Final answer:
To obtain 47.5 grams of sodium hydroxide, you will need 0.367 grams of sodium carbonate and 0.527 grams of calcium hydroxide.
Step-by-step explanation:
To obtain 47.5 grams of sodium hydroxide, you will need to determine the amounts of sodium carbonate and calcium hydroxide that can produce this amount. First, you need to balance the chemical equation for the reaction:
Na2CO3 + Ca(OH)2 → 2NaOH + CaCO3
Next, calculate the molar mass of sodium hydroxide:
Molar mass of NaOH = 22.99 g/mol + 16.00 g/mol + 1.01 g/mol = 39.00 g/mol
Using the balanced equation, you can set up a ratio:
2 moles of NaOH / 1 mole of Na2CO3 = 39.00 g of NaOH / x g of Na2CO3
Now solve for x, where x is the mass of sodium carbonate needed:
x = (39.00 g Na2CO3)(1 mole Na2CO3 / 105.99 g Na2CO3) = 0.367 g Na2CO3
Similarly, you can calculate the mass of calcium hydroxide needed using the same method:
x = (39.00 g Ca(OH)2)(1 mole Ca(OH)2 / 74.09 g Ca(OH)2) = 0.527 g Ca(OH)2