Answer :
To determine the \( pH \) of a solution with a hydronium ion concentration \([H_3O^+]\) of \( 3.2 \times 10^{-5} \) M, you need to use the formula for pH, which is:
[tex]\[ pH = -\log_{10}([H_3O^+]) \][/tex]
Here are the steps to solve the problem:
1. Identify the hydronium ion concentration:
[tex]\[ [H_3O^+] = 3.2 \times 10^{-5} \][/tex]
2. Apply the pH formula:
[tex]\[ pH = -\log_{10}(3.2 \times 10^{-5}) \][/tex]
3. Calculate the logarithm:
Use a calculator to find the base 10 logarithm of \( 3.2 \times 10^{-5} \).
[tex]\[ \log_{10}(3.2 \times 10^{-5}) \approx -4.49485 \][/tex]
4. Convert to positive pH value:
[tex]\[ pH = -(-4.49485) = 4.49485 \][/tex]
Now, round the result to one decimal place to match the options provided.
[tex]\[ pH \approx 4.5 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{4.5} \][/tex]
[tex]\[ pH = -\log_{10}([H_3O^+]) \][/tex]
Here are the steps to solve the problem:
1. Identify the hydronium ion concentration:
[tex]\[ [H_3O^+] = 3.2 \times 10^{-5} \][/tex]
2. Apply the pH formula:
[tex]\[ pH = -\log_{10}(3.2 \times 10^{-5}) \][/tex]
3. Calculate the logarithm:
Use a calculator to find the base 10 logarithm of \( 3.2 \times 10^{-5} \).
[tex]\[ \log_{10}(3.2 \times 10^{-5}) \approx -4.49485 \][/tex]
4. Convert to positive pH value:
[tex]\[ pH = -(-4.49485) = 4.49485 \][/tex]
Now, round the result to one decimal place to match the options provided.
[tex]\[ pH \approx 4.5 \][/tex]
Thus, the correct answer is:
[tex]\[ \boxed{4.5} \][/tex]
