The \(OH^-\) concentration in a mixture of 5.0 mL of 0.0504 M \(NH_4Cl\) and 2 mL of 0.0210 M \(NH_3\) solution is \(x \times 10^{-6}\) M. The value of \(x\) is _________. (Nearest integer)
[Given \(K_w = 1 \times 10^{-14}\) and \(K_b = 1.8 \times 10^{-5}\)]
Show Hint
In buffer calculations, you can use moles directly instead of concentrations in the ratio term because the volume cancels out. This avoids unnecessary division.
Step 1: Understanding the Concept:
The mixture consists of a weak base (\(NH_3\)) and its salt with a strong acid (\(NH_4Cl\)), forming a basic buffer solution. We can calculate the hydroxide ion concentration using Henderson-Hasselbalch equation principles or the \(K_b\) expression. Step 2: Key Formula or Approach:
\[ [OH^-] = K_b \times \frac{[\text{Base}]}{[\text{Salt}]} = K_b \times \frac{\text{moles of base}}{\text{moles of salt}} \] Step 3: Detailed Explanation:
1. Calculate millimoles of salt (\(NH_4Cl\)):
\(\text{mmoles of salt} = 5.0 \text{ mL} \times 0.0504 \text{ M} = 0.252 \text{ mmol}\)
2. Calculate millimoles of base (\(NH_3\)):
\(\text{mmoles of base} = 2.0 \text{ mL} \times 0.0210 \text{ M} = 0.042 \text{ mmol}\)
3. Calculate \([OH^-]\):
\[ [OH^-] = 1.8 \times 10^{-5} \times \frac{0.042}{0.252} \]
\[ [OH^-] = 1.8 \times 10^{-5} \times \frac{1}{6} = 0.3 \times 10^{-5} \text{ M} = 3.0 \times 10^{-6} \text{ M} \]
Comparing with \(x \times 10^{-6}\), we find \(x = 3\). Step 4: Final Answer:
The value of \(x\) is 3.
