Dilution of HCl and Its Effect on pH: An In-depth Analysis

The dilution of a HCl (Hydrochloric Acid) solution can significantly affect its pH. This article will explore the mathematical calculations and principles behind the dilution of 0.02 ml of a 0.5 M HCl solution diluted with 400 ml of water. Let's delve into the science and calculations step by step.

Understanding the Problem

The initial volume of the HCl solution is 0.02 ml, with a concentration of 0.5 M. When this is diluted with 400 ml of water, the new solution’s pH is of interest. This process involves understanding dilution ratios and the resulting changes in hydrogen ion concentration.

Calculation Steps

Method 1

Dilution Factor Calculation:
First, we need to calculate the dilution factor. The total volume after dilution is the sum of the initial volume of acid and the volume of water added.

Calculate total volume:
Total Volume (Vtotal) 400 ml 0.02 ml

Calculate dilution factor:
Dilution Factor Vtotal / Vacid 400.02 ml / 0.02 ml 20001 ≈ 20000

Calculate new concentration:
New Concentration (Cnew) Cinitial / Dilution Factor 0.5 M / 20000 2.5 × 10^-5 M

Calculate pH:
pH -log[H ] -log(2.5 × 10^-5) ≈ 5 - log(2.5) ≈ 4.6

Method 2

Using Molarity Equation:
The amount of HCl in moles does not change during the dilution process. We can use the molarity and volume relationship to find the new concentration.

Calculate moles of HCl:
Moles (n) M × V 0.5 M × 0.02 ml 0.0001 mol

Calculate new concentration:
New Concentration (Cnew) Moles / Total Volume (Vnew) 0.0001 mol / 400.02 ml 2.5 × 10^-5 M

Calculate pH:
pH -log[H ] -log(2.5 × 10^-5) ≈ 4.6

Method 3

Using Proper Fraction for Volume:
Considering the exact volume, we can calculate the dilution factor more precisely.

Calculate total volume:
Total Volume (Vtotal) 400 ml 0.02 ml 400.02 ml

Calculate dilution factor:
Dilution Factor 400.02 ml / 0.02 ml 20001 ≈ 20000

Calculate new concentration:
New Concentration (Cnew) 0.5 M / 20000 2.5 × 10^-5 M

Calculate pH:
pH -log[H ] -log(2.5 × 10^-5) ≈ 5 - log(2.5) ≈ 4.6

Principles Involved

The key principles involved in this calculation include the relationship between concentration and volume, dilution ratios, and the behavior of strong acids in water.

Dilution Ratios

The dilution ratio is calculated by dividing the total volume by the initial volume of the solute. This gives the factor by which the concentration decreases.

Strong Acids and Complete Dissociation

HCl is a strong acid and dissociates almost completely in water.

HCl (aq) H2O (l) ? H3O (aq) Cl- (aq)

Since HCl dissociates almost completely, the final concentration of H3O ions will be the same as the initial concentration of HCl.

Conclusion

The pH of the diluted HCl solution is approximately 4.6, which is lower than the original pH. This example highlights the importance of understanding the principles of dilution in chemistry and their application in real-world scenarios.

Additional Resources

For further reading and exploration, consider the following resources:

Acids and Bases Strong and Weak Acids and Bases The Hydrogen Ionic Concentration, or pH