Question

You want to make up a 0,100mol•dm³ Sodium Carbonate solution.You have a 200ml volumetric flask and a bottle of Sodium Carbonate decahydrate.Calculate the mass of crystals that you need to weigh off

Answer 1

To prepare a 0.100 mol/dm³ (or 0.100 M) solution of sodium carbonate (Na₂CO₃) in a 200 mL volumetric flask, you need to calculate the mass of sodium carbonate decahydrate (\(Na_2CO_3 \cdot 10H_2O\)) required.

1. **Calculate the number of moles needed:**

The volume of the solution you want to prepare is 200 mL, which is equivalent to 0.200 L.

\[
\text{moles of Na₂CO₃} = \text{Concentration} \times \text{Volume} = 0.100 \, \text{mol/dm}^3 \times 0.200 \, \text{dm}^3 = 0.0200 \, \text{mol}
\]

2. **Calculate the molar mass of sodium carbonate decahydrate:**

The molar mass of \(Na_2CO_3\):
- Sodium (Na): 23.0 g/mol × 2 = 46.0 g/mol
- Carbon (C): 12.0 g/mol = 12.0 g/mol
- Oxygen (O): 16.0 g/mol × 3 = 48.0 g/mol

So, the molar mass of \(Na_2CO_3 = 46.0 + 12.0 + 48.0 = 106.0 \, \text{g/mol}\).

Now, add the mass for the water in the decahydrate:
- Water (H₂O): 18.0 g/mol × 10 = 180.0 g/mol

Therefore, the molar mass of sodium carbonate decahydrate (\(Na_2CO_3 \cdot 10H_2O\)):

\[
\text{Molar mass of } Na_2CO_3 \cdot 10H_2O = 106.0 \, \text{g/mol} + 180.0 \, \text{g/mol} = 286.0 \, \text{g/mol}
\]

3. **Calculate the mass of sodium carbonate decahydrate needed:**

Now, use the number of moles and the molar mass to find the mass needed:

\[
\text{mass} = \text{moles} \times \text{molar mass}
\]

\[
\text{mass} = 0.0200 \, \text{mol} \times 286.0 \, \text{g/mol} = 5.72 \, \text{g}
\]

So, you need to weigh off **5.72 grams** of sodium carbonate decahydrate to prepare a 0.100 mol/dm³ solution in a 200 mL volumetric flask.