Washing soda is added to hard water to allow soap to lather.
A certain brand of washing soda contains partially hydrated
sodium carbonate solid. A 0.300 g sample completely reacts
with 20.0 mL of 0.250 M hydrochloric acid.
a What mass of sodium carbonate was present?
b Calculate the percentage by mass of sodium carbonate in
the washing soda.
Na2CO3 + 2HCl ==> 2NaCl + H2O + CO2
mols HCl used = L x M = 0.020 L x 0.250 M = ??
mols Na2CO3 = ?? mols HCl x 1/2 = ??
g Na2CO3 = mols x molar mass Na2CO3 = ??
%Na2CO3 = (grams Na2CO3/0.300) * 100 = ?
To solve this problem, we need to use stoichiometry and the concept of molarity to find the mass of sodium carbonate and calculate the percentage by mass.
a) To determine the mass of sodium carbonate present, we can use the balanced chemical equation between sodium carbonate and hydrochloric acid:
Na2CO3 + 2HCl -> 2NaCl + H2O + CO2
According to the equation, the molar ratio is 1:2 between sodium carbonate and hydrochloric acid. This means that for every mole of sodium carbonate, 2 moles of hydrochloric acid are required to react completely.
First, we need to calculate the number of moles of hydrochloric acid used. The volume of the hydrochloric acid solution is 20.0 mL, which can be converted to liters by dividing by 1000:
Volume of hydrochloric acid = 20.0 mL / 1000 = 0.0200 L
Next, we can use the formula Molarity = Moles/Liters to find the number of moles of hydrochloric acid:
Moles of HCl = Molarity × Volume
= 0.250 M × 0.0200 L
= 0.0050 moles of HCl
Since the molar ratio between sodium carbonate and hydrochloric acid is 1:2, the moles of sodium carbonate will be half of the moles of hydrochloric acid:
Moles of Na2CO3 = 0.0050 moles of HCl / 2
= 0.0025 moles of Na2CO3
Now, we can calculate the mass of sodium carbonate using the molar mass of Na2CO3:
Mass of Na2CO3 = Moles × Molar Mass
= 0.0025 moles × (2 × atomic mass of Na + atomic mass of C + 3 × atomic mass of O)
= 0.0025 moles × (2(22.99 g/mol) + 12.01 g/mol + 3(16.00 g/mol))
= 0.0025 moles × 105.99 g/mol
= 0.265 g
Therefore, the mass of sodium carbonate present in the 0.300 g sample is 0.265 g.
b) To calculate the percentage by mass of sodium carbonate in the washing soda, we use the formula:
Percentage by mass = (Mass of Na2CO3 / Mass of washing soda) × 100
For this question, the mass of washing soda is not explicitly given. However, we can calculate it from the information provided. The washing soda contains partially hydrated sodium carbonate, so we can assume that the partial hydration does not affect the stoichiometry of the reaction.
Since the molar ratio between sodium carbonate and hydrochloric acid is 1:2, the number of moles of sodium carbonate will be twice the number of moles of hydrochloric acid.
Moles of Na2CO3 = 2 × Moles of HCl
= 2 × 0.0050 moles of HCl
= 0.0100 moles of Na2CO3
Now, we can calculate the mass of the washing soda:
Mass of washing soda = Moles × Molar Mass
= 0.0100 moles × (2 × atomic mass of Na + atomic mass of C + 3 × atomic mass of O)
= 0.0100 moles × (2(22.99 g/mol) + 12.01 g/mol + 3(16.00 g/mol))
= 0.0100 moles × 105.99 g/mol
= 1.06 g
Finally, we can calculate the percentage by mass of sodium carbonate:
Percentage by mass = (0.265 g / 1.06 g) × 100
= 25%
Therefore, the percentage by mass of sodium carbonate in the washing soda is 25%.