The number of `H^(+)` ions present in 250 ml of lemon juice of pH=3 is

Options

A. `1.50 xx 10^(22)`
B. `1.50 xx 10^(23)`
C. `1.506 xx 10^(20)`
D. `3.012 xx 10^(21)`

Answer

To find the number of \( H^+ \) ions present in 250 ml of lemon juice with a pH of 3, we can follow these steps:

### Step 1: Understand the pH definition
The pH is defined as:
\[ \text{pH} = -\log_{10} [H^+] \]
where \([H^+]\) is the concentration of hydrogen ions in moles per liter (M).

### Step 2: Calculate the concentration of \( H^+ \) ions
Given that the pH is 3, we can rearrange the pH formula to find the concentration of \( H^+ \):
\[ 3 = -\log_{10} [H^+] \]
Taking the antilogarithm, we find:
\[ [H^+] = 10^{-3} \text{ M} \]
This means that the concentration of \( H^+ \) ions is \( 10^{-3} \) moles per liter.

### Step 3: Convert the volume from ml to liters
We need to convert the volume of lemon juice from milliliters to liters:
\[ 250 \text{ ml} = 0.250 \text{ L} \]

### Step 4: Calculate the number of moles of \( H^+ \) in 250 ml
Using the concentration and the volume, we can calculate the number of moles of \( H^+ \) ions in 250 ml:
\[ \text{Moles of } H^+ = [H^+] \times \text{Volume in L} = 10^{-3} \text{ moles/L} \times 0.250 \text{ L} \]
\[ \text{Moles of } H^+ = 2.5 \times 10^{-4} \text{ moles} \]

### Step 5: Calculate the number of \( H^+ \) ions
To find the number of \( H^+ \) ions, we use Avogadro's number, which is \( 6.022 \times 10^{23} \) ions/mole:
\[ \text{Number of } H^+ \text{ ions} = \text{Moles of } H^+ \times \text{Avogadro's number} \]
\[ \text{Number of } H^+ \text{ ions} = 2.5 \times 10^{-4} \text{ moles} \times 6.022 \times 10^{23} \text{ ions/mole} \]
\[ \text{Number of } H^+ \text{ ions} \approx 1.506 \times 10^{20} \text{ ions} \]

### Conclusion
Thus, the number of \( H^+ \) ions present in 250 ml of lemon juice with a pH of 3 is approximately \( 1.506 \times 10^{20} \) ions.

---