To determine which statements are correct given the pOH of the solution is 6.0, let's follow these steps:
### Step 1: Calculate pH from pOH
Using the relationship between pH and pOH, which is given by:
[tex]\[ pH + pOH = 14 \][/tex]
Substituting the given value of pOH:
[tex]\[ pH + 6.0 = 14 \][/tex]
Solving for pH:
[tex]\[ pH = 14 - 6.0 \][/tex]
[tex]\[ pH = 8.0 \][/tex]
### Step 2: Calculate the concentration of [tex]\([OH^-]\)[/tex] ions from pOH
The relationship between pOH and the concentration of hydroxide ions ([tex]\([OH^-]\)[/tex]) is given by:
[tex]\[ pOH = -\log [OH^-] \][/tex]
Rewriting this equation in terms of [tex]\([OH^-]\)[/tex]:
[tex]\[ [OH^-] = 10^{-pOH} \][/tex]
Substituting the given value of pOH:
[tex]\[ [OH^-] = 10^{-6.0} \][/tex]
Calculating the concentration:
[tex]\[ [OH^-] = 10^{-6} \][/tex]
[tex]\[ [OH^-] = 1.0 \times 10^{-6} \, \text{M} \][/tex]
### Step 3: Validate the given statements
Now, let's check each statement:
1. Statement: The pH of the solution is 20.0.
- From our calculation, [tex]\[ pH = 8.0 \][/tex].
- This statement is incorrect.
2. Statement: The concentration of [tex]\([OH^-]\)[/tex] ions is [tex]\(1.0 \times 10^{-8} \, \text{M}\)[/tex].
- From our calculation, [tex]\[ [OH^-] = 1.0 \times 10^{-6} \, \text{M} \][/tex].
- This statement is incorrect.
3. Statement: The concentration of [tex]\([OH^-]\)[/tex] ions is [tex]\(1.0 \times 10^6 \, \text{M}\)[/tex].
- From our calculation, [tex]\[ [OH^-] = 1.0 \times 10^{-6} \, \text{M} \][/tex], which is vastly different.
- This statement is incorrect.
4. Statement: The pH of the solution is 8.0.
- From our calculation, [tex]\[ pH = 8.0 \][/tex].
- This statement is correct.
### Conclusion
The correct statement given the pOH of the solution is 6.0 is:
- The pH of the solution is 8.0.
