Question

Calculate the volume in milliliters of a 2.38M sodium thiosulfate solution that contains 50.0 g of sodium thiosulfate (Na2S2O3). Round your answer to 3 significant digits.

Answer 1

To calculate the volume of a 2.38 M sodium thiosulfate solution that contains 50.0 g of sodium thiosulfate (Na\(_2\)S\(_2\)O\(_3\)), we first need to determine the number of moles of sodium thiosulfate in 50.0 g.

1. **Calculate the molar mass of sodium thiosulfate (Na\(_2\)S\(_2\)O\(_3\))**:
- Sodium (Na): 22.99 g/mol × 2 = 45.98 g
- Sulfur (S): 32.07 g/mol × 2 = 64.14 g
- Oxygen (O): 16.00 g/mol × 3 = 48.00 g

Now, add these together to find the molar mass of Na\(_2\)S\(_2\)O\(_3\):
\[
\text{Molar mass} = 45.98 \, \text{g} + 64.14 \, \text{g} + 48.00 \, \text{g} = 158.12 \, \text{g/mol}
\]

2. **Calculate the number of moles of Na\(_2\)S\(_2\)O\(_3\)** in 50.0 g:
\[
\text{Moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{50.0 \, \text{g}}{158.12 \, \text{g/mol}} \approx 0.3164 \, \text{mol}
\]

3. **Use the molarity to find the volume**:
Molarity (M) is defined as the number of moles of solute per liter of solution:
\[
M = \frac{\text{moles}}{\text{volume (L)}}
\]
Rearranging the equation to solve for volume gives:
\[
\text{Volume (L)} = \frac{\text{moles}}{M} = \frac{0.3164 \, \text{mol}}{2.38 \, \text{mol/L}} \approx 0.1335 \, \text{L}
\]

4. **Convert volume from liters to milliliters**:
\[
\text{Volume (mL)} = 0.1335 \, \text{L} \times 1000 \, \text{mL/L} = 133.5 \, \text{mL}
\]

5. **Round to 3 significant digits**:
The final volume of the solution is approximately:
\[
\boxed{134} \, \text{mL}
\]