Question

Hydrochloric acid \((75.0 \mathrm{~mL}\) of \(0.250 M\) ) is added to \(225.0 \mathrm{~mL}\) of \(0.0550 \mathrm{M} \mathrm{Ba}(\mathrm{OH})_{2}\) solution. What is the concentration of the excess \(\mathrm{H}^{+}\) or \(\mathrm{OH}^{-}\) ions left in this solution?

Short answer

The concentration of the excess H+ or OH- ions in the solution can be calculated by first determining the moles of H+ and OH- ions, identifying the limiting reactant, calculating the excess moles of the non-limiting reactant, and then dividing by the total volume of the solution. In this case, the moles of H+ ions are \(75.0 mL \times 0.250 M\) and the moles of OH- ions are 2 × \( (225.0 mL \times 0.0550 M)\). Compare the moles to find the limiting reactant and then calculate the excess moles of H+ or OH- ions accordingly. Finally, divide the excess moles by the total volume (75.0 mL + 225.0 mL) to obtain the concentration of the excess ions.

Step-by-step solution

Calculate moles of H+ and OH- ions

First, we need to find the moles of H+ ions from the hydrochloric acid solution and the moles of OH- ions from the barium hydroxide solution. The moles of H+ ions from hydrochloric acid can be calculated as follows: moles of H+ = volume of HCl x concentration of HCl moles of H+ = \(75.0 mL \times 0.250 M\) For barium hydroxide, we have 2 moles of OH- ions for each mole of the molecule. The moles of OH- ions can be calculated as follows: moles of OH- = 2 × (volume of Ba(OH)2 x concentration of Ba(OH)2) moles of OH- = 2 × \( (225.0 mL \times 0.0550 M)\)

Determine the limiting reactant

Now, we will compare the moles of H+ and OH- ions to determine the limiting reactant. H+:OH- = 1:2 If the amount of OH- ions were twice the amount of H+ ions, these ions would react completely with each other. Compare the moles of H+ and OH- ions to determine the limiting and excess reactant.

Calculate the excess moles of H+ or OH- ions

Based on the limiting reactant identified in the previous step, we will now calculate the excess moles of the other ion (H+ or OH-). For example, if H+ is the limiting reactant, subtract the moles of H+ ions from the twice the moles of OH- ions. excess moles of OH- = 2 × moles of OH- - moles of H+ If OH- is the limiting reactant, subtract twice the moles of OH- ions from the moles of H+ ions. excess moles of H+ = moles of H+ - 2 × moles of OH-

Calculate the concentration of excess H+ or OH- ions

Now that we have the excess moles of the H+ or OH- ion, we can calculate the concentration of the ion left in the solution. To do this, we need to divide the excess moles by the total volume of the solution. Total volume = volume of HCl + volume of Ba(OH)2 Total volume = 75.0 mL + 225.0 mL If H+ is the excess ion: Concentration of excess H+ ions = excess moles of H+ / total volume If OH- is the excess ion: Concentration of excess OH- ions = excess moles of OH- / total volume The solution will have either excess H+ ions or excess OH- ions, and their concentration will be the final answer to the problem.

Key concepts

Stoichiometry

Stoichiometry is the mathematical relationship between the quantities of reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Thus, the amount of each element must be the same in the reactants and products.

For titration problems, stoichiometry involves using the balanced chemical equation to find out the exact amount of one reactant needed to completely react with a known quantity of another reactant. In the given exercise, the reaction between hydrochloric acid (HCl) and barium hydroxide (Ba(OH)₂) involves the reaction of H⁺ ions with OH^- ions in a 1:2 ratio. Using stoichiometry helps to determine the exact moles of each ion present and the moles required for a complete reaction, thereby identifying the excess ion after the reaction.

Understanding stoichiometry is crucial in titration as it allows students to predict and calculate the outcomes of the reaction, and ensures that the titration procedure yields accurate and reliable results.

Limiting Reactant

In any chemical reaction, the limiting reactant is the substance that is completely used up first, thereby determining when the reaction stops. It limits the amount of product that can be formed. Identifying the limiting reactant is an important aspect of chemical calculations as any excess reactant remains unreacted.

In the context of acid-base titrations, understanding which reactant is the limiting one allows us to determine if there will be any excess acid or base left after the titration. For example, in the exercise, the relationship between moles of H⁺ and OH^- ions is compared to identify the limiting reactant. Based on this, we can then find the amount of the excess reactant, which is the reactant that is not completely consumed, and remains in the solution after the reaction has occurred.

Molarity

Molarity, often represented by the symbol M, is a measure of concentration in chemistry. Specifically, it quantifies the number of moles of solute (the substance being dissolved) contained in one liter of solution. It is calculated using the formula:
Molarity (M) = Moles of solute / Liters of solution

In titration calculations, molarity plays a critical role as it allows the comparison of concentrations between the titrant and the analyte. Properly understanding and calculating molarity ensures precise measurement of reactants. For example, in our problem, the molarity of hydrochloric acid and barium hydroxide solutions are given, which enables us to calculate the moles of H⁺ and OH^- ions present in the respective solutions before they react.

Concentration of Ions

Concentration of ions refers to the number of ions of a certain type in a given volume of solution. It can be affected by the dissociation of compounds in water and by the reactions occurring in the solution, such as neutralization between acids and bases.

After an acid-base reaction, the concentration of the excess ions — those not involved in the formation of the water during the neutralization reaction — must be calculated to understand the resulting solution's acidity or basicity. The concentration is determined by dividing the number of moles of the excess ions by the total volume of the solution. Following the exercise, once the acid and base react, calculating the concentration of excess H⁺ or OH^- ions, depending on the limiting reactant, helps us to find the pH of the resulting solution.