Grade 11

Advanced

8 min

Lesson 7 of 12

The pH and pOH Scales

Not Started

Mastering the logarithmic scales used to measure the acidity and alkalinity of solutions.

Did you know that a change of just one unit on the pH scale represents a tenfold difference in acidity? That means a pH 4 solution is ten times more acidic than pH 5, and a hundred times more acidic than pH 6!

Learning Objectives

1.By the end of this lesson, you will be able to calculate pH, pOH, [H+], and [OH-] using logarithmic and exponential functions.
2.You will understand the autoionization of water and the significance of the Kw constant at 25 degrees Celsius.
3.You will be able to relate the magnitude of pH values to the relative concentrations of hydronium and hydroxide ions.

The Secret Life of Water: Autoionization

Even in a sample of pure water, a tiny fraction of molecules react with each other. This process is called autoionization. One water molecule pulls a hydrogen ion (

H^+

) from another, creating a hydronium ion (

H_3O^+

) and a hydroxide ion (

OH^-

). In chemistry, we often simplify

H_3O^+

to just

H^+

. At

25^{\circ}C

, the product of these ion concentrations is always constant. This is known as the ion-product constant for water, or

K_w

. The relationship is expressed as:

K_w = [H^+][OH^-] = 1.0 \times 10^{-14}

In pure water, the concentrations are equal:

[H^+] = [OH^-] = 1.0 \times 10^{-7} M

. This balance is what we define as neutral.

Quick Check

If the concentration of [H+] increases in a solution, what must happen to the concentration of [OH-] to keep Kw constant?

Remember that their product must always equal

1.0 \times 10^{-14}

Answer

The concentration of [OH-] must decrease.

Defining pH and pOH

Because ion concentrations are often incredibly small (like

0.0000001 M

), scientists use a logarithmic scale to make the numbers manageable. The 'p' in pH stands for 'power' or 'potential.' By definition, pH is the negative logarithm of the molar hydronium ion concentration. Similarly, pOH measures the hydroxide concentration. Because of the

K_w

relationship, the sum of pH and pOH in any aqueous solution at

25^{\circ}C

is always 14. This provides a simple bridge to convert between acidity and alkalinity:

pH = -\log[H^+]

pOH = -\log[OH^-]

pH + pOH = 14.00

Calculate the pH of a $0.025 M$ solution of $HCl$ (a strong acid that ionizes completely).

1. Identify $[H^+]$ : Since $HCl$ is a strong monoprotic acid, $[H^+] = 0.025 M$ . 2. Apply the formula: $pH = -\log(0.025)$ . 3. Calculate: $pH \approx 1.60$ .

Quick Check

What is the pOH of a solution if the pH is 4.5?

Use the relationship

pH + pOH = 14

Answer

9.5

Reversing the Log: Finding Concentration

To find the actual concentration of ions from a pH value, we must perform the inverse of the logarithm. In mathematics, the inverse of a base-10 log is an exponent with base 10. If you are given a pH, you can find the concentration using the formula:

[H^+] = 10^{-pH}

A critical rule for significant figures in logarithms: the number of decimal places in the pH value determines the number of significant figures in the concentration. For example, a pH of 3.45 (two decimal places) results in a concentration with two significant figures (

3.5 \times 10^{-4} M

A cleaning solution has a pH of 11.40. What is the hydroxide ion concentration $[OH^-]$ ?

1. Find pOH first: $pOH = 14.00 - 11.40 = 2.60$ . 2. Use the inverse log formula: $[OH^-] = 10^{-pOH}$ . 3. Calculate: $[OH^-] = 10^{-2.60} = 2.5 \times 10^{-3} M$ .

If $10.0 mL$ of $0.10 M$ $NaOH$ is diluted to a final volume of $1.0 L$ , what is the final pH?

1. Calculate initial moles of $OH^-$ : $n = M \times V = 0.10 M \times 0.010 L = 0.0010 mol$ . 2. Calculate new concentration: $[OH^-] = \frac{0.0010 mol}{1.0 L} = 1.0 \times 10^{-3} M$ . 3. Find pOH: $pOH = -\log(1.0 \times 10^{-3}) = 3.00$ . 4. Convert to pH: $pH = 14.00 - 3.00 = 11.00$ .

Key Takeaways

1The autoionization of water creates a constant balance where $[H^+][OH^-] = 1.0 \times 10^{-14}$ at $25^{\circ}C$ .
2pH and pOH are logarithmic scales that sum to 14.00.
3A change of 1 pH unit represents a 10-fold change in ion concentration.
4To reverse a pH value into a concentration, use the formula $[H^+] = 10^{-pH}$ .

Quick Check

Multiple Choice

If a solution has a $[H^+]$ of $1.0 \times 10^{-9} M$ , what is the pH?

Multiple Choice

Which solution is the most basic?

True/False

In a neutral solution at $25^{\circ}C$ , the pH is always 7.0.

What's Next?

Review Tomorrow

In 24 hours, try to write down the four main conversion formulas between pH, pOH, [H+], and [OH-] from memory.

Practice Activity

Look at the labels of household liquids (vinegar, bleach, juice). Try to estimate their [H+] concentration based on their known approximate pH values.

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The pH and pOH Scales

Learning Objectives

The Secret Life of Water: Autoionization

Defining pH and pOH

Reversing the Log: Finding Concentration

Key Takeaways

Quick Check

What's Next?

The pH and pOH Scales

Learning Objectives

The Secret Life of Water: Autoionization

Defining pH and pOH

Reversing the Log: Finding Concentration

Key Takeaways

Quick Check

What's Next?