Question

Hydrochloric acid \((75.0 \mathrm{~mL}\) of \(0.250 \mathrm{M})\) 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\(^+\) ions remaining in the solution after the reaction is \(0.02125 \mathrm{M}\).

Step-by-step solution

Calculate the moles of HCI and Ba(OH)\(_2\)

In order to determine the excess ions, we need to first find out the number of moles of both HCl and Ba(OH)\(_2\) in their respective solutions. We can use the formula: Moles = Volume (L) × Molarity (M) For HCl: Moles of HCl = Volume of HCl (L) × Molarity of HCl = 0.075 L × 0.250 M = 0.01875 mol For Ba(OH)\(_2\): Moles of Ba(OH)\(_2\) = Volume of Ba(OH)\(_2\) (L) × Molarity of Ba(OH)\(_2\)= 0.225 L × 0.0550 M = 0.012375 mol

Identify the limiting reactant

To determine which reactant is the limiting reactant, we need to look at the stoichiometry of the reaction: HCl + Ba(OH)\(_2\) → BaCl\(_2\) + 2H\(_2\)O HCl and Ba(OH)\(_2\) react in a 1:1 ratio, hence, we can compare their moles to see which one is the limiting reactant. Since there are more moles of HCl (0.01875 mol) than Ba(OH)\(_2\) (0.012375 mol), Ba(OH)\(_2\) is the limiting reactant.

Calculate the moles of excess H\(^+\) ions

We know that HCl reacts with Ba(OH)\(_2\) in a 1:1 ratio. As Ba(OH)\(_2\) is the limiting reactant, all of it will react with HCl. From this, we can determine the moles of excess H\(^+\) ions that remain unreacted: Moles of excess H\(^+\) = Moles of HCl - (Moles of Ba(OH)\(_2\) × 1/1) Moles of excess H\(^+\) = 0.01875 mol - 0.012375 mol = 0.006375 mol

Calculate the concentration of excess H\(^+\) ions

To find the concentration of excess H\(^+\) ions, divide the moles of excess H\(^+\) ions by the total volume of the mixed solution. The total volume of the solution can be found by adding the volumes of both reactant solutions: Total Volume = Volume of HCl + Volume of Ba(OH)\(_2\) = 0.075 L + 0.225 L = 0.300 L Now calculate the concentration of excess H\(^+\) ions: Concentration of excess H\(^+\) = Moles of excess H\(^+\) / Total Volume (L) Concentration of excess H\(^+\) = 0.006375 mol / 0.300 L = 0.02125 M The concentration of the excess H\(^+\) ions remaining in the solution after the reaction is \(0.02125 \mathrm{M}\).

Key concepts

Stoichiometry in Acid-Base Titration

When we talk about stoichiometry, we're referring to the quantitative relationships between reactants and products in a chemical reaction. It's like a recipe that tells us exactly how much of each ingredient we need to make our final product—in this case, the products of an acid-base reaction.

In the context of acid-base titration, stoichiometry is crucial for determining how much acid is required to neutralize a given amount of base, or vice versa. For example, hydrochloric acid (HCl) and barium hydroxide (Ba(OH)₂) react in a one-to-one molar ratio: each mole of HCl neutralizes one mole of Ba(OH)₂, and understanding this relationship is key to finding the end point of a titration.

Importance of the Balanced Equation

The balanced chemical equation provides a ratio of moles of HCl to moles of Ba(OH)₂, and this ratio is used to determine the limiting reactant. Once the limiting reactant is consumed, the reaction stops, and any excess reactant remains unreacted. It is this excess that we often need to calculate in titration problems.

Molarity in Solution Chemistry

Molarity, symbolized as M, is a way of expressing the concentration of a solution. It's defined as the number of moles of a solute divided by the volume of the solution in liters. In the language of chemistry, the solute is the substance dissolved in the solution (like salt in water), while the solvent is the substance that does the dissolving (like the water itself).

For titration problems, knowing the molarity is like knowing the strength of each reactant. In the exercise, we use molarity to figure out how many moles of HCl and Ba(OH)₂ we have in the given volumes of each solution. This calculation is the first step towards finding out which reactant is in excess and by how much.

Role of Molarity in Calculations

Once we have the moles of our reactants, we can use them, along with the reaction stoichiometry, to understand the outcome of the reaction—in this case, calculating the concentration of excess hydrogen ions once the reaction is complete.

Limiting Reactant in Chemical Reactions

Imagine you're making sandwiches. You have 8 slices of bread but only 3 slices of cheese. You can't make more than 3 sandwiches, because you'll run out of cheese first. That's the idea behind the limiting reactant: it's the ingredient that runs out first, thus limiting the amount of product that can be formed.

In the given exercise, Ba(OH)₂ is the limiting reactant because it is present in fewer moles compared to HCl. After it's completely used up, no more reaction can occur, despite there still being some HCl left over. This is a pivotal concept in titration as it tells us when the reaction has reached completion and indirectly guides us to understand how much of the excess reactant (HCl in this case) remains.

Determining the Limiting Reactant

Calculating the moles of each reactant and comparing them to the reaction's stoichiometry allows us to identify the limiting reactant. This is an indispensable step in solving for the concentration of ions remaining after a titration.

Concentration of Ions After Reaction

In our daily lives, concentration talks about how strong or weak your coffee is based on how much water and coffee grounds you've used. Similarly, in chemistry, after an acid-base reaction, we often want to know the 'strength' of the leftover reactant—how concentrated it is in solution.

The concentration of ions is a measure of how many of these charged particles are present in a certain volume of solution. It relates directly to the properties and behavior of that solution. In the exercise, we calculate the concentration of excess H⁺ ions after the reaction between HCl and Ba(OH)₂ has taken place. It's worth noting that once the titration is done, the concentration of ions in the solution will give us useful information about the solution's pH, which is a measure of acidity or basicity.

Calculating Ion Concentration

We find the concentration of ions by dividing the moles of ions left in excess by the total volume of our combined solutions. This gives us a clear picture of how 'strong' our solution remains in terms of acidity or basicity, after the titration reaction.