To determine which solution has the greatest number of hydroxide ions [tex]\([OH^-]\)[/tex], we need to use the pH values provided for each substance and calculate their corresponding hydroxide ion concentrations.
The pH scale is related to the concentration of hydrogen ions [tex]\([H^+]\)[/tex] in a solution. The relationship between pH and [tex]\([H^+]\)[/tex] is given by:
[tex]\[ pH = -\log[H^+] \][/tex]
Additionally, the relationship between [tex]\([H^+]\)[/tex] and [tex]\([OH^-]\)[/tex] in water at 25°C is given by the ion product of water:
[tex]\[ [H^+][OH^-] = 10^{-14} \][/tex]
Given the pH values for each substance, we can find the [tex]\([H^+]\)[/tex] concentration using:
[tex]\[ [H^+] = 10^{-pH} \][/tex]
Then we relate [tex]\([H^+]\)[/tex] to [tex]\([OH^-]\)[/tex] using:
[tex]\[ [OH^-] = \frac{10^{-14}}{[H^+]} \][/tex]
With these formulas in mind, let's calculate the hydroxide ion concentration for each substance.
1. Baking soda ([tex]\(pH = 9\)[/tex]):
[tex]\[ [H^+] = 10^{-9} \][/tex]
[tex]\[ [OH^-] = \frac{10^{-14}}{10^{-9}} = 10^{-5} \][/tex]
2. Milk ([tex]\(pH = 6\)[/tex]):
[tex]\[ [H^+] = 10^{-6} \][/tex]
[tex]\[ [OH^-] = \frac{10^{-14}}{10^{-6}} = 10^{-8} \][/tex]
3. Tomato juice ([tex]\(pH = 3.5\)[/tex]):
[tex]\[ [H^+] = 10^{-3.5} \][/tex]
[tex]\[ [OH^-] = \frac{10^{-14}}{10^{-3.5}} = 10^{-10.5} \approx 3.162 \times 10^{-11} \][/tex]
4. Vinegar ([tex]\(pH = 2\)[/tex]):
[tex]\[ [H^+] = 10^{-2} \][/tex]
[tex]\[ [OH^-] = \frac{10^{-14}}{10^{-2}} = 10^{-12} \][/tex]
Summarizing the hydroxide ion concentrations:
- Baking soda: [tex]\( [OH^-] = 10^{-5} \)[/tex]
- Milk: [tex]\( [OH^-] = 10^{-8} \)[/tex]
- Tomato juice: [tex]\( [OH^-] = 3.162 \times 10^{-11} \)[/tex]
- Vinegar: [tex]\( [OH^-] = 10^{-12} \)[/tex]
Comparing these values, we see that:
[tex]\[ 10^{-5} > 10^{-8} > 3.162 \times 10^{-11} > 10^{-12} \][/tex]
Thus, baking soda, with a [tex]\(pH\)[/tex] of 9, has the greatest number of hydroxide ions.
