Strong Acid & Base pH Simulator

Watch two patterns as you drag. First, every tenfold change in concentration moves the pH by 1 unit, until the solution is very dilute. Second, pH and pOH always add to 14.00 and [H⁺] times [OH^-] is always $1.0 \times 10^{-14}$. At the dilute end the simulator includes water's own ionization, so a strong acid approaches pH 7 from below and never becomes basic. At $1.00 \times 10^{-6}$ M acid the pH reads 6.00, and at $1.00 \times 10^{-8}$ M, the lowest setting, it reads 6.98, not 8.

A strong acid or base ionizes completely, so for a monoprotic strong acid $[\text{H}^+] = C$ and for a strong base like NaOH $[\text{OH}^-] = C$. Then $$\text{pH} = -\log[\text{H}^+] \qquad \text{pOH} = -\log[\text{OH}^-]$$

At 25 °C, water's ionization constant links the two: $$K_w = [\text{H}^+][\text{OH}^-] = 1.0 \times 10^{-14} \qquad \text{pH} + \text{pOH} = 14.00$$ To go backward, $[\text{H}^+] = 10^{-\text{pH}}$.

For very dilute solutions the H⁺ from water is no longer negligible. Combining charge balance with $K_w$ gives $[\text{H}^+]^2 - C[\text{H}^+] - K_w = 0$, whose positive root is what the simulator calculates. When C is above about $10^{-6}$ M the correction is tiny and $[\text{H}^+] = C$ is fine.

A base such as Ba(OH)₂ or Ca(OH)₂ releases two OH^- per formula unit, so $[\text{OH}^-] = 2C$. The simulator's slider is the concentration of the ion that the solute releases, so set it to 2C for these bases.

Question. Find the pH of (a) 0.020 M HCl and (b) 0.025 M Ba(OH)₂ at 25 °C.

(a) HCl ionizes completely, so $[\text{H}^+] = 0.020$ M and $\text{pH} = -\log(0.020) = 1.70$. Then $\text{pOH} = 14.00 - 1.70 = 12.30$ and $[\text{OH}^-] = \dfrac{1.0 \times 10^{-14}}{0.020} = 5.0 \times 10^{-13}$ M.

(b) Each Ba(OH)₂ gives two OH^-, so $[\text{OH}^-] = 2 \times 0.025 = 0.050$ M. $\text{pOH} = -\log(0.050) = 1.30$ and $\text{pH} = 14.00 - 1.30 = 12.70$.

Check it in the simulator. Choose Strong acid and drag to 2.00e-2 M: the readouts show pH 1.70, pOH 12.30 and [OH^-] = 5.01e-13 (the slider value is $10^{-1.70}$, a hair under 0.020). For part (b), choose Strong base and drag to 5.01e-2 M, the setting for 0.050 M OH^-: pOH reads 1.30 and pH reads 12.70.

Dilution. Diluting the HCl tenfold, to 0.0020 M, raises the pH by 1 to 2.70. Diluting a strong acid enormously, say to $1 \times 10^{-8}$ M, does not give pH 8: including water's H⁺, the quadratic gives $[\text{H}^+] = 1.05 \times 10^{-7}$ M and a pH of 6.98. Drag the slider down to 1.00e-8 M to see the simulator give the same 6.98.

Topic 8.2 calculations are the foundation for the rest of Unit 8: the starting pH of a titration of a strong acid, the pH after mixing a strong acid with a strong base (find the excess moles, divide by the total volume, then take the log), and comparisons with weak acids of the same concentration. You should know the common strong acids (HCl, HBr, HI, HNO₃, HClO₄, H₂SO₄ for its first proton) and strong bases (group 1 hydroxides and the heavier group 2 hydroxides).