[CN¯] A buffer solution made from HCN and NaCN has a pH of 9.71. If pK for HCN is 9.40, what is the [HCN] [CN] [HCN] in the buffer?

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**Educational Content: Understanding Buffer Solutions**

A buffer solution made from HCN and NaCN has a pH of 9.71. If \( \text{p}K_a \) for HCN is 9.40, what is the \(\frac{[\text{CN}^-]}{[\text{HCN}]}\) in the buffer?

To find the ratio \(\frac{[\text{CN}^-]}{[\text{HCN}]}\), we can use the Henderson-Hasselbalch equation, which is:

\[
\text{pH} = \text{p}K_a + \log\left(\frac{[\text{CN}^-]}{[\text{HCN}]}\right)
\]

Given:
- \(\text{pH} = 9.71\)
- \(\text{p}K_a = 9.40\)

By substituting these values into the equation, we can solve for the ratio \(\frac{[\text{CN}^-]}{[\text{HCN}]}\).

The equation becomes:

\[
9.71 = 9.40 + \log\left(\frac{[\text{CN}^-]}{[\text{HCN}]}\right)
\]

By rearranging, we find:

\[
\log\left(\frac{[\text{CN}^-]}{[\text{HCN}]}\right) = 9.71 - 9.40 = 0.31
\]

Taking the antilog (base 10) of both sides:

\[
\frac{[\text{CN}^-]}{[\text{HCN}]} = 10^{0.31}
\]

Calculating that will provide the concentration ratio in the buffer solution.

There are no graphs or diagrams accompanying this text.
Transcribed Image Text:**Educational Content: Understanding Buffer Solutions** A buffer solution made from HCN and NaCN has a pH of 9.71. If \( \text{p}K_a \) for HCN is 9.40, what is the \(\frac{[\text{CN}^-]}{[\text{HCN}]}\) in the buffer? To find the ratio \(\frac{[\text{CN}^-]}{[\text{HCN}]}\), we can use the Henderson-Hasselbalch equation, which is: \[ \text{pH} = \text{p}K_a + \log\left(\frac{[\text{CN}^-]}{[\text{HCN}]}\right) \] Given: - \(\text{pH} = 9.71\) - \(\text{p}K_a = 9.40\) By substituting these values into the equation, we can solve for the ratio \(\frac{[\text{CN}^-]}{[\text{HCN}]}\). The equation becomes: \[ 9.71 = 9.40 + \log\left(\frac{[\text{CN}^-]}{[\text{HCN}]}\right) \] By rearranging, we find: \[ \log\left(\frac{[\text{CN}^-]}{[\text{HCN}]}\right) = 9.71 - 9.40 = 0.31 \] Taking the antilog (base 10) of both sides: \[ \frac{[\text{CN}^-]}{[\text{HCN}]} = 10^{0.31} \] Calculating that will provide the concentration ratio in the buffer solution. There are no graphs or diagrams accompanying this text.
Expert Solution
Step 1: Defining pH

Answer:

Buffer solution is a type of solution that resists the change in its pH on adding small quantity of acid or base. Solution of weak acid (HCN) and its conjugate base (CN-) can act like a buffer solution.

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