The number of molecules in 100 mL of 0.02 N `H_(2)SO_(4)` is

Options

A. `6.02 xx 10^22`
B. `6.02 xx 10^21`
C. `6.02 xx 10^20`
D. `6.02 xx 10^18`

Answer

To find the number of molecules in 100 mL of 0.02 N \( H_2SO_4 \), we can follow these steps:

### Step 1: Understand the relationship between Normality and Molarity
Normality (N) is related to molarity (M) by the equation:
\[ N = M \times n \]
where \( n \) is the number of equivalents. For sulfuric acid (\( H_2SO_4 \)), it can donate 2 protons (H⁺ ions), so \( n = 2 \).

### Step 2: Calculate the Molarity
Given that the normality of the solution is 0.02 N, we can find the molarity:
\[ M = \frac{N}{n} = \frac{0.02 \, \text{N}}{2} = 0.01 \, \text{M} \]

### Step 3: Convert the volume from mL to L
The volume of the solution is given as 100 mL. To convert this to liters:
\[ \text{Volume in L} = \frac{100 \, \text{mL}}{1000} = 0.1 \, \text{L} \]

### Step 4: Calculate the number of moles
Now, we can calculate the number of moles of \( H_2SO_4 \) in the solution using the formula:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume in L} \]
Substituting the values:
\[ \text{Number of moles} = 0.01 \, \text{M} \times 0.1 \, \text{L} = 0.001 \, \text{moles} \]

### Step 5: Calculate the number of molecules
To find the number of molecules, we use Avogadro's number (\( 6.022 \times 10^{23} \) molecules/mole):
\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]
Substituting the values:
\[ \text{Number of molecules} = 0.001 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} = 6.022 \times 10^{20} \, \text{molecules} \]

### Final Answer
The number of molecules in 100 mL of 0.02 N \( H_2SO_4 \) is \( 6.022 \times 10^{20} \) molecules.

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