Question

What are the \(\mathrm{pH}\) values of the following solutions at \(25^{\circ} \mathrm{C}\) ? (i) \(0.001 \mathrm{M}\) of \(\mathrm{HCl}\) (ii) \(0.05 \mathrm{M}\) of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (iii) \(0.01 \mathrm{M}\) of \(\mathrm{NaOH}\)

Short answer

Question: Determine the pH values for the following solutions at \(25^{\circ} \mathrm{C}\): (i) 0.001M HCl (ii) 0.05M H2SO4 (iii) 0.01M NaOH Answer: The pH values for the given solutions at \(25^{\circ} \mathrm{C}\) are: (i) HCl solution: pH = 3 (ii) H2SO4 solution: pH = 1 (iii) NaOH solution: pH = 12

Step-by-step solution

1. Identifying the acids and bases

In the given solutions: (i) HCl is a strong acid (ii) H2SO4 is a strong acid (iii) NaOH is a strong base

2. Calculate the concentration of H3O+ and OH- ions for each solution

In order to determine the pH, we first need to find the concentrations of H3O+ or OH- ions in solutions: (i) For a strong acid like HCl, the concentration of H3O+ is equal to the concentration of the acid. So, for 0.001M HCl, the concentration of H3O+ ions is 0.001M (ii) For a diprotic strong acid like H2SO4, each mole of the acid contributes two moles of H3O+ ions. So, for 0.05M H2SO4, the concentration of H3O+ ions is 2 x 0.05 = 0.1M. (iii) For a strong base like NaOH, we need to find the concentration of OH- ions. Since it's a strong base, the concentration of OH- equals the concentration of the base, which is 0.01M.

3. Calculate the pH or pOH using the respective ions

Next, we use these concentrations to calculate either pH or pOH depending on the nature of the substance (if acidic, we calculate pH; if basic, we calculate pOH): (i) pH = -log[H3O+] = -log[0.001] = 3 (ii) pH = -log[H3O+] = -log[0.1] = 1 (iii) pOH = -log[OH-] = -log[0.01] = 2

4. Convert pOH to pH for the basic solution (NaOH)

Finally, since we need to find the pH of the basic solution, we will convert pOH to pH using the following relation: pH + pOH = 14 For NaOH, pH = 14 - pOH = 14 - 2 = 12 The pH values for the given solutions at \(25^{\circ} \mathrm{C}\) are: (i) HCl solution: pH = 3 (ii) H2SO4 solution: pH = 1 (iii) NaOH solution: pH = 12

Key concepts

Strong Acids and Bases

Understanding the nature of strong acids and bases is crucial in chemistry, particularly when calculating the pH of a solution. Strong acids, like HCl and H₂SO₄, ionize completely in water, which means they donate all their available hydrogen ions (H⁺) to the solution. In contrast, strong bases like NaOH fully dissociate to release hydroxide ions (OH⁻). This complete dissociation is what makes calculating their pH straightforward because their concentration in the solution is directly related to the concentration of H⁺ or OH⁻ ions.

When dealing with strong acids and bases, it is important to consider the number of ions each molecule produces. For example, H₂SO₄ is a diprotic acid, capable of donating two H⁺ ions per molecule. Its ability to produce more ions per molecule affects pH calculations and must be accounted for when solving these problems.

Concentration of H3O+ Ions

In acid-base chemistry, the concentration of hydronium ions (H₃O⁺), often represented as H⁺, is a critical factor in determining a solution's acidity. For a strong acid, the concentration of H₃O⁺ matches the molarity of the acid because it fully dissociates in water. To calculate the pH of a strong acid, we use the formula pH = -log[H₃O⁺].

Remember, the -log function in this equation transforms the H₃O⁺ concentration into a more manageable number – the pH. In addition, when handling polyprotic acids like H₂SO₄, it's key to multiply the initial concentration by the number of ionizable hydrogens to find the correct H₃O⁺ concentration.

Concentration of OH- Ions

Similar to H₃O⁺ ions for acids, the concentration of hydroxide ions (OH⁻) dictates the basicity of a solution. In the case of strong bases, such as NaOH, these bases dissociate entirely in water, yielding a concentration of OH⁻ equal to the original concentration of the base. To find the pOH of a strong base, we can use the formula pOH = -log[OH⁻].

This concept of direct equivalence in concentration simplifies the process of determining the pOH. After calculating the pOH, it can easily be converted to pH if needed, which allows us to measure the acidity of a solution initially characterized by its basicity.

pOH to pH Conversion

The pOH of a solution is a measure of its hydroxide ion concentration and can be used to find pH, which is a more common scale for expressing solution acidity. The relationship between pH and pOH in aqueous solutions at room temperature (25&Celsius;) is defined by the equation pH + pOH = 14. By using this equation, we can convert a calculated pOH to pH and vice versa.

To convert pOH to pH, simply subtract the pOH value from 14. For instance, if we have a pOH of 2, the pH would be calculated as 14 - 2 = 12. This conversion is essential when you're working with strong bases since their direct effect on hydroxide ion concentration is more intuitive to express as pOH, yet pH is the universally recognized scale for how acidic or basic a solution is.