0.63 g of oxalic acid,`(COOH)_(2).2H_(2)O` are dissolved in 500 ml of solution. Calculate the molarity of the solution.

Explanation

To calculate the molarity of the oxalic acid solution, we will follow these steps:

### Step 1: Identify the given data
- Mass of oxalic acid, \( (COOH)_2 \cdot 2H_2O = 0.63 \, \text{g} \)
- Volume of the solution = 500 ml

### Step 2: Convert the volume from milliliters to liters
To convert milliliters to liters, we use the conversion factor \( 1 \, \text{L} = 1000 \, \text{mL} \).

\[ \text{Volume in liters} = \frac{500 \, \text{mL}}{1000} = 0.5 \, \text{L} \]

### Step 3: Calculate the molar mass of oxalic acid
The molar mass of oxalic acid, \( (COOH)_2 \cdot 2H_2O \), can be calculated as follows:
- Carbon (C): \( 2 \times 12.01 \, \text{g/mol} = 24.02 \, \text{g/mol} \)
- Hydrogen (H): \( 2 \times 1.008 \, \text{g/mol} + 4 \times 1.008 \, \text{g/mol} = 6.016 \, \text{g/mol} \)
- Oxygen (O): \( 4 \times 16.00 \, \text{g/mol} = 64.00 \, \text{g/mol} \)

Adding these together:
\[ \text{Molar mass} = 24.02 + 6.016 + 64.00 = 94.036 \, \text{g/mol} \]

### Step 4: Calculate the number of moles of oxalic acid
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{0.63 \, \text{g}}{126.0 \, \text{g/mol}} \approx 0.005 \, \text{moles} \]

### Step 5: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[ \text{Molarity} = \frac{\text{number of moles}}{\text{volume in liters}} \]
Substituting the values:
\[ \text{Molarity} = \frac{0.005 \, \text{moles}}{0.5 \, \text{L}} = 0.01 \, \text{M} \]

### Final Answer
The molarity of the oxalic acid solution is \( 0.01 \, \text{M} \).

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