Answer :
To determine the pH of a solution with a hydroxide ion concentration [tex]\(\left[ \text{OH}^- \right] = 1.0 \times 10^{-4}\)[/tex] M, we can follow these steps:
1. Calculate the pOH:
The pOH of a solution is calculated using the formula:
[tex]\[ \text{pOH} = -\log [\text{OH}^-] \][/tex]
Given [tex]\(\left[\text{OH}^- \right] = 1.0 \times 10^{-4}\)[/tex] M:
[tex]\[ \text{pOH} = -\log (1.0 \times 10^{-4}) = -( -4 ) = 4.0 \][/tex]
2. Calculate the pH:
The relationship between pH and pOH is given by the equation:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Now that we have the pOH, we can find the pH:
[tex]\[ \text{pH} = 14 - \text{pOH} = 14 - 4.0 = 10.0 \][/tex]
Based on these calculations, the pH of the solution is [tex]\( \boxed{10.0} \)[/tex].
Next, we look at the provided answer choices:
A) [tex]\(1.0 \times 10^{-10}\)[/tex]
B) [tex]\(-10.0\)[/tex]
C) [tex]\(10.0\)[/tex]
D) [tex]\(4.0\)[/tex]
E) [tex]\(-4.0\)[/tex]
The correct answer is:
C) [tex]\(10.0\)[/tex]
1. Calculate the pOH:
The pOH of a solution is calculated using the formula:
[tex]\[ \text{pOH} = -\log [\text{OH}^-] \][/tex]
Given [tex]\(\left[\text{OH}^- \right] = 1.0 \times 10^{-4}\)[/tex] M:
[tex]\[ \text{pOH} = -\log (1.0 \times 10^{-4}) = -( -4 ) = 4.0 \][/tex]
2. Calculate the pH:
The relationship between pH and pOH is given by the equation:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Now that we have the pOH, we can find the pH:
[tex]\[ \text{pH} = 14 - \text{pOH} = 14 - 4.0 = 10.0 \][/tex]
Based on these calculations, the pH of the solution is [tex]\( \boxed{10.0} \)[/tex].
Next, we look at the provided answer choices:
A) [tex]\(1.0 \times 10^{-10}\)[/tex]
B) [tex]\(-10.0\)[/tex]
C) [tex]\(10.0\)[/tex]
D) [tex]\(4.0\)[/tex]
E) [tex]\(-4.0\)[/tex]
The correct answer is:
C) [tex]\(10.0\)[/tex]
