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Answer :
To find the ratio of lactic acid to lactate in a solution with a pH of 4.59, we can use the expression for the equilibrium of a weak acid, the acid dissociation constant ([tex]\(K_a\)[/tex]). Here's how you can approach this problem step by step:
1. Identify Given Values:
- The acid dissociation constant for lactic acid ([tex]\(K_a\)[/tex]) is [tex]\(1.37 \times 10^{-4}\)[/tex].
- The pH of the solution is 4.59.
2. Convert pH to Hydrogen Ion Concentration [tex]\([H^+]\)[/tex]:
The pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration. To find [tex]\([H^+]\)[/tex], we can use the formula:
[tex]\[
[H^+] = 10^{-\text{pH}}
\][/tex]
By substituting the given pH value:
[tex]\[
[H^+] = 10^{-4.59} \approx 2.57 \times 10^{-5}
\][/tex]
3. Apply the Acid Equilibrium Formula:
For the dissociation of lactic acid ([tex]\(HA\)[/tex]) into hydrogen ions ([tex]\([H^+]\)[/tex]) and lactate ions ([tex]\([A^-]\)[/tex]), the equilibrium expression can be written as:
[tex]\[
K_a = \frac{[H^+][A^-]}{[HA]}
\][/tex]
We can rearrange this expression to find the ratio of lactic acid to lactate:
[tex]\[
\frac{[HA]}{[A^-]} = \frac{K_a}{[H^+]}
\][/tex]
Plug in the given values:
[tex]\[
\frac{[HA]}{[A^-]} = \frac{1.37 \times 10^{-4}}{2.57 \times 10^{-5}} \approx 5.33
\][/tex]
4. Conclusion:
The ratio of lactic acid to lactate in the solution is approximately 5.33. This means that for every part of lactate, there are about 5.33 parts of lactic acid in the solution.
1. Identify Given Values:
- The acid dissociation constant for lactic acid ([tex]\(K_a\)[/tex]) is [tex]\(1.37 \times 10^{-4}\)[/tex].
- The pH of the solution is 4.59.
2. Convert pH to Hydrogen Ion Concentration [tex]\([H^+]\)[/tex]:
The pH is defined as the negative logarithm (base 10) of the hydrogen ion concentration. To find [tex]\([H^+]\)[/tex], we can use the formula:
[tex]\[
[H^+] = 10^{-\text{pH}}
\][/tex]
By substituting the given pH value:
[tex]\[
[H^+] = 10^{-4.59} \approx 2.57 \times 10^{-5}
\][/tex]
3. Apply the Acid Equilibrium Formula:
For the dissociation of lactic acid ([tex]\(HA\)[/tex]) into hydrogen ions ([tex]\([H^+]\)[/tex]) and lactate ions ([tex]\([A^-]\)[/tex]), the equilibrium expression can be written as:
[tex]\[
K_a = \frac{[H^+][A^-]}{[HA]}
\][/tex]
We can rearrange this expression to find the ratio of lactic acid to lactate:
[tex]\[
\frac{[HA]}{[A^-]} = \frac{K_a}{[H^+]}
\][/tex]
Plug in the given values:
[tex]\[
\frac{[HA]}{[A^-]} = \frac{1.37 \times 10^{-4}}{2.57 \times 10^{-5}} \approx 5.33
\][/tex]
4. Conclusion:
The ratio of lactic acid to lactate in the solution is approximately 5.33. This means that for every part of lactate, there are about 5.33 parts of lactic acid in the solution.
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