To find the hydronium ion concentration from a given pH level, you can use the relationship between pH and hydrogen ion concentration, which is given by the equation:
[tex]\[ \text{pH} = -\log [H^+] \][/tex]
Where [tex]\( [H^+] \)[/tex] represents the concentration of hydronium ions (in moles per liter).
### Step-by-Step Solution
1. Understand the Problem:
You are given the pH level of a lemon juice, which is 2.1, and you need to find the hydronium ion concentration [tex]\([H^+]\)[/tex].
2. Rearrange the Formula:
To solve for [tex]\( [H^+] \)[/tex], we need to rearrange the equation:
[tex]\[ \text{pH} = -\log [H^+] \][/tex]
Rearrange it to isolate [tex]\( [H^+] \)[/tex]:
[tex]\[ [H^+] = 10^{-\text{pH}} \][/tex]
3. Substitute the Given pH Value:
Substitute [tex]\( \text{pH} = 2.1 \)[/tex] into the equation:
[tex]\[ [H^+] = 10^{-2.1} \][/tex]
4. Calculate the Hydronium Ion Concentration:
Calculate [tex]\( 10^{-2.1} \)[/tex]:
[tex]\[ [H^+] = 0.007943282347242814 \][/tex]
5. Express the Concentration in Scientific Notation:
The hydronium ion concentration [tex]\( [H^+] \)[/tex] can be expressed in scientific notation as:
[tex]\[ [H^+] \approx 7.943 \times 10^{-3} \][/tex]
6. Identify the Correct Answer:
Compare the calculated hydronium ion concentration to the provided options:
- [tex]\( 3.222 \times 10^{-1} \)[/tex]
- [tex]\( 1.259 \times 10^2 \)[/tex]
- [tex]\( 7.943 \times 10^{-3} \)[/tex]
- [tex]\( 1.668 \times 10^3 \)[/tex]
The correct choice is:
[tex]\[ 7.943 \times 10^{-3} \][/tex]
### Conclusion
The hydronium ion concentration of the lemon juice with a pH level of 2.1 is [tex]\( 7.943 \times 10^{-3} \)[/tex] M.
