Question

Calculate the \(\mathrm{pH}\) of each of the following strong acid solutions: (a) \(8.3 \times 10^{-4} \mathrm{MHCl},(\mathbf{b}) 1.20 \mathrm{~g}\) of \(\mathrm{HNO}_{3}\) in \(500 \mathrm{~mL}\) of solution, \((\mathbf{c}) 2.0 \mathrm{~mL}\) of \(0.250 \mathrm{M} \mathrm{HClO}_{4}\) diluted to \(40.0 \mathrm{~mL}\), (d) a solution formed by mixing \(25.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HBr}\) with \(25.0 \mathrm{~mL}\) of \(0.200 \mathrm{M} \mathrm{HCl}\).

Short answer

a) \(\mathrm{pH} = -\log(8.3 \times 10^{-4})\) b) \(\mathrm{pH} = -\log(0.038)\) c) \(\mathrm{pH} = -\log(0.0125)\) d) \(\mathrm{pH} = -\log(0.15)\)

Step-by-step solution

a) Calculating the pH of 8.3 × 10⁻⁴ M HCl solution

The strong acid HCl fully dissociates in water, so the concentration of H⁺ ions is the same as the concentration of the solution: [H⁺] = 8.3 × 10⁻⁴ M. Use the pH formula to calculate the pH: \[\mathrm{pH} = -\log([\ce{H+}]) = -\log(8.3 \times 10^{-4})\] Now, use a calculator to find the pH value.

b) Calculating the pH of 1.20 g of HNO₃ in 500 mL of solution

First, we need to find the concentration of the HNO₃ solution. The molar mass of HNO₃ is approximately 63.01 g/mol, so 1.20 g of HNO₃ is: \(\frac{1.20\,\text{g}}{63.01\,\text{g/mol}} \approx 0.019\,\text{mol}\) of HNO₃ Next, we calculate the molarity based on the volume: \[0.019\, \text{mol} \div 0.5\, \text{L} \approx 0.038\,\text{M}\] Since HNO₃ is a strong acid, the concentration of H⁺ ions is the same as the concentration of the solution: [H⁺] = 0.038 M. Apply the pH formula: \[\mathrm{pH} = -\log([\ce{H+}]) = -\log(0.038)\] Now, use a calculator to find the pH value.

c) Calculating the pH of 2.0 mL of 0.250 M HClO₄ diluted to 40.0 mL

First, we need to find the concentration of the diluted solution. We can use the dilution formula: \(M_1 V_1 = M_2 V_2\), where M1 and V1 are the initial molarity and volume, and M2 and V2 are the final molarity and volume. \[0.250\, \text{M} \times 0.002\, \text{L} = M_2 \times 0.040\, \text{L}\] Solving for M2: \[M_2 = \frac{0.250\, \text{M} \times 0.002\, \text{L}}{0.040\, \text{L}} \approx 0.0125\, \text{M}\] The concentration of H⁺ ions is the same as the concentration of the solution: [H⁺] = 0.0125 M. Apply the pH formula: \[\mathrm{pH} = -\log([\ce{H+}]) = -\log(0.0125)\] Now, use a calculator to find the pH value.

d) Calculating the pH of a solution formed by mixing 25.0 mL of 0.100 M HBr with 25.0 mL of 0.200 M HCl

First, we need to find the total amount of H⁺ ions in the mixed solution. Since H⁺ ions come from both HBr and HCl, we need to calculate the moles of H⁺ ions from each acid: HBr: \(0.100\, \text{M} \times 0.025\, \text{L} = 0.0025\, \text{mol}\) HCl: \(0.200\, \text{M} \times 0.025\, \text{L} = 0.0050\, \text{mol}\) Now, add the moles of H⁺ ions to get the total moles of H⁺ ions: \[0.0025\, \text{mol} + 0.0050\, \text{mol} = 0.0075\, \text{mol}\] Next, we need the new total volume: \[0.025\,\text{L} + 0.025\,\text{L} = 0.050\,\text{L}\] Now, we can find the concentration of H⁺ ions in the mixed solution: \[\frac{0.0075\, \text{mol}}{0.050\, \text{L}} = 0.15\, \text{M}\] Finally, apply the pH formula: \[\mathrm{pH} = -\log([\ce{H+}]) = -\log(0.15)\] Now, use a calculator to find the pH value.

Key concepts

Understanding Strong Acids

Strong acids are a class of acids that completely dissociate into ions when they are dissolved in water. This means that every molecule of a strong acid breaks up into its component ions, leaving no undissociated molecules in the solution.

In practical terms, if you have a strong acid solution at a concentration of 0.1 M, you can assume that the concentration of hydrogen ions \([H^+]\) is also 0.1 M. This makes calculations straightforward, as you don't need to consider any association—just use the molarity of the acid directly for calculating \([H^+]\).

Common examples of strong acids include:

• Hydrochloric acid (HCl)
• Nitric acid (HNO₃)
• Perchloric acid (HClO₄)
• Hydrobromic acid (HBr)

The straightforward behavior of strong acids makes them easier to work with in calculations compared to weak acids, which only partially dissociate.

Defining Molarity

Molarity is a measure of the concentration of solute in a solution, expressed as the number of moles of solute per liter of solution. In chemical notation, it is often denoted by the symbol M. For instance, a 1 M solution of HCl means there is one mole of hydrochloric acid in one liter of solution.

To calculate molarity, use the formula: \[ M = \frac{n}{V} \] where \(n\) is the number of moles of solute, and \(V\) is the volume of the solution in liters.

Knowing the molarity of a solution is crucial in acid-base chemistry because it allows you to calculate the concentration of hydrogen ions in a solution, which is key for determining the pH.

Molarity also helps when performing stoichiometric calculations in reactions, as it provides a bridge between the amount of reactants and products. This is particularly useful when dealing with titrations or dilutions.

The Dilution Formula

In chemistry, the dilution formula is used when you need to prepare a solution of a specific concentration from a more concentrated stock solution. The formula is: \[ M_1V_1 = M_2V_2 \] where \(M_1\) and \(V_1\) are the molarity and volume of the initial concentrated solution, and \(M_2\) and \(V_2\) are the molarity and volume of the final diluted solution.

This equation ensures that the number of moles of solute remains constant before and after dilution. By rearranging the equation, you can solve for any of the four variables, giving you flexibility in experimental design.

Using the dilution formula is often necessary in laboratory settings where you might need to create solutions of precise concentrations for experiments. It's also crucial in calculating the final molarity of a solution after mixing or diluting strong acids.

The Basics of Acid-Base Chemistry

Acid-base chemistry revolves around the concept of acids and bases, which are fundamental components of many chemical reactions. In simple terms, an acid is a substance that donates protons (H⁺ ions) in a reaction, while a base is a substance that accepts these protons.

When acids and bases react, they typically form water and a salt, a process known as neutralization. The reaction can be generalized as: \[ ext{Acid} + ext{Base} \rightarrow ext{Salt} + ext{Water} \] The pH scale is a crucial part of acid-base chemistry, providing a way to express the acidity or basicity of a solution. The scale ranges from 0 to 14, with 7 being neutral. Values below 7 indicate acidic solutions, while those above 7 indicate basic solutions.

Calculating the pH of a solution is essential in both academic and professional chemistry settings, as it affects reaction rates, product formation, and chemical equilibrium. For strong acids, knowing the concentration of H⁺ directly gives us the pH using the formula: \[ ext{pH} = -\log([ ext{H}^+]) \] This relationship makes strong acids a prime choice for studying fundamental concepts of acid-base chemistry.