Calculate pH from an exponent

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. Formula: a. Variable key: a = positive exponent a in hydronium 10^(-a) mol/L
• Distinct worked inputs and result: A distinct idealized concentration 10^-7 mol/L gives pH 7 because -log10(10^-7)=7.
• Assessment case 1: Supplied case 1: positive exponent a in hydronium 10^(-a) mol/L=2, using the explicitly named quantities. If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. What result follows?
• Assessment case 2: Supplied case 2: positive exponent a in hydronium 10^(-a) mol/L=3, using the explicitly named quantities. If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. What result follows?
• Assessment case 3: Supplied case 3: positive exponent a in hydronium 10^(-a) mol/L=4, using the explicitly named quantities. If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. What result follows?
• Assessment case 4: Supplied case 4: positive exponent a in hydronium 10^(-a) mol/L=5, using the explicitly named quantities. If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. What result follows?
• Assessment case 5: Supplied case 5: positive exponent a in hydronium 10^(-a) mol/L=6, using the explicitly named quantities. If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. What result follows?
• Assessment case 6: Supplied case 6: positive exponent a in hydronium 10^(-a) mol/L=8, using the explicitly named quantities. If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. What result follows?

Learn the idea

For these dilute idealized aqueous examples, pH is the negative base-ten logarithm of hydronium concentration. A lower pH represents a higher hydronium concentration; the scale is logarithmic.

If hydronium concentration is 10 raised to negative a mol/L, model pH equals a. The formula in the supplied model is a. Variable key: a = positive exponent a in hydronium 10^(-a) mol/L. Use the negative logarithm, not concentration multiplied by ten. A one-unit pH difference corresponds to a tenfold concentration factor.

A distinct idealized concentration 10^-7 mol/L gives pH 7 because -log10(10^-7)=7. These are idealized educational values. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Changed-input task: use the same stated model with positive exponent a in hydronium 10^(-a) mol/L=3. Expected result: 3 pH units. Explain what changes and keep this assumption: These are idealized educational values.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.