To determine the pH of an aqueous solution given the concentration of hydrogen ions [tex]\([H^+]\)[/tex], you can use the following formula:
[tex]\[ \text{pH} = -\log [H^+] \][/tex]
Here, the [tex]\( [H^+] \)[/tex] is the concentration of hydrogen ions in moles per liter (M). For this specific problem, the [tex]\([H^+]\)[/tex] is given as [tex]\(0.00250\)[/tex] M.
Let's solve this step by step:
1. Identify the given hydrogen ion concentration:
[tex]\[ [H^+] = 0.00250 \text{ M} \][/tex]
2. Calculate the logarithm base 10 of the hydrogen ion concentration:
We'll convert [tex]\(0.00250\)[/tex] to scientific notation for ease of calculation:
[tex]\[ 0.00250 = 2.50 \times 10^{-3} \][/tex]
3. Use the logarithm property to break it down:
[tex]\[ \log(2.50 \times 10^{-3}) = \log(2.50) + \log(10^{-3})\][/tex]
By the properties of logarithms:
[tex]\[ \log(10^{-3}) = -3 \][/tex]
Now, using a calculator or logarithm tables for the other term:
[tex]\[ \log(2.50) \approx 0.3979 \][/tex]
4. Combine the results:
[tex]\[ \log(2.50 \times 10^{-3}) = 0.3979 - 3 = -2.6021 \][/tex]
5. Take the negative of the result to find the pH:
[tex]\[ \text{pH} = -(-2.6021) = 2.6021 \][/tex]
Therefore, rounding to two decimal places, the pH of the solution is approximately [tex]\(2.60\)[/tex].
So, the correct answer is:
[tex]\[ \boxed{2.60} \][/tex]
