The pH of a 0.10 M solution of a certain acid is 3.25 at 25°C. What is the pH of a 0.010 M solution of the same acid at the same temperature?
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To find the pH of a 0.010 M solution of the same acid at the same temperature, we can use the concept of the pH scale. The pH of a substance indicates how acidic or basic it is.
The pH scale ranges from 0 to 14, with pH values less than 7 considered acidic and pH values greater than 7 considered basic. A neutral solution, such as pure water, has a pH of 7.
Here's how to find the pH of the 0.010 M solution using the given information:
1. Recall that pH is a measure of the concentration of hydrogen ions (H+) in a solution. The lower the concentration of H+, the more acidic the solution.
2. Given that the pH of the 0.10 M solution is 3.25, we can conclude that it is acidic since the pH is below 7.
3. The pH scale is logarithmic, meaning that each unit represents a tenfold difference in hydrogen ion concentration. For every decrease of one unit on the pH scale, the concentration of H+ increases by a factor of 10.
4. Since the concentration of the solution is decreasing from 0.10 M to 0.010 M, we can expect the pH to increase.
5. To calculate the change in pH, we need to determine the difference in concentration of H+ between the two solutions.
6. The concentration of H+ in the 0.10 M solution can be found using the formula: [H+] = 10^(-pH). Substituting the given pH of 3.25: [H+] = 10^(-3.25) ≈ 5.62 x 10^(-4) M.
7. Similarly, we can find the concentration of H+ in the 0.010 M solution using the same formula: [H+] = 10^(-pH).
8. Using the logarithmic relationship between [H+] and pH, we can calculate the new pH as follows:
[H+] = 10^(-pH) = 10^(-log([H+])) ≈ 10^(-log(5.62 x 10^(-4))) ≈ 0.00313 M.
Taking the logarithm of 0.00313, we get log(0.00313) ≈ -2.504.
Therefore, the pH is calculated as -log(0.00313) ≈ 2.504.
Hence, the pH of the 0.010 M solution of the same acid at the same temperature is approximately 2.504.