The density of a `"3 M Na_(2)S_(2)O_(3)` (sodium thiosulphate) solution is `"1.25 g cm"^(-3)`. Calculate (i) the percentage by weight of sodium thiosulphate

Explanation

To calculate the percentage by weight of sodium thiosulfate (Na₂S₂O₃) in a 3 M solution with a density of 1.25 g/cm³, we can follow these steps:

### Step 1: Understand the Molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. A 3 M Na₂S₂O₃ solution means there are 3 moles of sodium thiosulfate in 1 liter of solution.

### Step 2: Calculate the Molar Mass of Na₂S₂O₃
To find the weight of sodium thiosulfate, we first need its molar mass:
- Sodium (Na): 22.99 g/mol
- Sulfur (S): 32.07 g/mol
- Oxygen (O): 16.00 g/mol

The molar mass of Na₂S₂O₃ is calculated as:
\[ \text{Molar Mass} = (2 \times 22.99) + (2 \times 32.07) + (3 \times 16.00) = 45.98 + 64.14 + 48.00 = 158.12 \text{ g/mol} \]

### Step 3: Calculate the Weight of Sodium Thiosulfate
Using the molar mass, we can calculate the weight of sodium thiosulfate in 1 liter of solution:
\[ \text{Weight of Na₂S₂O₃} = \text{Number of moles} \times \text{Molar mass} = 3 \text{ moles} \times 158.12 \text{ g/mol} = 474.36 \text{ g} \]

### Step 4: Calculate the Weight of the Solution
Next, we need to calculate the total weight of the solution using its density. The density of the solution is given as 1.25 g/cm³. Since 1 liter is equivalent to 1000 cm³:
\[ \text{Weight of solution} = \text{Volume} \times \text{Density} = 1000 \text{ cm}^3 \times 1.25 \text{ g/cm}^3 = 1250 \text{ g} \]

### Step 5: Calculate the Percentage by Weight
The percentage by weight of sodium thiosulfate in the solution can be calculated using the formula:
\[ \text{Percentage by weight} = \left( \frac{\text{Weight of solute}}{\text{Weight of solution}} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage by weight} = \left( \frac{474.36 \text{ g}}{1250 \text{ g}} \right) \times 100 \approx 37.89\% \]

### Final Answer
The percentage by weight of sodium thiosulfate in the solution is approximately **37.89%**.

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