pH Calculations - Bases

Calculating the pH of bases requires an extra step, as they dissociate with water to make hydroxide ions, OH^-, instead of hydronium ions, H₃O⁺.

WATER DISSOCIATION CONSTANT, K_W

The extra step requires us to have an understanding of the dissociation of water:

H₂O + H₂O ⇌ H₃O⁺ + OH^-

In pure water, the pH = 7.0, so the concentration of hydronium ions is 10^-7 mol L^-1. As the number of moles of hydronium ions is the same as the number of moles of hydroxide ions, the concentration of hydroxide ions is also 10^-7 mol L^-1.

Therefore, the equilibrium constant for this (called K_W) is 10^-7 × 10^-7 = 10^-14. This will become very important shortly.

K_W = [H₃O⁺][OH^-] = 10^-14

Acids increase the concentration of hydronium ions, so shift this equilibrium to the left, reducing the concentration of hydroxide ions, to return the equilibrium constant to 10^-14.

Likewise, bases increase the concentration of hydroxide ions, so shift this equilibrium to the left, reducing the concentration of hydronium ions, to return the equilibrium constant to 10^-14.

CALCULATING HYDRONIUM ION CONCENTRATION

This is the key extra step, and uses the water dissociation constant. This assumes that you know the hydronium ion concentration.

OPTION ONE: Using K_W

1. Rearrange  K_W = [H₃O⁺][OH^-]

[H₃O⁺] = K_W/[OH^-] = 10^-14/[OH^-]

2. Now, you have the hydronium ion concentration, so can calculate pH:

pH = ^-log₁₀[H₃O⁺]

OPTION TWO: Using pOH

1. Calculate pOH:

pOH = ^-log₁₀[OH^-]

2. Use pK_W to find the pH:

pH = pK_W - pOH = 14 - pOH

pH Calculations - Acids

The hydronium ion concentration, [H₃O⁺], can be used to determine the pH of a solution:

pH = ^- log [H₃O⁺]

For example:

The pH of a solution with a hydronium ion concentration of 8.2 × 10^-5 mol L^-1 will be 4.09 (acidic)

The pH of a solution with a hydronium ion concentration of 5.9 × 10^-9 mol L^-1 will be 8.23 (basic/alkaline)

pH of a Strong Acid

Recall that our strong acids are:

• HCl
• HNO₃
• H₂SO₄

The pH of the first two is simply the concentration of the acid, because they fully dissociate to form one hydronium ion per acid molecule:

HCl + H₂O → H₃O⁺ + Cl^-

Therefore, if we had 0.150 mol L^-1 of HCl, the pH will be 0.82 (yes, they can be lower than 1.0)

Sulfuric acid is diprotic, donating two hydrogen ions when it dissociates:

H₂SO₄ + 2H₂O → 2H₃O⁺ + SO₄^2-

Therefore, if we had 0.150 mol L^-1 of HCl, the pH will be 0.52, not 0.82 (like HCl was).

pH of a Weak Acid/Acidic Salts

Because these partially dissociate, we need to be given the hydronium ion concentration to calculate its pH. This is the process shown at the top of this blog post.

Finding [H₃O⁺] from pH

If we know the pH, we can very easily calculate the hydronium ion concentration:

[H₃O⁺] = 10 ^-pH

For example:

The hydronium ion concentration of a solution with a pH of 4.77 is 1.70 × 10^-5 mol L^-1.

The hydronium ion concentration of a solution with a pH of 8.50 is 3.16 × 10^-9 mol L^-1.

Polyprotic Acids and Amphiprotic Species

POLYPROTIC ACIDS

Most of the acids we work with can only donate one proton (H⁺ ion). However, some acids have more than one hydrogen ion that can be donated when they react (or dissociate in water).

For example, sulfuric acid:

H₂SO₄ + 2H₂O → SO₄^2- + 2H₃O⁺

However, this is not the whole picture.

First, sulfuric acid loses just one hydrogen ion to become the hydrogen sulfate ion. This ion will become important shortly... it can act as either a Brønsted-Lowry acid or a Brønsted-Lowry base!!

H₂SO₄ + H₂O ⇋ HSO₄^- + H₃O⁺

Secondly, the hydrogen sulfate ion loses a hydrogen ion to complete the dissociation of the acid:

HSO₄^- + H₂O ⇋ SO₄^2- + H₃O⁺

AMPHIPROTIC SPECIES

Amphiprotic means "can act as both an acid or as a base". Water is the amphiprotic species you have met before:

H₂O + H₂O → OH^- + H₃O⁺

The red water molecule is acting as a Brønsted-Lowry acid - it is losing a proton to become the hydroxide ion.

The blue water molecule is acting as a Brønsted-Lowry base - it is gaining a proton to become the hydronium ion.

Hydrogen sulfate can also do this because:

• it is negatively charged, so can attract a hydrogen ion (proton). Opposites attract.
• it also has a hydrogen ion, which it can lose.

Acting as an acid:

HSO₄^- + H₂O ⇋ SO₄^2- + H₃O⁺

^{Acting as a base:}

HSO₄^- + H₂O ⇋ H₂SO₄ + OH^-

Salts

When an acid and a base react, we call it a neutralisation reaction. The products are water and a salt. Until now, we have looked at strong acids (like HCl) reacting with strong bases (like NaOH). The salt is neutral (pH = 7), so the final (salt) solution is neutral.

SOURCE: https://byjus.com/chemistry/neutralization-reaction/

However, this is not the case when we use a weak acid or a weak base. The salts themselves react with water, so affect the pH. For example, when we react hydrochloric acid (strong acid) with ammonia (weak base), the product is acidic ammonium chloride.

SOURCE: http://acids-are-pretty-basic.weebly.com/conjugate-acids-and-bases.html

We know it is acidic because one of the ions in the salt, ammonium, can act as a weak acid.

We see that the ammonium ion increases the concentration of hydronium ions, so making the solution more acidic (lowering the pH).

NOTE; The chloride ion does not react with water, so has no effect upon pH.

Learning Outcomes

• Identify the ion in the salt that affects the pH
• Use an equilibrium equation to show how this ion reacts with water
• Use the equation to explain the nature of the salt (acidic or alkaline)