Calculate the pH of a buffer solution containing 0.250 M of ammonia and 0.0500 M of ammonium chloride. The value for for the
ammonium ion is ?
6 10
O9
8

Ask by King Gonzalez. in Canada

Mar 26,2025

Question

Calculate the pH of a buffer solution containing 0.250 M of ammonia and 0.0500 M of ammonium chloride. The value for for the
ammonium ion is ?
6 10
O9
8

Ask by King Gonzalez. in Canada

Mar 26,2025

UpStudy AI · Accepted Answer

**Step 1. Identifying the species in the buffer**

The buffer solution consists of ammonia, $$\mathrm{NH_3}$$, a weak base, and ammonium chloride, $$\mathrm{NH_4Cl}$$, which provides the conjugate acid, $$\mathrm{NH_4^+}$$.

**Step 2. Determining the acid dissociation constant**

The given equilibrium constant for the ammonium ion is 
$$
K_a = 5.62 \times 10^{-10}.
$$
We need the $$\mathrm{p}K_a$$ value:
$$
\mathrm{p}K_a = -\log(K_a) = -\log(5.62 \times 10^{-10}).
$$
Calculating:
$$
\log(5.62 \times 10^{-10}) = \log(5.62) + \log(10^{-10}) \approx 0.75 - 10 = -9.25,
$$
therefore:
$$
\mathrm{p}K_a \approx 9.25.
$$

**Step 3. Using the Henderson–Hasselbalch equation**

For a buffer solution, the Henderson–Hasselbalch equation is:
$$
\mathrm{pH} = \mathrm{p}K_a + \log\left(\frac{[\text{base}]}{[\text{acid}]}\right).
$$
Here, the base is $$\mathrm{NH_3}$$ and the acid is $$\mathrm{NH_4^+}$$.

**Step 4. Plugging in the concentrations**

The concentrations are:
- $$[\mathrm{NH_3}] = 0.250\,\mathrm{M}$$
- $$[\mathrm{NH_4^+}] = 0.0500\,\mathrm{M}$$

Thus:
$$
\mathrm{pH} = 9.25 + \log\left(\frac{0.250}{0.0500}\right).
$$
Calculate the ratio:
$$
\frac{0.250}{0.0500} = 5.
$$
Next, calculate the logarithm:
$$
\log(5) \approx 0.699.
$$
So:
$$
\mathrm{pH} \approx 9.25 + 0.699 = 9.949.
$$

**Step 5. Final Answer**

The pH of the buffer solution is approximately 
$$
9.95.
$$
The pH of the buffer solution is approximately 9.95.

Calculate the pH of a buffer solution containing 0.250 M of ammonia and 0.0500 M of ammonium chloride. The value for for the
ammonium ion is ?
6 10
O9
8

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Calculate the pH of a buffer solution containing 0.250 M of ammonia and 0.0500 M of ammonium chloride. The value for for the ammonium ion is ? 6 10 O9 8

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Calculate the pH of a buffer solution containing 0.250 M of ammonia and 0.0500 M of ammonium chloride. The value for for the
ammonium ion is ?
6 10
O9
8