Sulfuric acid is a
strong acid and a dibasic acid which is highly used in analytical laboratories and
chemical industry. Sulfuric acid solution gives
low pH values in aqueous solutions. When concentration of H_{2}SO_{4} is known in units of mol dm^{-3},
pH value can be calculated easily by the pH equation. In this tutorial, we will teach you how to calculate pH of Sulfuric acid
by hand and also how to use our online calculator to check your answer.

It's straight forward to say that Sulfuric acid is a strong acid. But, in most of the textbooks define Sulfuric acid
in a different aspect because there are two releasable H^{+} ions to the water.

- Definition 1: First hydrogen atom is completely dissociated and second hydrogen atom is partially dissociated. Therefore,
second dissociation reaction is a reversible reaction and comes to a equilibrium status. This is the most accurate
definition for the dissociation sulfuric acid.
- Definition 2: Both hydrogen atoms in Sulfuric acid molecule are completely dissociated to two H
^{+}cations.

However, Sulfuric acid is a strong acid and gives higher H^{+} ion concentration in the aqueous solution. Usually dilute
sulfuric acid shows low pH values like Hydrochloric acid
(HCl) and Nitric acid (HNO_{3}).

We have provided you two calculator options to calculate pH of Sulfuric acid for both definitions.

As explained earlier, there are two definitions for calculating the pH value of Sulfuric acid. In this section, we will see how to calculate pH value in both ways.

- Definition 1: First hydrogen atom is completely dissociated and second hydrogen atom is partially dissociated. Therefore,
second dissociation reaction is a reversible reaction and comes to a equilibrium status. This is the most accurate
definition for the dissociation sulfuric acid.
- Definition 2: Both hydrogen atoms in Sulfuric acid molecule are completely dissociated to two H
^{+}cations.

Write the both complete dissociation reaction and partial dissociation reaction. Then, write down the dissociated concentrations and equilibrium concentrations of each constituent.

Because H_{2}SO_{4} is a dibasic acid, Sulfuric acid can give two H^{+} ions. That means, one sulfuric acid
molecule can reacts with two hydroxyl ions.

H_{2}SO_{4} → 2H^{+} + SO_{4}^{2-}

*H ^{+} ions can be expressed as H_{3}O^{+} ions.*

According to the stoichiometry, concentration of H^{+} ions is twice as the H_{2}SO_{4} concentration.

[H^{+}] = 2 * [H_{2}SO_{4}]

Substitute H^{+} concentration to the pH equation.

pH = -log_{10}[H^{+}_{(aq)}]

We are going to tabulate pH values of some sulfuric acid solutions with their concentrations. These values are theoretical and may have different from slightly from an actual acid solution. For this tabulation, we consider the best definition available for Sulfuric acid, first hydrogen atom is completely dissociated and second hydrogen atom is partially dissociated.

Concentration of sulfuric acid in mol dm^{-3} |
pH |
---|---|

1 | 0 |

0.1 | 0.96 |

0.05 | 1.22 |

0.01 | 1.7 |

- 0.1 M HCl
- 0.06 M H
_{2}SO_{4} - 0.11 M CH
_{3}COOH - 0.11 M HNO
_{3}

In above list, four acids are given. From those acids, HCl, H_{2}SO_{4} and HNO_{3} are strong acids and CH_{3}COOH is the only weak acid.

Any acid's pH value decreases when concentration of H+ ions given by the acid increases. Though CH_{3}COOH concentration is high, its pH value is higher because it is a weak acid give a very low H+ ions to water. So CH_{3}COOH can be removed from correct choices.

*Now, which solution will give higher H+ ion concentration.*

Sulfuric acid gives 0.12 M H+ ion concentration which is higher than H^{+} ion concentration of HCl and HNO_{3} acid solutions. So lowest pH value is shown by H_{2}SO_{4} acid due to its dibasic characteristic.

Questions

For this question, we can give two answers in two methods and they are explained below as case 1 and case 2.

Case 1. We can consider sulfuric acid with complete two dissociationa: It means, sulfuric acid release its both H^{+} ions completely in aqueous solution and the equation is given below.

H_{2}SO_{4} → 2H^{+} + SO_{4}^{2-}

OR

Case 2. First dissociation is complete and second dissociation is partial, these equations are given below.

H_{2}SO_{4} → H^{+} + HSO_{4}^{-}

HSO_{4}^{-} ⇌ H^{+} + SSO_{4}^{2-}

How to find pH for these two cases?

Case 1: Finding pH for case 1 is easy. Find H+ concentration and substitute it to pH equation.

- H
^{+}concentration = H_{2}SO_{4}concentration * 2 - H
^{+}concentration = 0.00896 * 2 - H
^{+}concentration = 0.01792 M

- pH = -log[H+]
- pH = -log[0.01792]
- pH = 1.74

**Case 2:** In this case, we think first dissociation is complete and secod dissociation is partial. Due to second dissocation is partial, we assume H+ concentration is given only by first dissociation.

- H
^{}concentration = H_{2}SO_{4}concentration - H
^{+}concentration = 0.00896 M

- pH = -log[H+]
- pH = -log[0.00896]
- pH = 2.047

Because you know the pH value, you can calculate the H^{+} ion concentration. When you know the H^{+} ion concentration, H_{2}SO_{4} concentration can be found.

Then, you can find amount and mass of H_{2}SO_{4} in a certain value. But, you need to know the density of the solution to calculate the mass of solution. When you know the density, you can calculatee thr mass percentage of H_{2}SO_{4}.

If sulfuric mass fraction is 50%, you can know the concentration of sulfuric acid. But, you need to know the density of the solution.

But, you need to know whether, will concentrated sulfuric acid show strong acid characteristics as the dilute acid. Otherwise we have to consider dissociation constant to calculate pH of 50% sulfuric acid.

Usually dilute sulphuric acid solutions shows very less pH values 1, 2.1 ,3.66. If concentrated sulphuric acid solutions are measured, pH may be a negative one.

When you know pH, you can calculate concentration of H_{3}O^{+} ions from pH equation.

Due to pH = 1, H_{3}O^{+} concentration is 0.1 mol dm^{-3}. Due to dibasic acid, when sulfuric acid molecule dissociate, two H_{3}O^{+} ions are given. Therefore, concentration of sulfuric acid should be a half of concentration of H_{3}O^{+}.

concentration of sulfuric acid at pH 1 is 0.05 mol dm^{-3}

Sulfuric acid shows very low pH value. Same concentration sulfuric acid show low pH value than HCl acid.

Sulfuric acid can release two H^{+} ions. But HCl can release only one H^{+} ion. So H^{+} concentration of sulfuric acid is high. So pH value also low in sulfuric acid solution.

IF we consider sulfuric acid as a strong acid which dissociates completely to release H^{+} ions. Therefore, concentration of H^{+} is 2.0 M. You can find pH by substituting in pH equation. As the answer, pH = -0.3 will be given.

To calculate the density, you need to know mass and volume of the solution. Usually, in commercial sulfuric acid bottles, density is mentioned in the lable. Otherwise you have to measure mass of certain volume of sulfuric acid solution and calculatte the density.

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