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Mass of unknown metal sulfate = 0.323 g
Mass of precipitated BaSO
4
= 0.433 g Contains all of the SO
4
2-
in the unknown metal sulfate sample
We need the molar mass of the metal in order to identify it.
molar mass =
mass in a given sample
moles in a given sample
If we find:
- the mass of the metal in 0.323 g sample
- the number of moles that the metal’s mass represents
Then we can find the molar mass of the metal
We can calculate both the mass and the moles of the metal from the mass of precipitated BaSO
4
To arrive at the moles of the metal, we need to calculate the moles of SO
4
2-
Moles of sulfate =
233.38 g BaSO
4
1 mol BaSO
4
0.433 g BaSO
4
= 0.0018553 mol SO 4
2-
×
×
1 mol BaSO
4
1 mol SO 4
2-
If we assume M
2
SO
4
and relate it to the moles of metal via the formula of the compound, which depends on the charge of the metal cation:
M
2
SO
4
for M
MSO
4
for M
2+
M
2
(SO
4
3
for M
3+
Moles of M =
2 mol M
= 0.0037106 mol M × 0.0018553 mol SO
4
2-
1 mol SO
4
2-
What is the metal in the unknown metal sulfate?
To calculate the molar mass of M, we also need the mass of M in the unknown sample.
Since the unknown sample mass is composed of M and SO
4
2-
, we can get the mass of M by subtracting the mass of SO
4
2-
from the sample mass.
We already calculated the moles of SO 4
2-
, so we convert it to mass:
Mass of SO
4
2-
=
96.06 g SO
4
2-
= 0.17822 g SO 4
2-
×
0.0018553 mol SO
4
2-
1 mol SO
4
2-
Mass of M = ‒ 0.17822 g SO 4
2-
0.323 g M
2
SO
4
= 0.14478 g M
0.0037106 mol
molar mass of M
mass of M in 0.323 g sample
moles of M in 0.323 g sample
0.14478 g
= 39.0 g/mol M is potassium (K)
Alternatively, since we have a finite set of possibilities, we can calculate the mass % of sulfate (or mass
% metal) for each possibility. Then we can identify the metal by matching the mass % for our unknown
with one of the possibilities.
- In that case, we don’t need to assume a cation charge (hence the formula) for our unknown, since
we calculate the experimental mass % directly from the data, without assuming a specific formula.
Mass of sulfate =
96.06 g SO
4
2-
1 mol SO
4
2-
0.0018553 mol SO 4
2-
×
= 0.1782 g SO
4
2-
Mass % of sulfate =
0.1782 g
0.323 g
which would match the sulfate mass % in K
2
SO
4
(pre-calculated, along with the other possible metal sulfates).
Do you remember how to calculate mass % of an element (or that of a polyatomic ion) from the chemical formula?
×
Mass of SO
4
2-
Mass of sample
×
