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What are the hydroxide-ion concentrations for solutions with the following pH values?

a. pH = 4.00
b. pH = 8.00
c. pH = 12.00

Answer :

To find the hydroxide-ion concentrations for solutions with different pH values, we can use the relationship between pH, pOH, and hydroxide ion concentration [tex]\([OH^-]\)[/tex]. Let's go through the steps for each pH value:

1. Understand the relationship between pH, pOH, and ion concentrations:

- The pH scale measures the acidity of a solution. It is defined as [tex]\( pH = -\log [H^+] \)[/tex], where [tex]\([H^+]\)[/tex] is the concentration of hydrogen ions.
- The pOH is related to hydroxide ions: [tex]\( pOH = -\log [OH^-] \)[/tex].
- In pure water (or neutral solutions), the sum of pH and pOH is always [tex]\(14\)[/tex], so:
[tex]\[
pH + pOH = 14
\][/tex]
- Therefore, to find pOH from a given pH, use:
[tex]\[
pOH = 14 - pH
\][/tex]
- From pOH, you can find the concentration of hydroxide ions with:
[tex]\[
[OH^-] = 10^{-pOH}
\][/tex]

2. Calculate the hydroxide-ion concentration for each pH value:

a. For a pH of 4.00:
- Calculate pOH:
[tex]\[
pOH = 14 - 4.00 = 10.00
\][/tex]
- Calculate [tex]\([OH^-]\)[/tex]:
[tex]\[
[OH^-] = 10^{-10} = 1 \times 10^{-10} \text{ M}
\][/tex]

b. For a pH of 8.00:
- Calculate pOH:
[tex]\[
pOH = 14 - 8.00 = 6.00
\][/tex]
- Calculate [tex]\([OH^-]\)[/tex]:
[tex]\[
[OH^-] = 10^{-6} = 1 \times 10^{-6} \text{ M}
\][/tex]

c. For a pH of 12.00:
- Calculate pOH:
[tex]\[
pOH = 14 - 12.00 = 2.00
\][/tex]
- Calculate [tex]\([OH^-]\)[/tex]:
[tex]\[
[OH^-] = 10^{-2} = 1 \times 10^{-2} = 0.01 \text{ M}
\][/tex]

In summary, the hydroxide-ion concentrations for the given pH values are:
- For pH 4.00: [tex]\(1 \times 10^{-10} \text{ M}\)[/tex]
- For pH 8.00: [tex]\(1 \times 10^{-6} \text{ M}\)[/tex]
- For pH 12.00: [tex]\(0.01 \text{ M}\)[/tex]

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