To find the hydronium ion concentration ([tex]\([H^+]\)[/tex]) of a vinegar solution given its pH level, we can use the relationship between pH and hydronium ion concentration, which is given by the formula:
[tex]\[ pH = -\log [H^+] \][/tex]
In this case, we are given that the pH is 2.5. To find [tex]\([H^+]\)[/tex], we need to rearrange the formula:
[tex]\[ [H^+] = 10^{-\text{pH}} \][/tex]
Substitute the given pH value into the formula:
[tex]\[ [H^+] = 10^{-2.5} \][/tex]
Calculating this, we get:
[tex]\[ [H^+] \approx 0.0031622776601683794 \][/tex]
Which can be written in scientific notation as:
[tex]\[ [H^+] \approx 3.162 \times 10^{-3} \][/tex]
Therefore, the hydronium ion concentration for a vinegar solution with a pH of 2.5 is approximately [tex]\( 3.162 \times 10^{-3} \)[/tex].
Given the choices:
1. [tex]\( 3.162 \times 10^{-3} \)[/tex]
2. [tex]\( 3.979 \times 10^{-1} \)[/tex]
3. [tex]\( 3.162 \times 10^2 \)[/tex]
4. [tex]\( 9.536 \times 10^3 \)[/tex]
The correct answer is:
[tex]\[ 3.162 \times 10^{-3} \][/tex]
