Calculate the ratio of NaF to HF required to create a buffer with pH = 4.20. [NaF]/[HF]

This question aims to find the ratio of Sodium Fluoride (NaF) to Hydrogen Fluoride (HF) that is used to create a buffer having pH 4.20 .

The pH of a solution determines whether a solution is basic or acidic. pH is measured by a pH scale which ranges from 0-14. A solution giving a pH reading of 7 is considered neutral whereas a solution giving a pH greater than 7 is considered a basic solution. Similarly, a solution having a pH less than 7 is considered an acidic solution. Water has a pH of 7.

A buffer solution is a solution that resists the pH from changing. If a small concentration of an acid or base is added to the solution, it helps to maintain the pH of the solution. Buffer solution consists of a weak acid and its conjugate base or a weak base or its conjugate acid.

Expert Answer

To derive the expression for the given data:

$p H = p K_{a} + l o g \frac{[F]}{[H F]}$

$p H = p K_{a} + l o g \frac{[N a F]}{[H F]}$

$p H - p K_{a} = l o g \frac{[N a F]}{[H F]}$

Taking anti-log on both sides of the expression:

$10^{p H} - p K_{a} = \frac{[N a F]}{[H F]}$

This ratio of $N a F$ to $H F$ can be found by further simplification of the above mentioned expression:

$\frac{[N a F]}{[H F]} = 10^{p H} - p K_{a}$

$= 10^{p H - (- l o g K_{a})}$

$= 10^{p H + l o g K_{a}}$

Numerical Solution

By putting values of $p H$ and $K_{a}$ for $H F$ is $3.5 \times 10^{- 4}$ :

$= 10^{4.20 + l o g (3.5 \times 10^{- 4})}$

$\frac{[N a F]}{[H F]} = 5.5$

The ratio of $N a F$ to $H F$ is $3.5$ when a buffer solution having $p H$ of $4.0$ is used.

Example

Consider the $p H$ of the buffer solution is $4.0$ . Calculate the ratio of $N a F$ to $H F$ required to make this buffer solution.

$p H = p K_{a} + l o g \frac{[F]}{[H F]}$

$p H = p K_{a} + l o g \frac{[N a F]}{[H F]}$

$p H - p K_{a} = l o g \frac{[N a F]}{[H F]}$

$10^{p H} - p K_{a} = \frac{[N a F]}{[H F]}$

This ratio of $N a F$ to $H F$ can be found by:

$\frac{[N a F]}{[H F]} = 10^{p H} - p K_{a}$

$= 10^{p H - (- l o g K_{a})}$

$= 10^{p H + l o g K_{a}}$

By putting values:

$= 10^{4.20 + l o g (3.5 \times 10^{- 4)}}$

$\frac{[N a F]}{[H F]} = 3.5$

The ratio of $N a F$ to $H F$ is $3.5$ when a buffer solution having $p H$ of $4.0$ is used.

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Calculate the ratio of NaF to HF required to create a buffer with pH =4.20.

Expert Answer

Numerical Solution

Example

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