What is the concentration of OH in a solution with an H^+ concentration of 1.3 imes 10⁻⁴ M? What is the pH of 0.1 M hydrochloric acid? When pH falls by 1 unit, what is the change in the hydrogen ion

$$
1.0 \times 10^{-14} = (1.3 \times 10^{-4} \text{ M})[\text{OH}^-]
$$
$$
[\text{OH}^-] = \frac{1.0 \times 10^{-14}}{1.3 \times 10^{-4} \text{ M}}
$$
$$
[\text{OH}^-] \approx 7.69 \times 10^{-11} \text{ M}
$$
The concentration of $\text{OH}^-$ is $\boxed{\text{7.69} \times 10^{-11} \text{ M}}$.

2. What is the pH of 0.1 M hydrochloric acid?

$$
\text{pH} = -\log(0.1)
$$
$$
\text{pH} = -\log(10^{-1})
$$
$$
\text{pH} = 1
$$
The pH of 0.1 M hydrochloric acid is $\boxed{1}$.

3. When pH falls by 1 unit, what is the change in the hydrogen ion concentration?

The new hydrogen ion concentration is $[\text{H}^+]_2$. $[\text{H}^+]_2 = 10^{-\text{pH}_2} = 10^{-(\text{pH}_1 - 1)}$ $[\text{H}^+]_2 = 10^{-\text{pH}_1 + 1}$ $[\text{H}^+]_2 = 10^1 \times 10^{-\text{pH}_1}$ $[\text{H}^+]_2 = 10 \times [\text{H}^+]_1$ When pH falls by 1 unit, the hydrogen ion concentration increases by a factor of 10.

4. Which equation describes the relationship between pH and pK?

   The relationship between pH and pK (specifically pK$_a$) for a buffer solution is described by the Henderson-Hasselbalch equation:

   $$\boxed{\text{pH} = \text{pK}_a + \log\left(\frac{[\text{conjugate base}]}{[\text{weak acid}]}\right)}$$

5. What determines the pH of buffer?

   The pH of a buffer solution is primarily determined by two factors:

   • The pK$_a$ of the weak acid component of the buffer system.
   • The ratio of the concentration of the conjugate base to the concentration of the weak acid in the buffer solution.

6. When is a buffer most effective?

   A buffer is most effective when the concentration of the weak acid is approximately equal to the concentration of its conjugate base. This occurs when the pH of the buffer is equal to the pK$_a$ of the weak acid. Buffers are also more effective when the absolute concentrations of the weak acid and conjugate base are high.

7. What do you understand by the term "buffering capacity"?

   Buffering capacity refers to the amount of acid or base that a buffer solution can neutralize before its pH changes significantly. It is determined by the absolute concentrations of the weak acid and its conjugate base present in the solution. A higher concentration of buffer components means a greater buffering capacity.