To determine which solution has the greatest number of hydroxide ions, let's go through the calculations step-by-step. We'll use the given pH values to find the corresponding pOH values and then calculate the concentration of hydroxide ions [tex]\([OH^-]\)[/tex] for each solution.
1. Understanding the relationship between pH and pOH:
[tex]\[
pH + pOH = 14
\][/tex]
From this equation, we can find the pOH for each solution.
2. Given pH values:
- Baking soda: [tex]\( \text{pH} = 9 \)[/tex]
- Milk: [tex]\( \text{pH} = 6 \)[/tex]
- Tomato juice: [tex]\( \text{pH} = 3.5 \)[/tex]
- Vinegar: [tex]\( \text{pH} = 2 \)[/tex]
3. Calculate the pOH values:
- Baking soda:
[tex]\[
\text{pOH} = 14 - 9 = 5
\][/tex]
- Milk:
[tex]\[
\text{pOH} = 14 - 6 = 8
\][/tex]
- Tomato juice:
[tex]\[
\text{pOH} = 14 - 3.5 = 10.5
\][/tex]
- Vinegar:
[tex]\[
\text{pOH} = 14 - 2 = 12
\][/tex]
4. Calculate the hydroxide ion concentration [tex]\([OH^-]\)[/tex]:
The concentration of hydroxide ions [tex]\([OH^-]\)[/tex] is given by:
[tex]\[
[OH^-] = 10^{-\text{pOH}}
\][/tex]
- Baking soda:
[tex]\[
[OH^-] = 10^{-5} = 1 \times 10^{-5}
\][/tex]
- Milk:
[tex]\[
[OH^-] = 10^{-8} = 1 \times 10^{-8}
\][/tex]
- Tomato juice:
[tex]\[
[OH^-] = 10^{-10.5} = 3.162277660168379 \times 10^{-11}
\][/tex]
- Vinegar:
[tex]\[
[OH^-] = 10^{-12} = 1 \times 10^{-12}
\][/tex]
5. Compare the hydroxide ion concentrations:
- Baking soda: [tex]\( 1 \times 10^{-5} \)[/tex]
- Milk: [tex]\( 1 \times 10^{-8} \)[/tex]
- Tomato juice: [tex]\( 3.162277660168379 \times 10^{-11} \)[/tex]
- Vinegar: [tex]\( 1 \times 10^{-12} \)[/tex]
We see that the concentration of hydroxide ions [tex]\([OH^-]\)[/tex] is greatest in the baking soda solution.
Therefore, the solution with the greatest number of hydroxide ions is baking soda with a concentration of [tex]\(1 \times 10^{-5} \)[/tex] M.
