To determine which solution has the greatest number of hydroxide ions [tex]\([OH^-]\)[/tex], we need to understand the relationship between pH and pOH. The pH of a solution is a measure of the concentration of hydrogen ions [tex]\([H^+]\)[/tex] in the solution, while pOH is a measure of the concentration of hydroxide ions [tex]\([OH^-]\)[/tex]. The key relationships we will use are:
1. [tex]\( \text{pH} + \text{pOH} = 14 \)[/tex]
2. [tex]\( \text{pOH} = 14 - \text{pH} \)[/tex]
3. [tex]\( [OH^-] = 10^{-\text{pOH}} \)[/tex]
Let's calculate the pOH and [tex]\([OH^-]\)[/tex] for each solution:
### Baking Soda
- pH = 9
- pOH = [tex]\( 14 - 9 = 5 \)[/tex]
- [tex]\( [OH^-] = 10^{-5} \)[/tex]
### Milk
- pH = 6
- pOH = [tex]\( 14 - 6 = 8 \)[/tex]
- [tex]\( [OH^-] = 10^{-8} \)[/tex]
### Tomato Juice
- pH = 3.5
- pOH = [tex]\( 14 - 3.5 = 10.5 \)[/tex]
- [tex]\( [OH^-] = 10^{-10.5} \)[/tex]
### Vinegar
- pH = 2
- pOH = [tex]\( 14 - 2 = 12 \)[/tex]
- [tex]\( [OH^-] = 10^{-12} \)[/tex]
Now, let's compare the values of [tex]\([OH^-]\)[/tex]:
- Baking Soda: [tex]\( [OH^-] = 10^{-5} \)[/tex]
- Milk: [tex]\( [OH^-] = 10^{-8} \)[/tex]
- Tomato Juice: [tex]\( [OH^-] = 10^{-10.5} \)[/tex]
- Vinegar: [tex]\( [OH^-] = 10^{-12} \)[/tex]
Since [tex]\(10^{-5}\)[/tex] is the largest value among the hydroxide ion concentrations calculated, baking soda has the greatest number of hydroxide ions.
### Conclusion:
The solution with the greatest number of hydroxide ions is baking soda.
