To determine the pH of a 0.048 M solution of hydrochloric acid (HCl), follow these steps:
1. Understand the relationship between concentration and pH:
The pH of a solution is calculated using the formula:
[tex]\[ \text{pH} = -\log_{10} [\text{H}^+] \][/tex]
where [tex]\([\text{H}^+]\)[/tex] is the concentration of hydrogen ions in the solution.
2. Identify the concentration of hydrogen ions:
Hydrochloric acid (HCl) is a strong acid, which means it completely dissociates in water. Therefore, the concentration of hydrogen ions [tex]\([\text{H}^+]\)[/tex] is equal to the concentration of the HCl solution.
Given:
[tex]\[ [\text{H}^+] = [\text{HCl}] = 0.048 \, \text{M} \][/tex]
3. Apply the pH formula:
Substitute the concentration of hydrogen ions into the pH formula:
[tex]\[ \text{pH} = -\log_{10} (0.048) \][/tex]
4. Perform the logarithmic calculation:
When you take the logarithm (base 10) of 0.048 and then multiply by -1, you get the pH value.
Therefore:
[tex]\[ \text{pH} \approx 1.3188 \][/tex]
5. Conclusion:
The pH of the 0.048 M solution of hydrochloric acid is approximately 1.3188.
