Question

How many grams of \(\mathrm{NaOH}\) must be added to \(1.00 \mathrm{~L}\) of a buffer made from \(0.150 \mathrm{M} \mathrm{NH}_{3}\) and \(10.0 \mathrm{~g}\) of \(\mathrm{NH}_{4} \mathrm{Cl}\) so that the pH increases by one unit (e.g., from 5 to 6\() ? K_{\mathrm{a}}\) for \(\mathrm{NH}_{4}{ }^{+}\) is \(5.6 \times 10^{-10}\).

Short answer

(Ka for NH4+ = 5.6 x 10^(-10)) Answer: To find the mass of NaOH needed, follow the steps below: 1. Calculate the initial moles of NH3 and NH4+ in the solution. 2. Find the Kb value for NH3 using the Ka value for NH4+. 3. Determine the initial pH of the buffer solution using the Henderson-Hasselbalch equation. 4. Calculate the required concentration of added NaOH needed to achieve the desired final pH. 5. Convert the concentration of NaOH to moles and then to grams. By following these steps, you will find the mass of NaOH needed to increase the pH of the buffer solution by one unit.

Step-by-step solution

Initial information and formula

We are given the following information: - Volume of buffer = 1.00 L - [NH3] = 0.150 M - Mass of NH4Cl = 10.0 g - Ka for NH4+ = 5.6 x 10^(-10) First, find the initial number of moles of NH3 and NH4+ in the buffer solution. Then, use the Ka value to find the Kb value and apply the Henderson-Hasselbalch equation to find the initial pH of the buffer.

Calculate moles of NH3 and NH4+

We are given the concentration of NH3, but we need to find the moles of NH4+ by converting the mass of NH4Cl to moles. To do this, we need the molar mass of NH4Cl. Molar mass of NH4Cl = 14.01 (N) + 1.01 (H) * 4 + 35.45 (Cl) = 53.49 g/mol Now convert the mass of NH4Cl to moles: moles of NH4Cl = (10.0 g NH4Cl) / (53.49 g/mol) = 0.187 mol

Find Kb value

We are given the Ka value for NH4+. We need to find the Kb value for NH3. Use the relationship between Ka, Kb, and Kw to find the Kb value. Kw = Ka x Kb = 1.0 x 10^(-14) Kb = (1.0 x 10^(-14)) / (5.6 x 10^(-10)) = 1.79 x 10^(-5)

Determine initial pH of the buffer solution

Use the Henderson-Hasselbalch equation for buffers: pH = pKa + log ([A-]/[HA]). However, since we deal with bases, we will use the analogous equation: pOH = pKb + log ([HB+]/[B]), where B is NH3, and HB+ is NH4+. Then, we can find the pH. Initial pOH = -log(Kb) + log ([NH4+]/[NH3]) Initial pOH = -log(1.79 x 10^(-5)) + log (0.187 mol / 0.150 mol) = 4.76 Initial pH = 14 - pOH = 9.24

Calculate the required concentration of added NaOH

Now, we want to increase the pH by one unit. So, the final pH will be: Final pH = 9.24 + 1 = 10.24 Final pOH = 14 - 10.24 = 3.76 Now, we use the Henderson-Hasselbalch equation again for the final pOH: 3.76 = -log(1.79 x 10^(-5)) + log (x / 0.150) We solve this equation to find the required concentration of added NaOH (x).

Convert the concentration of NaOH to grams

Here, x represents the required concentration of NH4+ after the addition of NaOH. Since the volume of the buffer is 1.00 L, we need to find the number of moles of NaOH, which will be equal to the moles of NH4+. Then, we can convert this to grams of NaOH needed. moles of NaOH = x moles - 0.187 moles (initial moles of NH4+) Mass of NaOH needed = moles of NaOH x molar mass of NaOH Calculate the mass of NaOH needed using the obtained values of x and moles of NaOH, and molar mass of NaOH = 40 g/mol. This is the final answer, representing the number of grams of NaOH that must be added to the buffer solution.