Answer :
To determine the concentration of [tex]\( OH^- \)[/tex] ions in an ammonia solution with a pH of 11.8, we will follow several steps using the provided formulas.
### Step 1: Calculate pOH
First, we use the relation between pH and pOH:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Given that the pH is 11.8, we can calculate the pOH as follows:
[tex]\[ \text{pOH} = 14 - \text{pH} \][/tex]
[tex]\[ \text{pOH} = 14 - 11.8 \][/tex]
[tex]\[ \text{pOH} = 2.2 \][/tex]
### Step 2: Calculate [tex]\([OH^-]\)[/tex] ion concentration
Next, we use the formula that relates pOH to the concentration of hydroxide ions [tex]\([OH^-]\)[/tex]:
[tex]\[ [OH^-] = 10^{-\text{pOH}} \][/tex]
With pOH = 2.2, the concentration of [tex]\( OH^- \)[/tex] is:
[tex]\[ [OH^-] = 10^{-2.2} \][/tex]
The value [tex]\( 10^{-2.2} \)[/tex] can be calculated precisely:
[tex]\[ 10^{-2.2} \approx 0.00631 \][/tex]
### Step 3: Interpret the result
Hence, the concentration of [tex]\( OH^- \)[/tex] ions in the solution is approximately [tex]\( 0.00631 \, M \)[/tex].
So, the correct answer is:
[tex]\[ 6.31 \times 10^{-3} \, M \][/tex]
### Step 1: Calculate pOH
First, we use the relation between pH and pOH:
[tex]\[ \text{pH} + \text{pOH} = 14 \][/tex]
Given that the pH is 11.8, we can calculate the pOH as follows:
[tex]\[ \text{pOH} = 14 - \text{pH} \][/tex]
[tex]\[ \text{pOH} = 14 - 11.8 \][/tex]
[tex]\[ \text{pOH} = 2.2 \][/tex]
### Step 2: Calculate [tex]\([OH^-]\)[/tex] ion concentration
Next, we use the formula that relates pOH to the concentration of hydroxide ions [tex]\([OH^-]\)[/tex]:
[tex]\[ [OH^-] = 10^{-\text{pOH}} \][/tex]
With pOH = 2.2, the concentration of [tex]\( OH^- \)[/tex] is:
[tex]\[ [OH^-] = 10^{-2.2} \][/tex]
The value [tex]\( 10^{-2.2} \)[/tex] can be calculated precisely:
[tex]\[ 10^{-2.2} \approx 0.00631 \][/tex]
### Step 3: Interpret the result
Hence, the concentration of [tex]\( OH^- \)[/tex] ions in the solution is approximately [tex]\( 0.00631 \, M \)[/tex].
So, the correct answer is:
[tex]\[ 6.31 \times 10^{-3} \, M \][/tex]