To find the concentration of [tex]\( \left[ H_3O^+ \right] \)[/tex] ions in lemon juice given that its pH is 2.32, you can use the relationship between pH and hydronium ion concentration:
[tex]\[ \left[ H_3O^+ \right] = 10^{-pH} \][/tex]
Here’s a step-by-step solution to compute the concentration:
1. Understand the given value:
The pH of the lemon juice is 2.32.
2. Write down the formula for hydronium ion concentration:
[tex]\( \left[ H_3O^+ \right] = 10^{-pH} \)[/tex]
3. Substitute the pH value into the formula:
[tex]\( \left[ H_3O^+ \right] = 10^{-2.32} \)[/tex]
4. Calculate the power of 10:
When calculating [tex]\( 10^{-2.32} \)[/tex], you get approximately [tex]\( 0.004786300923226385 \)[/tex].
5. Express the result in scientific notation:
* The result [tex]\( 0.004786300923226385 \)[/tex] can be rewritten as [tex]\( 4.79 \times 10^{-3} \)[/tex].
Therefore, the concentration of [tex]\( \left[ H_3O^+ \right] \)[/tex] ions in the lemon juice is:
[tex]\[ 4.79 \times 10^{-3} \, \text{M} \][/tex]
Among the given options:
- [tex]\( 1.05 \times 10^{-3} \, \text{M} \)[/tex]
- [tex]\( 4.79 \times 10^{-3} \, \text{M} \)[/tex]
- [tex]\( 2.09 \times 10^2 \, \text{M} \)[/tex]
- [tex]\( 9.55 \times 10^2 \, \text{M} \)[/tex]
The correct answer is [tex]\( 4.79 \times 10^{-3} \, \text{M} \)[/tex].
