Question

Calculate the pH of a solution formed by mixing 100.0 \(\mathrm{mL}\) of 0.100 \(\mathrm{M}\) NaF and 100.0 \(\mathrm{mL}\) of 0.025 \(\mathrm{M} \mathrm{HCl} .\)

Short answer

The pH of the solution formed by mixing 100.0 mL of 0.100 M NaF and 100.0 mL of 0.025 M HCl is approximately 3.78.

Step-by-step solution

Calculate the moles of NaF and HCl in each solution

First, we need to calculate the moles of NaF and HCl in the original solutions. To do this, use the formula: moles = molarity × volume For NaF: moles NaF = \(0.100 \, \mathrm{M}\) × \(100.0 \, \mathrm{mL}\) moles NaF = \(0.100 \, \mathrm{M}\) × \(0.100 \, \mathrm{L}\) moles NaF = 0.0100 moles For HCl: moles HCl = \(0.025 \, \mathrm{M}\) × \(100.0 \, \mathrm{mL}\) moles HCl = \(0.025 \, \mathrm{M}\) × \(0.100 \, \mathrm{L}\) moles HCl = 0.00250 moles

Determine the moles of NaF and HCl after mixing

When mixing the solutions, NaF, a salt, will dissociate into Na+ and F- ions, while HCl, a strong acid, will dissociate into H+ and Cl- ions. The H+ ions from HCl and the F- ions from NaF will then react to form HF, according to the following equation: H+ + F- -> HF Since there are more F- ions than H+ ions, after the reaction, we will have an excess of F- ions left. In order to find the remaining F- ions, subtract the moles of H+ ions from the initial moles of F- ions. Remaining F- ions: moles F- = moles NaF - moles HCl moles F- = 0.0100 - 0.00250 = 0.00750 moles

Calculate the concentration of F- ions and [HF] after dilution

Now, we need to calculate the concentration of the F- ions and [HF] after mixing the solutions. Since the volume of the mixed solutions is 200.0 mL (100.0 mL from NaF and 100.0 mL from HCl), we can calculate the concentrations using the following formula: concentration = (moles) / (final volume in liters) For F- ions: concentration F- = 0.00750 / 0.200 = \(0.0375 \, \mathrm{M}\) For HF: Since the moles of HF formed are equal to the moles of HCl consumed (0.00250 moles), the concentration of HF is: concentration HF = 0.00250 / 0.200 = \(0.0125 \, \mathrm{M}\)

Calculate the pH of the solution

Now we can use the Ka expression for HF (Ka = [H+][F-] / [HF]) to calculate the concentration of H+ ions and determine the pH of the solution. The Ka for HF is 6.6 x 10^(-4). \(6.6 \times 10^{-4} = \frac{[H^+][0.0375]}{0.0125 - [H^+]}\) We can solve for [H+] using the quadratic formula or make an approximation (assuming that [H+] is much smaller than 0.0125) and obtain: >H+ concentration = \(6.6 \times 10^{-4} \cdot \frac{0.0125}{0.0375}\) >[H+] = \(1.65 \times 10^{-4} \mathrm{M}\) Now, we can use the pH formula to calculate the pH of the solution: pH = -log10[H+] pH = -log10(\(1.65 \times 10^{-4}\)) pH ≈ 3.78 The pH of the solution formed by mixing 100.0 mL of 0.100 M NaF and 100.0 mL of 0.025 M HCl is approximately 3.78.

Key concepts

Acid-Base Reaction

When you mix an acid and a base, they undergo a reaction to form water and a salt. In our exercise, we are mixing NaF (a salt) and HCl (an acid). HCl is a strong acid that dissociates completely into H+ and Cl- ions in water. On the other hand, NaF dissociates into Na+ and F- ions.

This is a classic acid-base reaction where the H+ from the HCl reacts with the F- from the NaF. The reaction is:

• H+ + F- → HF

This leads to the formation of HF, which is actually a weak acid. Notice that we have excess F- ions leftover after all the H+ ions react, leaving us with a solution that also contains unreacted F- ions together with HF.

Buffer Solution

A buffer solution is a system that resists changes in pH when small amounts of acid or base are added. They are made usually from a combination of a weak acid and its conjugate base or a weak base and its conjugate acid.

In this exercise, the solution becomes a buffer solution after the reaction, because it contains HF (a weak acid) and excess F- ions (the conjugate base). The presence of both allows the solution to resist drastic changes in pH when small amounts of additional acids or bases are introduced. The solution maintains its pH through these reversible reactions:

• HF ⇌ H+ + F-

Buffers are crucial in many biological and chemical systems, helping to stabilize pH levels.

Molarity

Molarity is a key concept in chemistry that tells us how concentrated a solution is. It is defined as the number of moles of solute per liter of solution, often symbolized as "M."

In the exercise, we calculated the initial molarity of NaF and HCl to find out how many moles were in the starting volumes. This tells us the exact amount of reactive particles present in each solution:

• Moles of NaF = (0.100 M) x (0.100 L) = 0.0100 moles
• Moles of HCl = (0.025 M) x (0.100 L) = 0.00250 moles

By knowing the molarity, we can understand how strong or weak a solution is, which is vital when predicting the outcomes of reactions and conducting quantitative analysis.

Dilution

Dilution involves adding more solvent to a solution to decrease its concentration. It's a common practice when handling solutions to achieve desired concentration levels. In this exercise, when the two solutions are mixed, the total volume doubles from 100 mL to 200 mL, thereby diluting each solute present.

After mixing, the concentrations of F- and HF need to be recalculated due to the change in volume:

• Concentration of F- = 0.00750 moles / 0.200 L = 0.0375 M
• Concentration of HF = 0.00250 moles / 0.200 L = 0.0125 M

Dilution not only changes concentrations but also affects the chemical dynamics of the solution. Thus, calculating concentration after dilution is key to understanding further chemical manipulations and pH calculations.