Answered

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The pH of a solution is 2.0. Which statement is correct?

Useful formulas:
[tex]\[ \left[ H _3 O ^{+}\right]=10^{- pH }, \left[ OH ^{-}\right]=10^{- pOH }, pH + pOH =14, \text{and} \left[ H _3 O ^{+}\right]\left[ OH ^{-}\right]=10^{-14} \][/tex]

A. The pOH of the solution is 12.0.
B. The concentration of [tex]\(\text{OH}^{-}\)[/tex] ions is [tex]\(1.0 \times 10^{-2} \, M\)[/tex].
C. The concentration of [tex]\(\text{H}_3 \text{O}^{+}\)[/tex] ions is [tex]\(100.0 \, M\)[/tex].
D. The pOH of the solution is 16.0.

Sagot :

GinnyAnswer
To determine which statement is correct, we will use the provided formulas and the given pH value of 2.0.

### Step 1: Calculate pOH
First, we calculate the pOH of the solution using the formula:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Given that the pH is 2.0, we have:
[tex]\[ \text{pOH} = 14 - 2.0 = 12.0 \][/tex]

### Step 2: Determine the concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex] ions
The formula to calculate the concentration of hydronium ions [tex]\( \left[ \text{H}_3\text{O}^+ \right] \)[/tex] is:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 10^{-\text{pH}} \][/tex]
Substitute the given pH of 2.0:
[tex]\[ \left[ \text{H}_3\text{O}^+ \right] = 10^{-2} = 0.01 \, \text{M} \][/tex]

### Step 3: Determine the concentration of [tex]\( \text{OH}^- \)[/tex] ions
The formula to calculate the concentration of hydroxide ions [tex]\( \left[ \text{OH}^- \right] \)[/tex] is:
[tex]\[ \left[ \text{OH}^- \right] = 10^{-\text{pOH}} \][/tex]
Using the previously calculated pOH of 12.0:
[tex]\[ \left[ \text{OH}^- \right] = 10^{-12} = 1.0 \times 10^{-12} \, \text{M} \][/tex]

### Summary of Results
Based on our calculations:
- The pOH of the solution is indeed 12.0.
- The concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex] ions is [tex]\( 0.01 \, \text{M} \)[/tex].
- The concentration of [tex]\( \text{OH}^- \)[/tex] ions is [tex]\( 1.0 \times 10^{-12} \, \text{M} \)[/tex].

### Analyzing the Given Statements
1. The pOH of the solution is 12.0.
- This statement is correct as per our calculated pOH.

2. The concentration of [tex]\( \text{OH}^- \)[/tex] ions is [tex]\( 1.0 \times 10^{-2} \, \text{M} \)[/tex].
- This statement is incorrect. The concentration of [tex]\( \text{OH}^- \)[/tex] ions is [tex]\( 1.0 \times 10^{-12} \, \text{M} \)[/tex].

3. The concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex] ions is [tex]\( 100.0 \, \text{M} \)[/tex].
- This statement is incorrect. The concentration of [tex]\( \text{H}_3\text{O}^+ \)[/tex] ions is [tex]\( 0.01 \, \text{M} \)[/tex].

4. The pOH of the solution is 16.0.
- This statement is incorrect. The pOH is 12.0, not 16.0.

Therefore, the correct statement is:
- The pOH of the solution is 12.0.
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