11. A 39.75 g sample of unknown metal carbonate (Y2CO3) was dissolved to make
200.00 cm3
of a solution. The solution was titrated with 1.0000 M sulphuric acid.
If 20.00 cm3
of the solution reacted completely with 37.50 cm3
of the sulphuric
acid, calculate the:
(a) Number of moles of sulphuric acid in the reaction.
(b) Number of moles of the metal carbonate in 20.00 cm3
of the metal carbonate
solution.
(c) Molar mass of the metal carbonate.
(d) Relative atomic mass of the metal Y in the formula unit and identify the
metal.
(Note that Y is not the actual symbol of the metal; C = 12, O = 16, H = 1, S = 32).
To solve this problem, we need to use the balanced chemical equation for the reaction between sulphuric acid (H2SO4) and the metal carbonate (Y2CO3):
H2SO4 + Y2CO3 -> Y2(SO4)3 + H2O + CO2
(a) Number of moles of sulphuric acid in the reaction:
From the balanced equation, we can see that the mole ratio between sulphuric acid and metal carbonate is 1:1. Therefore, the number of moles of sulphuric acid is equal to the number of moles of metal carbonate that reacted.
Since 37.50 cm3 of 1.0000 M sulphuric acid reacted with the metal carbonate, we can calculate the number of moles of sulphuric acid using the equation:
moles of sulphuric acid = volume (in liters) x molarity
moles of sulphuric acid = 37.50 cm3 x (1 L/1000 cm3) x 1.0000 M
moles of sulphuric acid = 0.03750 L x 1.0000 M
moles of sulphuric acid = 0.03750 mol
Therefore, the number of moles of sulphuric acid in the reaction is 0.03750 mol.
(b) Number of moles of the metal carbonate in 20.00 cm3 of the metal carbonate solution:
Since the mole ratio between sulphuric acid and metal carbonate is 1:1, the number of moles of metal carbonate that reacted is also 0.03750 mol.
Therefore, the number of moles of the metal carbonate in 20.00 cm3 of the metal carbonate solution is 0.03750 mol.
(c) Molar mass of the metal carbonate:
To calculate the molar mass of the metal carbonate, we can use the number of moles of the metal carbonate and the mass of the metal carbonate.
mass of the metal carbonate = number of moles x molar mass
Molar mass = mass of the metal carbonate / number of moles
Molar mass = 39.75 g / 0.03750 mol
Molar mass = 1060 g/mol
Therefore, the molar mass of the metal carbonate is 1060 g/mol.
(d) Relative atomic mass of the metal Y in the formula unit and identify the metal:
From the balanced equation, we can see that the metal Y has a 2:1 stoichiometric ratio with the carbonate ion (CO3). Therefore, the molar mass of the metal Y is half the molar mass of the metal carbonate.
Relative atomic mass of metal Y = molar mass of the metal Y / 2
Relative atomic mass of metal Y = 1060 g/mol / 2
Relative atomic mass of metal Y = 530 g/mol
To identify the metal Y, we need to compare the relative atomic mass of Y with the atomic masses of known elements. However, we do not have enough information to determine the specific metal without further data.