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

Options

A. `1.506xx10^(22)`
B. `1.506xx10^(23)`
C. `1.506xx10^(20)`
D. `3.012xx10^(21)`

Explanation

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 relationship between pH and \( H^+ \) concentration
The pH of a solution is defined as:
\[ \text{pH} = -\log[H^+] \]
Where \([H^+]\) is the concentration of hydrogen ions in moles per liter (M).

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

### Step 3: Convert the volume from ml to liters
Since the concentration is given in moles per liter, 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
Now, we can calculate the number of moles of \( H^+ \) ions in 250 ml of lemon juice:
\[ \text{Moles of } H^+ = [H^+] \times \text{Volume in L} = 10^{-3} \, \text{mol/L} \times 0.250 \, \text{L} = 2.5 \times 10^{-4} \, \text{mol} \]

### Step 5: Convert moles to number of ions
To find the total number of \( H^+ \) ions, we need to multiply the number of moles by Avogadro's number (\( 6.022 \times 10^{23} \) ions/mol):
\[ \text{Number of } H^+ \text{ ions} = 2.5 \times 10^{-4} \, \text{mol} \times 6.022 \times 10^{23} \, \text{ions/mol} \]

### Step 6: Perform the multiplication
Calculating this gives:
\[ \text{Number of } H^+ \text{ ions} = 1.506 \times 10^{20} \, \text{ions} \]

### Final Answer
The number of \( H^+ \) ions present in 250 ml of lemon juice with a pH of 3 is approximately:
\[ 1.506 \times 10^{20} \, \text{ions} \]

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