To determine the percentage of sodium carbonate in your sample, we first need to understand the chemical reaction that occurs when sodium hydrogen carbonate (NaHCO₃) is heated. At around 300°C, sodium hydrogen carbonate decomposes into sodium carbonate (Na₂CO₃), carbon dioxide (CO₂), and water (H₂O). The reaction can be summarized as follows:
Chemical Reaction
The decomposition reaction is:
- 2 NaHCO₃ (s) → Na₂CO₃ (s) + CO₂ (g) + H₂O (g)
Calculating Molar Masses
To find the percentage of sodium carbonate in the original sample, we need to calculate the molar masses of the compounds involved:
- Molar mass of NaHCO₃ = 23 (Na) + 1 (H) + 12 (C) + 3 × 16 (O) = 84 g/mol
- Molar mass of Na₂CO₃ = 2 × 23 (Na) + 12 (C) + 3 × 16 (O) = 106 g/mol
Understanding Mass Loss
When the sample is heated, it loses mass due to the release of carbon dioxide and water. The total mass lost (0.248 g) corresponds to the amount of sodium hydrogen carbonate that decomposed. We can find out how much sodium hydrogen carbonate was present in the original sample by using the molar mass.
Finding Moles of NaHCO₃ Lost
First, we need to determine how many moles of NaHCO₃ correspond to the mass lost:
- Mass lost = 0.248 g
- Moles of NaHCO₃ = Mass lost / Molar mass of NaHCO₃ = 0.248 g / 84 g/mol ≈ 0.00295 mol
Calculating Sodium Carbonate Produced
From the balanced equation, we see that 2 moles of NaHCO₃ produce 1 mole of Na₂CO₃. Therefore, the moles of sodium carbonate produced from the moles of sodium hydrogen carbonate decomposed is:
- Moles of Na₂CO₃ = 0.00295 mol NaHCO₃ × (1 mol Na₂CO₃ / 2 mol NaHCO₃) ≈ 0.001475 mol
Calculating Mass of Sodium Carbonate
Now, we can find the mass of sodium carbonate produced:
- Mass of Na₂CO₃ = Moles of Na₂CO₃ × Molar mass of Na₂CO₃ = 0.001475 mol × 106 g/mol ≈ 0.156 g
Finding the Percentage of Sodium Carbonate
Finally, to find the percentage of sodium carbonate in the original 2 g sample, we use the formula:
- Percentage of Na₂CO₃ = (Mass of Na₂CO₃ / Original mass of sample) × 100
- Percentage of Na₂CO₃ = (0.156 g / 2 g) × 100 ≈ 7.8%
In summary, the percentage of sodium carbonate in your original sample is approximately 7.8%. This calculation illustrates how thermal decomposition reactions can be quantitatively analyzed to determine the composition of a mixture.
