5.3 g of `Na_(2)CO_(3)` taken in a 250 ml flask and water added upto the mark. 10 ml of that solution was taken in a 50 ml flask water added upto the mark. Find molarity of that dilute solution.

Options

A. 0.1 M
B. 0.02 M
C. 0.04 M
D. None

Explanation

To find the molarity of the dilute solution of sodium carbonate (Na₂CO₃), we will follow these steps:

### Step 1: Calculate the number of moles of Na₂CO₃
First, we need to find the molar mass of sodium carbonate (Na₂CO₃):
- Sodium (Na) has a molar mass of approximately 23 g/mol.
- Carbon (C) has a molar mass of approximately 12 g/mol.
- Oxygen (O) has a molar mass of approximately 16 g/mol.

The molar mass of Na₂CO₃ can be calculated as follows:
\[ \text{Molar mass of Na}_2\text{CO}_3 = (2 \times 23) + (1 \times 12) + (3 \times 16) = 46 + 12 + 48 = 106 \text{ g/mol} \]

Now, we can calculate the number of moles of Na₂CO₃ using the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
Given that the mass of Na₂CO₃ is 5.3 g:
\[ \text{Number of moles} = \frac{5.3 \text{ g}}{106 \text{ g/mol}} \approx 0.050 \text{ moles} \]

### Step 2: Calculate the molarity of the original solution
Molarity (M) is defined as the number of moles of solute per liter of solution. The volume of the solution is 250 mL, which is 0.250 L.
\[ \text{Molarity (M)} = \frac{\text{Number of moles}}{\text{Volume (L)}} \]
\[ \text{Molarity} = \frac{0.050 \text{ moles}}{0.250 \text{ L}} = 0.20 \text{ M} \]

### Step 3: Calculate the molarity of the diluted solution
We will use the dilution formula:
\[ M_1 V_1 = M_2 V_2 \]
Where:
- \(M_1\) = initial molarity (0.20 M)
- \(V_1\) = volume of the initial solution taken (10 mL = 0.010 L)
- \(M_2\) = final molarity (unknown)
- \(V_2\) = final volume after dilution (50 mL = 0.050 L)

Now, substituting the known values into the equation:
\[ 0.20 \text{ M} \times 0.010 \text{ L} = M_2 \times 0.050 \text{ L} \]
\[ 0.002 = M_2 \times 0.050 \]
Now, solve for \(M_2\):
\[ M_2 = \frac{0.002}{0.050} = 0.040 \text{ M} \]

### Final Answer
The molarity of the dilute solution is **0.040 M**.

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