Relationship between pH, pOH, hydrogen ion concentration, and hydroxide ion concentration in aqueous solutions.

Let’s work through this step by step.

We are given a diagram that shows the relationships between H⁺, OH⁻, pH, and pOH in water at 25°C. The key formulas shown are:

1. [H⁺] = 10^(-pH)
2. pH = -log[H⁺]
3. [OH⁻] = 10^(-pOH)
4. pOH = -log[OH⁻]
5. [H⁺][OH⁻] = 1 × 10⁻¹⁴ (this is the ion product of water, Kw)
6. pH + pOH = 14

These are all connected — if you know one value, you can find the others.

But wait — the user didn’t actually ask a specific question! They just uploaded an image with these relationships.

Since there’s no explicit problem to solve (like “find pH if [H⁺] = 0.001 M”), I need to assume what might be expected.

Looking at the diagram, it’s likely meant to help students understand how to convert between [H⁺], [OH⁻], pH, and pOH using those equations.

So perhaps the implied task is: “Explain how to use these relationships to go from any one value to the others.”

Let me demonstrate with an example.

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Suppose we’re told: [H⁺] = 1 × 10⁻³ M

Step 1: Find pH
→ pH = -log[H⁺] = -log(1 × 10⁻³) = 3

Step 2: Find pOH
→ Since pH + pOH = 14 → pOH = 14 - 3 = 11

Step 3: Find [OH⁻]
→ [OH⁻] = 10^(-pOH) = 10^(-11) = 1 × 10⁻¹¹ M

Check: [H⁺][OH⁻] = (10⁻³)(10⁻¹¹) = 10⁻¹⁴ ✔

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Another example: Suppose we’re told pOH = 5

Step 1: Find pH
→ pH = 14 - pOH = 14 - 5 = 9

Step 2: Find [H⁺]
→ [H⁺] = 10^(-pH) = 10⁻⁹ M

Step 3: Find [OH⁻]
→ [OH⁻] = 10^(-pOH) = 10⁻⁵ M

Check: (10⁻⁹)(10⁻⁵) = 10⁻¹⁴ ✔

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You can start from any point — [H⁺], [OH⁻], pH, or pOH — and use these formulas to get the other three values.

The key things to remember:
- pH and pOH add up to 14 (at 25°C).
- To go from concentration to log scale: take negative log.
- To go from log scale back to concentration: raise 10 to the negative power.

This system helps us describe how acidic or basic a solution is without dealing with tiny numbers like 0.0000001.

Final Answer:
The diagram shows how to interconvert [H⁺], [OH⁻], pH, and pOH using the relationships:
pH = -log[H⁺], pOH = -log[OH⁻], pH + pOH = 14, and [H⁺][OH] = 1×10⁻¹⁴.
Given any one value, you can calculate the other three using these formulas.