To determine the concentration of hydroxide ions ([tex]\([OH^-]\)[/tex]) in a solution of ammonia with a pH of 11.8, we need to perform a few calculations using key principles of chemistry.
Step 1:
First, we can use the relationship between pH and pOH, which is given by the equation:
[tex]\[ pH + pOH = 14 \][/tex]
Given the pH of the solution:
[tex]\[ pH = 11.8 \][/tex]
We can rearrange the equation to solve for pOH:
[tex]\[ pOH = 14 - pH \][/tex]
[tex]\[ pOH = 14 - 11.8 \][/tex]
[tex]\[ pOH = 2.2 \][/tex]
Step 2:
Next, we use the relationship between pOH and the concentration of hydroxide ions ([tex]\([OH^-]\)[/tex]), which is given by the formula:
[tex]\[ [OH^-] = 10^{-pOH} \][/tex]
Using the pOH value calculated:
[tex]\[ pOH = 2.2 \][/tex]
We can then find the concentration of hydroxide ions:
[tex]\[ [OH^-] = 10^{-2.2} \][/tex]
Step 3:
To find the numerical value of [tex]\(10^{-2.2}\)[/tex], we use logarithmic calculations. Consequently, the concentration of hydroxide ions is:
[tex]\[ [OH^-] \approx 0.00631 \, M \][/tex]
This numerical value can be compared to the given options:
1. [tex]\(1.58 \times 10^{-12} \, M\)[/tex]
2. [tex]\(6.31 \times 10^{-3} \, M\)[/tex]
3. [tex]\(2.20 \, M\)[/tex]
4. [tex]\(158 \, M\)[/tex]
Conclusion:
The concentration of hydroxide ions [tex]\([OH^-]\)[/tex] in the solution with a pH of 11.8 is [tex]\(6.31 \times 10^{-3} \, M\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{6.31 \times 10^{-3} \, M} \][/tex]
