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# Calculating pH of Acids and Bases

## Introduces and gives examples of pH calculation from the concentration of strong acids or bases

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Calculating pH of Acids and Bases

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#### How do you raise tropical fish?

Many people enjoy having tropical fish in their homes or businesses. These brightly-colored creatures are relaxing to watch, but do require a certain amount of maintenance in order for them to survive. Tap water is usually too alkaline when it comes out of the faucet, so some adjustments need to be made. The pH of the water will change over time while it is in the tank, which means you need to test it every so often. Then you get to be a chemist for your fish.

### Calculating pH of Acids and Bases

Calculation of pH is simple when there is a 1 × 10power problem. However, in real life that is rarely the situation. If the coefficient is not equal to 1, a calculator must be used to find the pH. For example, the pH of a solution with [H+] = 2.3 × 10-5 M  can be found as shown below.

pH = -log[2.3 × 10-5] = 4.64

When the pH of a solution is known, the concentration of the hydrogen ion can be calculated. The inverse of the logarithm (or antilog) is the 10x key on a calculator.

[H+] = 10-pH

For example, suppose that you have a solution with a pH of 9.14. To find the [H+] use the 10x key.

[H+] = 10-pH = 10-9.14 = 7.24 × 10-10 M

#### Hydroxide Ion Concentration and pH

As we saw earlier, the hydroxide ion concentration of any aqueous solution is related to the hydrogen ion concentration through the value of \begin{align*}K_w\end{align*}. We can use that relationship to calculate the pH of a solution of a base.

#### Sample Problem: The pH of a Base

Sodium hydroxide is a strong base. Find the pH of a solution prepared by dissolving 1.0 g of NaOH into enough water to make 1.0 L of solution.

Step 1: List the known values and plan the problem.

Known

• mass NaOH = 1.0 g
• molar mass NaOH = 40.00 g/mol
• volume solution = 1.0 L
• \begin{align*}K_w= 1.0 \times 10^{-14}\end{align*}

Unknown

• pH of solution = ?

First, convert the mass of NaOH to moles. Second, calculate the molarity of the NaOH solution. Because NaOH is a strong base and is soluble, the [OH] will be equal to the concentration of the NaOH. Third, use \begin{align*}K_w\end{align*} to calculate the [H+] in the solution. Lastly, calculate the pH.

Step 2: Solve.

\begin{align*}& 1.00 \ {\cancel{\text{g NaOH}}} \times \frac{1 \ \text{mol NaOH}}{40.00 \ {\cancel{\text{g NaOH}}}}=0.025 \ \text{mol NaOH} \\ & \text{Molarity}=\frac{0.025 \ \text{mol NaOH}}{1.00 \ \text{L}}=0.025 \ \text{M NaOH}=0.025 \ \text{M OH}^- \\ & \left [ \text{H}^+ \right ]=\frac{K_w}{\left [ \text{OH}^- \right ]}=\frac{1.0 \times 10^{-14}}{0.025 \ \text{M}}=4.0 \times 10^{-13} \ \text{M} \\ & \text{pH}=- \log \left [ \text{H}^+ \right ]=- \log(4.0 \times 10^{-13})=12.40\end{align*}

The solution is basic and so its pH is greater than 7. The reported pH is rounded to two decimal places because the original mass and volume has two significant figures.

### Summary

• Calculations of pH for acidic and basic solutions are described.

### Review

1. What is the pH of a 4.5 × 10-3 M HI solution?
2. What is the pH of a 3.67 × 10-5 M NaBr solution?
3. If we have a weak base with a low ionization constant, can we assume that the [OH-] in the solution is equal to the concentration of the base?

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