Question

A solution is prepared by adding \(50.0 \mathrm{mL}\) of \(0.050 \mathrm{M}\) HBr to 150.0 mL of 0.10 \(M\) HI. Calculate \(\left[\mathrm{H}^{+}\right]\) and the pH of this solution. HBr and HI are both considered strong acids.

Short answer

The concentration of hydrogen ions \(\left(\mathrm{[H^{+}}\right]\) in the solution is \(0.0875\, M\), and the pH of the solution is approximately 1.06.

Step-by-step solution

Calculate moles of HBr and HI

First, we need to determine the moles of HBr and HI in each solution using their molarities and the respective volumes of each solution. The formula to calculate moles is: Moles = Molarity × Volume For HBr: Moles of HBr = \(0.050\, M \times 50.0\, mL = 2.50 \times 10^{-3}\, moles\). For HI: Moles of HI = \(0.10\, M \times 150.0\, mL = 15.0 \times 10^{-3}\, moles\).

Calculate the total moles of H⁺ ions

Since both HBr and HI are strong acids and dissociate completely in water, the moles of HBr and HI will contribute to the number of moles of H⁺ ions in the solution. Therefore, the total moles of H⁺ ions are: Moles of H⁺ = Moles of HBr + Moles of HI Moles of H⁺ = \(2.50 \times 10^{-3}\, moles + 15.0 \times 10^{-3}\, moles = 17.5 \times 10^{-3}\, moles\).

Calculate the final concentration of H⁺ ions

Next, we need to calculate the resulting concentration of H⁺ ions in the mixed solution. To do this, we'll divide the total moles of H⁺ ions by the total volume of the solution. The total volume of the solution is the sum of the volumes of the individual solutions: Total volume = \(50.0\, mL + 150.0\, mL = 200\, mL\, or \, 0.200\, L\). Now, we can find the concentration of H⁺ ions: \([\mathrm{H^{+}}] = \frac{\text{Total moles of H⁺ ions}}{\text{Total volume of solution}}\). \[\mathrm{[H^{+}]} = \frac{17.5 \times 10^{-3}\, \text{moles}}{0.200\, L}\]. \[\mathrm{[H^{+}]} = 0.0875\, M\].

Calculate the pH of the solution

Finally, we can use the formula for pH to calculate the pH value of the solution: pH = - \(\log_{10}\)(H⁺ concentration) pH = - \(\log_{10}(0.0875\, M)\). pH ≈ 1.06 Thus, the concentration of hydrogen ions \(\left(\mathrm{[H^{+}}\right]\) in the solution is \(0.0875\, M\), and the pH of the solution is approximately 1.06.

Key concepts

Strong Acids

Strong acids are fascinating chemical compounds known for their ability to fully dissociate in solution. This means when they dissolve in water, they split into ions completely. Take hydrochloric acid (HCl) or hydrobromic acid (HBr) as examples. They both release their hydrogen ions (\( ext{H}^+\)) readily into the solution.
This trait is why strong acids significantly affect the pH of their solutions—pH measures the concentration of hydrogen ions (\( ext{H}^+\)) in the solution. The more \( ext{H}^+\) ions, the lower the pH, making the solution more acidic.

• Examples include HCl, HBr, and HI.
• They are fully dissociative.
• Result in low pH values.

This full dissociation is different from weak acids, which only partially dissociate in solution.

Molarity

Molarity is a key concept in chemistry referring to the concentration of a solution. It's expressed as the number of moles of solute per liter of solution. Let's break that down: a solute is the substance being dissolved (like salt or sugar), and the solution is the resulting liquid mix.
For example, if you have 1 mole of hydrogen ion (\( ext{H}^+\)) in 1 liter of water, the molarity is 1 M (molar). Understanding molarity helps chemists know how concentrated a solution is.

• Measured in moles per liter (\( ext{M}\) represents "molar").
• Allows for easy calculation and comparison of concentrations.
• Helps predict reactions and their yields.

Calculating molarity is fundamental for reactions involving solutions, as seen in our solution mixing problem.

Solution Concentration

Solution concentration involves understanding the amount of a substance (solute) in a specific volume of solvent or solution. It's critical for predicting how a reaction will proceed.
You determine concentration by measuring how much solute is in a given amount of solvent, often expressed in terms like molarity, molality, or percent concentration. Among these, molarity is most commonly used in chemical calculations.

• Affects reaction rates.
• Essential for achieving desired chemical properties.
• Allows calculation of dilute or concentrate solutions.

Knowing solution concentration is crucial when mixing solutions like HBr and HI, as it determines the number of ions available for interaction.

Acid Dissociation

Acid dissociation refers to how an acid breaks apart into ions when it dissolves in water. It's an essential concept for understanding how acids behave in solutions. For strong acids like HBr and HI, dissociation is complete.
This is why they are strong acids—each molecule of HBr or HI splits entirely into \( ext{H}^+\) ions and their respective anions. The degree of dissociation affects properties like the solution's conductivity and pH.various indicators, such as the acid dissociation constant (Ka), to express this behavior in weak acids.

• Full dissociation is a hallmark of strong acids.
• Directly affects the concentration of \( ext{H}^+\) ions.
• Influences the resulting pH of the solution.

Comprehending the extent of dissociation helps in calculating exactly how many ions are present in any given acidic solution.