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What is the pH of a solution with [tex]\left[ H^{+} \right] = 1.25 \times 10^{-10} \, \text{M}[/tex]?

Use [tex]pH = -\log \left[ H_3O^{+} \right][/tex].

A. -10.1
B. -9.90
C. 7.90
D. 9.90


Sagot :

To find the pH of a solution given its hydrogen ion concentration [tex]\([H^{+}] = 1.25 \times 10^{-10} \, \text{M}\)[/tex], we use the formula:

[tex]\[ \text{pH} = -\log \left[ H ^{+} \right] \][/tex]

Here's the step-by-step process:

1. Plug in the value of the hydrogen ion concentration into the formula:

[tex]\[ \text{pH} = -\log (1.25 \times 10^{-10}) \][/tex]

2. Calculate the logarithm part:

[tex]\[ \log (1.25 \times 10^{-10}) = \log (1.25) + \log (10^{-10}) \][/tex]

3. The logarithm of [tex]\(10^{-10}\)[/tex] is [tex]\(-10\)[/tex], because:

[tex]\[ \log (10^{-10}) = -10 \][/tex]

4. Now, let’s calculate [tex]\(\log (1.25)\)[/tex]:

Using a calculator, [tex]\(\log (1.25) \approx 0.09691\)[/tex]

5. Add these values together:

[tex]\[ \log (1.25 \times 10^{-10}) = 0.09691 - 10 \][/tex]

6. Combine the results:

[tex]\[ 0.09691 - 10 = -9.90309 \][/tex]

7. Finally, take the negative of this result to find the pH:

[tex]\[ \text{pH} = -(-9.90309) = 9.90309 \][/tex]

Rounding it to two decimal places, the pH is approximately:

[tex]\[ \text{pH} \approx 9.90 \][/tex]

Therefore, the pH of the solution is [tex]\(9.90\)[/tex]. The correct answer is:

[tex]\[ \boxed{9.90} \][/tex]