Problem 44 - Chemistry The Central Science

Question

Calculate the \(\mathrm{pH}\) of each of the following strong acid solutions: (a) \(0.0167 \mathrm{M} \mathrm{HNO}_{3},\) (b) \(0.225 \mathrm{~g}\) of \(\mathrm{HClO}_{3}\) in \(2.00 \mathrm{~L}\) of solution, (c) \(15.00 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{HCl}\) diluted to \(0.500 \mathrm{~L}, (\mathrm{~d})\) a mixture formed by adding \(50.0 \mathrm{~mL}\) of \(0.020 \mathrm{M} \mathrm{HCl}\) to \(125 \mathrm{~mL}\) of \(0.010 \mathrm{M} \mathrm{HI}\)

Step-by-Step Solution

Answer

The pH values for each of the given strong acid solutions are: (a) pH ≈ 1.78, (b) pH ≈ 2.88, (c) pH ≈ 1.52, and (d) pH ≈ 1.89.

Step 1: a) Calculate the pH of \(0.0167\mathrm{M}\) HNO3 solution

Since HNO3 is a strong acid, it completely dissociates in water. Therefore, the concentration of H+ ions is equal to the concentration of HNO3 provided: [H+] = \(0.0167\mathrm{M}\) Now, we can calculate the pH using the formula: pH = -log10[H+] pH = -log10(\(0.0167\)) pH ≈ \(1.78\)

Step 2: b) Calculate the pH of \(0.225\mathrm{g}\) HClO3 in \(2.00\mathrm{L}\) of solution

First, we need to find the molar concentration of HClO3 in the solution. To do this, we'll divide the mass of HClO3 by its molar mass and then divide by the volume of the solution. Molar mass of HClO3 = 84.46 g/mol Molar concentration of HClO3 = \(\frac{0.225\mathrm{~g}}{84.46 \mathrm{~g/mol}}\) × \(\frac{1}{2.00\mathrm{L}}\) Molar concentration of HClO3 ≈ \(0.00133\mathrm{M}\) Since HClO3 is a strong acid, it completely dissociates in water, so [H+] = \(0.00133\mathrm{M}\). Now, we can calculate the pH using the formula: pH = -log10[\(0.00133\)] pH ≈ \(2.88\)

Step 3: c) Calculate the pH of \(15.00\mathrm{mL}\) of \(1.00\mathrm{M}\) HCl diluted to \(0.500\mathrm{L}\)

First, let's find the new concentration of HCl after dilution using the formula: \(C_1V_1 = C_2V_2\) \((1.00\mathrm{M})(0.015\mathrm{L}) = C_2(0.5\mathrm{L})\) \(C_2\) ≈ \(0.030\mathrm{M}\) Since HCl is a strong acid, the concentration of H+ ions will be equal to the concentration of the acid: [H+] = \(0.030\mathrm{M}\) Now we can calculate the pH using the formula: pH = -log10[\(0.030\)] pH ≈ \(1.52\)

Step 4: d) Calculate the pH of a mixture of \(50.0\mathrm{mL}\) of \(0.020\mathrm{M}\) HCl and \(125\mathrm{mL}\) of \(0.010\mathrm{M}\) HI

First, we need to calculate the total amount of H+ ions in the mixture. We can do this by finding the moles of H+ ions in each of the individual solutions and then adding them together: Moles of H+ from HCl = \((0.020\mathrm{M}) \times (0.050\mathrm{L})\) = \(0.0010\mathrm{mol}\) Moles of H+ from HI = \((0.010\mathrm{M}) \times (0.125\mathrm{L})\) = \(0.00125\mathrm{mol}\) Total moles of H+ = \(0.0010\mathrm{mol}\) + \(0.00125\mathrm{mol}\) = \(0.00225\mathrm{mol}\) Now, we need to find the total volume of the mixture: Total Volume = \(0.050\mathrm{L}\) + \(0.125\mathrm{L}\) = \(0.175\mathrm{L}\) Next, we can calculate the concentration of H+ ions in the mixed solution: [H+] = \(\frac{0.00225\mathrm{mol}}{0.175\mathrm{L}}\) ≈ \(0.01286\mathrm{M}\) Finally, we can calculate the pH using the formula: pH = -log10[\(0.01286\)] pH ≈ \(1.89\)

Key Concepts

pH Scale

Understanding the pH scale is essential when studying chemistry, especially acids and bases. The pH scale measures the acidity or basicity of a solution and ranges from 0 to 14. A pH value of 7 is considered neutral, which is the pH of pure water. Solutions with pH values less than 7 are acidic, and those with pH values greater than 7 are basic (or alkaline).

The term 'pH' is derived from the potential of hydrogen' and is a logarithmic scale based on the concentration of hydrogen ions (H^+) in a solution. The formula to calculate pH is: pH = -log[H^+], where [H^+] represents the molarity of hydrogen ions. Because the pH scale is logarithmic, each integer pH value represents a tenfold difference in acidity. For instance, a solution with a pH of 2 is ten times more acidic than one with a pH of 3 and a hundred times more acidic than a solution with a pH of 4.

Acid Dissociation

Acid dissociation refers to the process by which an acid releases hydrogen ions (H^+) into a solution. In water, the dissociation of an acid (HA) can be represented as HA → H^+ + A^-. For strong acids, this process is considered to be complete, meaning that every molecule of acid dissociates to release H^+ ions. This is why the concentration of H^+ ions in a solution of a strong acid is equal to the concentration of the acid itself.

Knowing the extent of acid dissociation is vital for calculating the pH of a solution. In the case of strong acids, because the dissociation is complete, one can simply take the negative logarithm of the concentration of the acid to find the pH. In contrast, weak acids do not fully dissociate in water, and additional calculations involving the acid dissociation constant (K_a) are required to determine the pH.

Molarity and Dilution

Molarity is a measure of the concentration of a solute in a solution and is defined as the number of moles of solute per liter of solution. It is represented by the symbol M and is calculated using the formula: M = frac{n}{V}, where n is the number of moles of solute and V is the volume of solution in liters.

Dilution involves adding more solvent to a solution, decreasing the concentration of the solute. The process of dilution is crucial in laboratories when preparing solutions of a particular molarity. The relationship between the initial and final molarities and volumes in a dilution can be expressed using the dilution formula: C_1V_1 = C_2V_2, where C_1 and C_2 are the initial and final molarities, and V_1 and V_2 are the initial and final volumes, respectively. This formula helps preserve the number of moles of solute before and after dilution, thus allowing for the calculation of the new concentration after dilution.

Strong Acids

Strong acids are acids that completely dissociate into their ions in aqueous solutions. Examples of strong acids include hydrochloric acid (HCl), nitric acid (HNO_3), and perchloric acid (HClO_4). Because of their complete dissociation, the concentration of hydrogen ions (H^+) in a solution of a strong acid is equal to the concentration of the acid itself.

When calculating the pH of strong acid solutions, one does not need to consider the acid's dissociation constant since the dissociation is complete. However, it is essential to know the molarity of the acid, as that directly impacts the pH. Converting the mass of an acid to moles by using the molar mass, then finding its molarity when dissolved in a known volume of solution, allows one to calculate the pH straightforwardly using the pH equation mentioned earlier.