Proust copper carbonate
Solution
a) To obtain moles, divide the mass by the molar mass. Relevant molar masses are:
(2x1.008 + 16.00) g/mol = 18.02 g/mol ,
(12.01+2x16.00) g/mol = 44.01 g/mol ,
63.55 g/mol ,
16.00 g/mol ;
1 mol
so
mol H2O = 10 g 
= 0.56 mol ,
18.02 g
1 mol
mol CO2 = 46 g 
= 1.05 mol ,
44.01 g
1 mol
mol Cu = 100 g 
= 1.57 mol ,
63.55 g
1 mol
mol additional O = 25 g 
= 1.56 mol .
16.00 g
The mole ratio is:
H2O : CO2 : Cu : O = 0.56 : 1.05 : 1.57 : 1.56 .
Divide all numbers in the ratio by the smallest as a first step toward expressing the ratio in terms
of integers:
H2O : CO2 : Cu : O = 1 : 1.88 : 2.84 : 2.82 .
This is fairly close to 1 : 2 : 3 : 3 . In fact, dividing all of the original numbers of moles by moles
of water makes the ratios seem further from whole numbers than they really are. If we divide the
numbers of moles by moles of Cu and multiply by 3, we get:
H2O : CO2 : Cu : O = 1.06 : 1.99 : 3 : 3.02 .
So the ratio is 1 : 2 : 3 : 3 . (See teaching notes for further discussion of why the ratio looks
better, i.e., more like integers, when we divide through by copper rather than water.)
H2O:
CO2:
Cu:
O:
b) Empirical formulas have to do with the elemental composition. For example, we need
moles of hydrogen rather than moles of water for the empirical formula.
mol H = 2 x mol H2O = 2(0.56 mol) = 1.11 mol ,*
mol C = mol CO2 = 1.05 mol ,
total mol O = mol H2O + 2 x mol CO2 + mol additional O ,
total mol O = (0.56 + 2x1.05 +1.56) mol = 4.21 mol ,
and
mol Cu = 1.57 mol .
The mole ratio is:
Cu : C : H : O = 1.57 : 1.05 : 1.11 : 4.21
Once again, dividing through by the smallest number can provide a start to expressing a ratio in
terms of integers:
Cu : C : H : O = 1.51 : 1 : 1.06 : 4.03 .
* I am not rounding until the end of the calculation. For instance, this result is really

1 mol 
210 g 
= 1.11 mol, not 1.12 . There are some other slight discrepancies due to

18.02 g 
rounding below.
All of these numbers are close to integers except the first one. Multiplying all the numbers by
two gives:
Cu : C : H : O = 3.01 : 2 : 2.12 : 8.05 ,
very close to 3 : 2 : 2 : 8 . So the empirical formula is Cu3C2H2O8 .
c) If the compound is Cux(CO3)y(OH)z, then the subscripts x, y, and z must be the same
as the subscripts on Cu, C, and H in the empirical formula (or at least stand in the same
proportion). To make sure that this formula makes sense, add up the oxygen atoms: 3y + z must
equal the subscript on O in the empirical formula. In fact, Cu3(CO3)2(OH)2 is consistent with
the empirical formula. It also is electrically neutral, with three 2+ charges from copper balancing
two 2– charges from carbonate and two 1– charges from hydroxide. The compound is the basic
copper carbonate of the mineral azurite, which tends to be more blue than green. Its formula
may also be expressed as 2CuCO3·Cu(OH)2 .