Calculate the number of molecules of oxalic acid (`H_2C_2O_4`) in 100 mL of 0.2 N oxalic acid

Answer

To calculate the number of molecules of oxalic acid (H₂C₂O₄) in 100 mL of a 0.2 N solution, we can follow these steps:

### Step 1: Understand the relationship between Normality, Molarity, and Basicity
Normality (N) is related to molarity (M) by the equation:
\[ N = M \times n \]
where \( n \) is the basicity of the acid. For oxalic acid (H₂C₂O₄), which has two acidic protons, the basicity \( n \) is 2.

### Step 2: Convert Normality to Molarity
Given that the normality of the solution is 0.2 N, we can calculate the molarity (M) as follows:
\[ M = \frac{N}{n} = \frac{0.2}{2} = 0.1 \, \text{M} \]

### Step 3: Calculate the number of moles
To find the number of moles of oxalic acid in the solution, we use the formula:
\[ \text{Number of moles} = M \times V \]
where \( V \) is the volume in liters. Since we have 100 mL, we convert this to liters:
\[ V = 100 \, \text{mL} = 0.1 \, \text{L} \]
Now we can calculate the number of moles:
\[ \text{Number of moles} = 0.1 \, \text{M} \times 0.1 \, \text{L} = 0.01 \, \text{moles} \]

### Step 4: 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 we have:
\[ \text{Number of molecules} = 0.01 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \]
\[ \text{Number of molecules} = 6.022 \times 10^{21} \, \text{molecules} \]

### Final Answer
The number of molecules of oxalic acid in 100 mL of a 0.2 N solution is:
\[ 6.022 \times 10^{21} \, \text{molecules} \]

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