \mathrm{~mL}\) of \(\mathrm{Ca}(\mathrm{OH})_{2}\). What is the concentration of \(\mathrm{Ca}(\mathrm{OH})_{2}\) ? You will need to write the balanced chemical equation first.

Short answer

The concentration of \(\mathrm{Ca(OH)_2}\) is approximately 0.119 M.

Step-by-step solution

Write the Balanced Chemical Equation

Identify the reactants and products to formulate the balanced equation. The reaction between hydrochloric acid (HCl) and calcium hydroxide (Ca(OH)₂) results in water (H₂O) and calcium chloride (CaCl₂). The balanced chemical equation is: \[\mathrm{Ca(OH)_2} + 2\mathrm{HCl} \rightarrow \mathrm{CaCl_2} + 2\mathrm{H_2O}\] It shows that 1 mole of calcium hydroxide reacts with 2 moles of hydrochloric acid.

Calculate Moles of HCl Used

Use the concentration and volume of HCl to find the moles of HCl used in the titration. The formula is \(\text{moles} = \text{concentration} \times \text{volume in liters}\). So, convert the volume to liters: 23.77 mL = 0.02377 L. The moles of HCl are \(0.1505 \times 0.02377 = 0.003576385\) moles.

Use Stoichiometry to Find Moles of Ca(OH)₂

From the balanced equation, 1 mole of \(\mathrm{Ca(OH)_2}\) reacts with 2 moles of \(\mathrm{HCl}\). Therefore, the moles of \(\mathrm{Ca(OH)_2}\) is half of the moles of \(\mathrm{HCl}\), which is \(\frac{0.003576385}{2} = 0.0017881925\) moles.

Calculate the Concentration of Ca(OH)₂

To find the concentration of \(\mathrm{Ca(OH)_2}\), use the moles of \(\mathrm{Ca(OH)_2}\) and the volume of \(\mathrm{Ca(OH)_2}\) solution in liters (15.00 mL = 0.015 L). The concentration is \(\frac{0.0017881925}{0.015} = 0.119213\, \mathrm{M}\). Therefore, the concentration of \(\mathrm{Ca(OH)_2}\) is approximately 0.119 M.

Key concepts

Balanced Chemical Equation

A balanced chemical equation is essential for understanding the substances involved in a chemical reaction. It portrays the number of atoms and molecules involved, illustrating how reactants transform into products. In our case, when hydrochloric acid (HCl) reacts with calcium hydroxide (Ca(OH)_{2}), they produce calcium chloride (CaCl_{2}) and water (H_{2}O). This reaction can be written as: \[ \mathrm{Ca(OH)_{2} + 2HCl \rightarrow CaCl_2 + 2H_2O} \] This equation is balanced because it contains the same number of each type of atom on both sides of the equation. The ratio of - 1 mole of Ca(OH)_{2} - and 2 moles of HCl is crucial to the stoichiometric calculations that follow.

Molar Concentration

Molar concentration, often termed molarity, refers to the number of moles of a solute present in one liter of solution. It is a key metric in chemical titrations as it allows us to measure and understand the strength of solutions. The molarity of a solution is calculated by the formula: \[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}} \] In this exercise, we know:

• The hydrochloric acid (HCl) has a concentration of 0.1505 M.
• We are trying to find the concentration of calcium hydroxide (Ca(OH)_{2}).

By converting the HCl volume to liters and using its molarity, we find the moles of HCl, which helps us eventually determine the moles—and thus the molarity—of Ca(OH)_{2} used in the reaction.

Stoichiometry

Stoichiometry revolves around calculating the amounts of reactants and products in a chemical reaction. Based on the balanced equation, it allows chemists to predict how much product will form from a given amount of reactants, or vice versa. In our reaction: - 1 mole of Ca(OH) _{2} will react with 2 moles of HCl. Given that we calculated 0.003576385 moles of HCl used, stoichiometry helps us determine that the amount of Ca(OH) _{2} is half this amount, due to the 1:2 ratio. Discovering this proportion is key to identifying the unknown concentration of Ca(OH) _{2} in the titration scenario. This process demonstrates how stoichiometry is a vital tool in transforming measured chemical quantities into meaningful insights.