Question

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. What is the approximate pH of a solution if the concentration of hydrogen ions is 5.0 × 10–4 moles per liter?

Answer 1

pH is a measure of how acidic or basic a chemical solution is. The pH scale runs from 0 to 14—a value of seven is considered neutral, less than seven acidic, and greater than seven basic.

pH is the negative base 10 logarithm ("log" on a calculator) of the hydrogen ion concentration of a solution. To calculate it, take the log of a given hydrogen ion concentration and reverse the sign. See more information about the pH formula below.

Here's a more in-depth review of how to calculate pH and what pH means with respect to hydrogen ion concentration, acids, and bases.

Review of Acids and Bases

There are several ways to define acids and bases, but pH specifically only refers to hydrogen ion concentration and is applied to aqueous (water-based) solutions. When water dissociates, it yields a hydrogen ion and a hydroxide. See this chemical equation below.

H2O ↔ H+ + OH-

When calculating pH, remember that [ ] refers to molarity, M. Molarity is expressed in units of moles of solute per liter of solution. If you are given concentration in any other unit than moles (mass percent, molality, etc.), convert it to molarity in order to use the pH formula.

The relationship between pH and molarity can be expressed as:

Kw = [H+][OH-] = 1x10-14 at 25°C

for pure water [H+] = [OH-] = 1x10-7

Kw is the dissociation constant of water

Acidic Solution: [H+] > 1x10-7

Basic Solution: [H+] < 1x10-7

How to Calculate pH and [H+]

The equilibrium equation yields the following formula for pH:

pH = -log10[H+]

[H+] = 10-pH

In other words, pH is the negative log of the molar hydrogen ion concentration or the molar hydrogen ion concentration equals 10 to the power of the negative pH value. It's easy to do this calculation on any scientific calculator because more often than not, these have a "log" button. This is not the same as the "ln" button, which refers to the natural logarithm.

pH and pOH

You can easily use a pH value to calculate pOH if you recall:

pH + pOH = 14

This is particularly useful if you're asked to find the pH of a base since you'll usually solve for pOH rather than pH.

Example Calculation Problems

Try these sample problems to test your knowledge of pH.

Example 1

Calculate the pH for a specific [H+]. Calculate pH given [H+] = 1.4 x 10-5 M

Answer:

pH = -log10[H+]

pH = -log10(1.4 x 10-5)

pH = 4.85

Example 2

Calculate [H+] from a known pH. Find [H+] if pH = 8.5

Answer:

[H+] = 10-pH

[H+] = 10-8.5

[H+] = 3.2 x 10-9 M

Example 3

Find the pH if the H+ concentration is 0.0001 moles per liter.

Here it helps to rewrite the concentration as 1.0 x 10-4 M because this makes the formula: pH = -(-4) = 4. Or, you could just use a calculator to take the log. This gives you:

Answer:

pH = - log (0.0001) = 4

Usually, you aren't given the hydrogen ion concentration in a problem but have to find it from a chemical reaction or acid concentration. The simplicity of this will depend on whether you have a strong acid or a weak acid. Most problems asking for pH are for strong acids because they completely dissociate into their ions in water. Weak acids, on the other hand, only partially dissociate, so at equilibrium, a solution contains both the weak acid and the ions into which it dissociates.

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Answer 2

The value of PH for the solution = 3.301

Step-by-step explanation:

We know that PH value is given by

⇒ PH = - ㏒ [$H^{+}$]

where  $H^{+}$ = concentration of hydrogen ions in the solution = 0.0005 $\frac{moles}{ltr}$

⇒ PH = - ㏒ [0.0005]

⇒ PH = - (- 3.301)

⇒ PH = + 3.301

This is the value of PH for the solution.