Final answer:
To produce 1.00 kg of sodium bicarbonate, 630.53 grams of soda ash would be required, based on the stoichiometry of the relevant chemical reaction.
Step-by-step explanation:
To calculate the amount of soda ash (sodium carbonate, Na₂CO₃) needed to produce 1.00 kg of sodium bicarbonate (NaHCO₃), we need to use stoichiometry based on the chemical reaction:
Na₂CO₃(aq) + CO₂(g) + H₂O(l) → 2 NaHCO₃(aq)
From the reaction, 1 mole of Na₂CO₃ produces 2 moles of NaHCO₃. First, we convert the mass of NaHCO₃ to moles:
- 1.00 kg NaHCO₃ is 1000 g.
- The molar mass of NaHCO₃ is 84.007 g/mol.
- Moles of NaHCO₃ = 1000 g / 84.007 g/mol = 11.903 moles.
Since it requires half the number of moles of Na₂CO₃ to produce the moles of NaHCO₃, we have:
- Moles of Na₂CO₃ required = 11.903 moles / 2 = 5.9515 moles.
Next, find the molar mass of Na₂CO₃:
- The molar mass of Na₂CO₃ is approximately 105.99 g/mol.
- Then, mass of Na₂CO₃ required = 5.9515 moles × 105.99 g/mol = 630.53 g.
Therefore, 630.53 grams of soda ash would be needed to produce 1.00 kg of sodium bicarbonate.