What mass of ammonium chloride must be added to a 0.500 L solution of 0.250 M ammonia to make a buffer with a pH of 9.26? Kb (NH3) = 1.8 × 10–5?
To solve this problem, we need to understand the concept of a buffer solution and how to calculate the mass of a solute needed to make the buffer.
A buffer solution is a solution that can resist changes in pH when small amounts of acid or base are added to it. It consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. In this case, we are dealing with a base-buffer system where ammonia (NH3) is the base and ammonium chloride (NH4Cl) is the conjugate acid.
The buffer capacity is determined by the ratio of the concentrations of the weak base and its conjugate acid. To calculate the mass of ammonium chloride needed, we will use the Henderson-Hasselbalch equation, which relates the pH of a buffer solution to the pKa or pKb of the weak acid or base, and the ratio of the concentrations of the conjugate acid and base.
The Henderson-Hasselbalch equation for a base-buffer system is:
pOH = pKb + log([conjugate acid]/[weak base])
Given:
- pH = 9.26
- Kb (NH3) = 1.8 × 10–5
- Volume of the solution (V) = 0.500 L
- Concentration of ammonia (weak base) = 0.250 M
First, we need to find the pOH value using the given pH:
pOH = 14 - pH
= 14 - 9.26
= 4.74
Next, we can calculate the concentration of hydroxide ions ([OH-]) from the pOH:
[OH-] = 10^(-pOH)
= 10^(-4.74)
≈ 4.44 × 10^(-5) M
Now, we can calculate the concentration of ammonium ions ([NH4+]) using the relation with hydroxide ions:
Kb = [NH4+][OH-] / [NH3]
Since [NH3] = 0.250 M, we can rearrange the equation to solve for [NH4+]:
[NH4+] = (Kb * [NH3]) / [OH-]
= (1.8 × 10^(-5) * 0.250) / (4.44 × 10^(-5))
= 1.02 M
The concentration of ammonium ions in the final buffer solution should be 1.02 M.
To find the mass of ammonium chloride needed, we can use the formula:
mass = (concentration * volume * molar mass) / 1000
Since the concentration is given in M (mol/L) and the volume is in liters, the mass of ammonium chloride would be:
mass = (1.02 * 0.500 * molar mass(NH4Cl)) / 1000
To find the molar mass of NH4Cl (ammonium chloride), we can add up the atomic masses of the elements present: nitrogen (N), hydrogen (H), and chlorine (Cl).
molar mass (NH4Cl) = (1 * atomic mass(N)) + (4 * atomic mass(H)) + atomic mass(Cl)
Substituting the values and using the periodic table, we get:
molar mass (NH4Cl) = (1 * 14.01) + (4 * 1.01) + 35.45
= 53.49 g/mol
Now, we can substitute the values into the formula to find the mass:
mass = (1.02 * 0.500 * 53.49) / 1000
= 0.270 g
Therefore, you would need to add approximately 0.270 grams of ammonium chloride to the 0.500 L solution of 0.250 M ammonia to make a buffer with a pH of 9.26.
To solve this problem, we first need to calculate the amount of ammonia (NH3) and ammonium chloride (NH4Cl) needed to make the desired buffer.
Step 1: Write the balanced equation for the reaction between ammonia and water:
NH3 + H2O ⇌ NH4+ + OH-
Step 2: Identify the initial concentration of ammonia (NH3) in the 0.500 L solution:
Initial concentration of NH3 (C1) = 0.250 M
Step 3: Calculate the concentration of hydroxide ions (OH-) in the solution using the given pH value:
pOH = 14 - pH = 14 - 9.26 = 4.74
[OH-] = 10^(-pOH) = 10^(-4.74) = 4.28 x 10^(-5) M
Step 4: Use the given Kb value to calculate the concentration of ammonium (NH4+) ions:
Kb = [NH4+][OH-] / [NH3]
Assuming the concentration of NH4+ ions after the reaction is negligible, we can simplify the equation to:
Kb = [OH-] * (x) / (C1 - x)
where x is the change in concentration of NH4+.
Plugging in the known values:
1.8 x 10^(-5) = 4.28 x 10^(-5) * x / (0.250 - x)
Step 5: Solve the quadratic equation for x:
1.8 x 10^(-5) * (0.250 - x) = 4.28 x 10^(-5) * x
0.000045 - 1.8 x 10^(-5) * x = 4.28 x 10^(-5) * x
(4.28 x 10^(-5) + 1.8 x 10^(-5)) * x = 0.000045
6.08 x 10^(-5) * x = 0.000045
x = 0.000045 / 6.08 x 10^(-5)
x ≈ 0.00074 M
Step 6: Calculate the moles of NH4Cl needed to achieve the desired concentration:
Moles of NH4Cl = concentration * volume = 0.00074 M * 0.500 L = 0.00037 mol
Step 7: Calculate the mass of NH4Cl using its molar mass:
Mass of NH4Cl = moles * molar mass = 0.00037 mol * (14.01 g/mol + 1.01 g/mol + 35.45 g/mol) = 0.018 g
Therefore, approximately 0.018 grams of ammonium chloride must be added to the 0.500 L solution of 0.250 M ammonia to make a buffer with a pH of 9.26.