How many grams of `Na_(2)CO_(3)` should be dissolved in 250 g of water to prepare 0.1 m solution?

Explanation

To determine how many grams of Na₂CO₃ should be dissolved in 250 g of water to prepare a 0.1 M solution, we can follow these steps:

### Step 1: Understand the formula for molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula is given by:
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]

### Step 2: Identify the given values
From the question:
- Molarity (M) = 0.1 M
- Mass of water = 250 g

### Step 3: Convert mass of water to volume of solution
Since the density of water is approximately 1 g/mL, the volume of 250 g of water is:
\[ \text{Volume of water} = 250 \, \text{g} = 250 \, \text{mL} = 0.250 \, \text{L} \]

### Step 4: Calculate the number of moles of Na₂CO₃ needed
Using the molarity formula:
\[ 0.1 = \frac{\text{moles of Na₂CO₃}}{0.250} \]
Rearranging to find the moles of Na₂CO₃:
\[ \text{moles of Na₂CO₃} = 0.1 \times 0.250 = 0.025 \, \text{moles} \]

### Step 5: Calculate the mass of Na₂CO₃ required
To find the mass, we need the molar mass of Na₂CO₃. The molar mass can be calculated as follows:
- Sodium (Na) = 23 g/mol (2 Na = 46 g)
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (3 O = 48 g)

Thus, the molar mass of Na₂CO₃ is:
\[ \text{Molar mass of Na₂CO₃} = 46 + 12 + 48 = 106 \, \text{g/mol} \]

Now, we can calculate the mass of Na₂CO₃ required:
\[ \text{Mass of Na₂CO₃} = \text{moles} \times \text{molar mass} \]
\[ \text{Mass of Na₂CO₃} = 0.025 \, \text{moles} \times 106 \, \text{g/mol} = 2.65 \, \text{g} \]

### Final Answer
To prepare a 0.1 M solution of Na₂CO₃ in 250 g of water, you need to dissolve **2.65 grams of Na₂CO₃**.

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