Transcript
DETERMINING EMPIRICAL AND MOLECULAR FORMULAE
Let's start with a few definitions. The empirical formula is the simplest formula for a compound. A molecular formula is the same as or a multiple of the empirical formula, and is based on the actual number of atoms of each type in the compound. For example, if the empirical formula of a compound is C3H8 , its molecular formula may be C3H8 , C6H16 , etc.
An empirical formula is often calculated from elemental composition data. The weight percentage of each of the elements present in the compound is given by this elemental composition.
Let's determine the empirical formula for a compound with the following elemental composition:
40.00% C, 6.72% H, 53.29% O.
The first step will be to assume exactly 100 g of this substance. This means in 100 g of this compound, 40.00 g will be due to carbon, 6.72 g will be due to hydrogen, and 53.29 g will be due to oxygen. We will need to compare these elements to each other stoichiometrically. In order to compare these quantities, they must be expressed in terms of moles. So the next task will be to convert each of these masses to moles, using their respective atomic weights:
Take notice that since the composition data was given to four significant figures, the atomic weights used in the calculation were to at least four significant figures. Using fewer significant figures may actually lead to an erroneous formula.
Now that the moles of each element are known, a stoichiometric comparison between the elements can be made to determine the empirical formula. This is achieved by dividing through each of the mole quantities by whichever mole quantity is the smallest number of moles. In this example, the smallest mole quantity is either the moles of carbon or moles of oxygen (3.331 mol):
The ratio of C:H:O has been found to be 1:2:1, thus the empirical formula is: CH2O. Again, as a reminder, this is the simplest formula for the compound, and not necessarily the molecular formula. Suppose we know that the molecular weight of this compound is 180 g/mol. With this information, the molecular formula may be determined. The formula weight of the empirical formula is 30 g/mol. Divide the molecular weight by the empirical formula weight to find a multiple:
The molecular formula is a multiple of 6 times the empirical formula:
C(1 x 6) H(2 x 6) O(1 x 6) which becomes C6H12O6
Alternatively, the empirical and molecular formula may be determined from experimental data. Suppose we have a compound containing the elements, C, H and S. A 7.96 mg sample of this compound is burned in oxygen and found to form 16.65 mg of CO2. The sulfur in 4.31 mg of the compound is converted into sulfate by a series of reactions, and precipitated as BaSO4 . The BaSO4 was found to have a mass of 11.96 mg. The molecular weight of the compound was found to be 168 g/mol. Using this data, what is the molecular formula of the compound?
The strategy will be to use stoichiometry to determine the mass percent of each of the elements in the compound, and then use the mass percentages to determine the empirical formula. Notice that since all the data is in milligrams, we may carry out the calculations using milli- units throughout.
The only source of carbon for the CO2 formed came from the compound, thus, determine the milligrams of carbon found in 16.65 mg of CO2 :
Now that the "part" of the sample due to carbon is known, one may calculate the percent carbon in the compound, using the mass the sample as the "whole":
The only source of sulfur for the precipitate of BaSO4 , came from the compound, thus, determine the milligrams of sulfur in 11.96 mg of BaSO4 :
Similarly, determine the percent sulfur in the compound, using the mass of sulfur as the "part" and the mass of compound as the "whole":
The percentage of hydrogen may determined by difference:
%H = 100.0% - 57.1 %C - 38.1 %S = 4.8 %H
From the elemental composition, we may determine the empirical formula, in the same manner as used in the first example. First, assume exactly 100 g of the compound. In 100 grams of the compound, 57.1 g would be due to carbon, 38.0 g would be due to sulfur and 4.9 g would be due to hydrogen. Convert each of these masses into moles using the corresponding atomic weight for each element:
Now that the moles of each element are known, the empirical formula may be determined by dividing the moles of each element by the smallest number of moles. This yields a ratio of the number of each element in the empirical formula.
The ratio of C:H:S has been found to be 4:4:1, thus the empirical formula is: C4H4S. The molar mass of the empirical formula is 84 g/mol. Since the molecular weight of the actual compound is 168 g/mol, and is double the molar mass of the empirical formula, the molecular formula must be twice the empirical formula:
C(4 x 2) H(4 x 2) S(1 x 2) which becomes C8H8S2
Problems
1. The analgesic, aspirin, has the following elemental percent composition: 60.00% C, 4.48% H, and
35.53% O.
a. Find the empirical formula of aspirin.
b. If the molar mass of aspirin is 180 g/mol, what is the molecular formula of aspirin?
2. Paradichlorobenzene is the active ingredient in the insecticide known as mothballs. The elemental
percent composition of paradichlorobenzene is: 49.02% C, 2.74% H, and 48.24% Cl.
a. Find the empirical formula of paradichlorobenzene.
b. If the molar mass of paradichlorobenzene 147 g/mol, what is the molecular formula of this
compound?
3. Many sunscreens contain the compound para-aminobenzoic acid (PABA). The elemental percent
composition of PABA is: 61.31% C, 5.15% H, 10.21% N, and 23.33% O.
a. Find the empirical formula of PABA.
b. If the molar mass of PABA is 137 g/mol, what is the molecular formula of PABA?
4. Potassium Ferricyanide is a water soluble red dye used in products such as bingo dabbers. The
elemental percent composition of potassium ferricyanide: 35.62% K, 21.89% C, 16.96% Fe, and
25.53% N.
a. Find the empirical formula of potassium ferricyanide.
b. If the molar mass of potassium ferricyanide is 329 g/mol, what is the molecular formula of
potassium ferricyanide?
5. Lindane is an insecticide used to kill lice. The elemental percent composition of lindane is: 24.78% C,
2.08% H, and 73.14% Cl.
a. Find the empirical formula of lindane.
b. If the molar mass of lindane is 290 g/mol, what is the molecular formula of lindane?
Answers
General comments: Always use at least the same number of significant figures for the molar masses of the elements as are given for the elemental composition. For example, if you are given 43.89% C, then use at least 12.01g/mol for the molar mass of carbon. Using fewer significant figures (12 g/mol or 12.0 g/mol, in this case) could actually lead to the incorrect formula. On the other hand, when determining the multiple for converting the empirical formula to a molecular formula, whole number molar masses are typically sufficient.
When given the elemental percent composition, it is convenient to assume 100 grams of the substance. Doing so allows you to have a reference point in that the percentage of the element becomes the mass. For example, if the elemental composition of a compound is 54.3 %A and 45.7 %B, assuming 100 grams allows you to start with 54.3 g of A and 45.7 g of B.
1 a. Assume exactly 100 grams of aspirin. As a result, 60.00% C becomes 60.00 g C, 4.48% H becomes 4.48 g H and 35.53% O becomes 35.53 g O. Convert each of these masses to moles:
60.00 g C x 1 mol C12.01 g C = 4.996 mol C
4.48 g H x 1 mol H1.008 g H = 4.44 mol H
35.53 g O x 1 mol O16.00 g O = 2.221 mol O
Divide through by the smallest moles to find the ratio of C:H:O :
4.006 mol C2.221 mol O : 4.44 mol H2.221 mol O : 2.221 mol O2.221 mol O
2.250 : 2.00 : 1.000
The ratio does not work out to a whole numbers, so since 2.25 is 2 ¼, which is 9/4, multiply the entire ratio by 4:
2.250 x 4 = 9 C 2.00 x 4 = 8 H 1.000 x 4 = 4 O
The empirical formula is thus: C9H8O4. The empirical formula is the simplest possible formula for a compound.
1 b. The molecular formula is either the same as, or a multiple of the empirical formula. To find the multiple, one must compare the molar mass (MM) of the actual compound to the empirical formula weight (EFW). It is not necessary to use many significant figures to find this multiple.
Calculate the EFW: 9(12 g C/mol C) + 8(1 g H/mol H) + 4(16 g O/mol O) = 180 g/mol
The molar mass of aspirin is given to be 180 g/mol
Determine the multiple:
MMEFW = 180 g/mol180 g/mol = 1
Since the multiple is “1”, the empirical formula is identical to the molecular formula: C9H8O4.
2 a. Assume exactly 100 g of para-dichlorobenzene. As a result, 49.02% C becomes 29.02 g C, 2.74 % H becomes 2.74 g H and 48.24% Cl becomes 48.24 g Cl. Convert each of the masses to moles:
49.02 g C x 1 mol C12.01 g C = 4.082 mol C
2.74 g H 1 mol H1.008 g H = 2.72 mol H
48.24 g Cl 1 mol Cl35.45 g Cl = 1.361 mol Cl
Divide through by the smallest moles to find the ratio of C:H:Cl :
4.082 mol C1.361 mol Cl : 2.72 mol H1.361 mol Cl : 1.361 mol Cl1.361 mol Cl
3.00 : 2.00 : 1.00
The empirical formula of para-dichlorobenzene is C3H2Cl. This is the simplest formula for the compound.
2 b. The molecular formula is either the same as, or a multiple of the empirical formula. To find the multiple, one must compare the molar mass (MM) of the actual compound to the empirical formula weight (EFW). It is not necessary to use many significant figures to find this multiple.
Calculate the EFW: 3(12 g/mol) + 2(1 g/mol) + 1(35.5 g/mol) = 73.5 g/mol
The molar mass of para-dichlorobenzene is given to be 147 g/mol.
Determine the multiple:
147 g/mol73.5 g/mol = 2
The molecular formula is found by multiplying the subscripts of the empirical formula by the multiple of 2:
C3 x 2H2 x 2Cl1 x 2 = C6H4Cl2
3 a. Assume exactly 100 g of PABA. Thus, 61.31% C becomes 61.31 g C, 5.15% H becomes 5.15 g H, 10.21 g N becomes 10.21 g N and 23.33% O becomes 23.33 g O. Convert each of these masses to moles:
61.31 g C x 1 mol C12.01 g C = 5.105 mol C
5.15 g H x 1 mol H1.008 g H = 5.109 mol H
10.21 g N x 1 mol N14.01 g N = 0.7288 mol N
23.33 g O x 1 mol O16.00 g O = 1.458 mol O
Divide through by the smallest moles to find the ratio of C:H:N:O :
5.105 mol C0.7288 mol N : 5.109 mol H0.7288 mol N : 0.7288 mol N0.7288 mol N : 1.458 mol O0.7288 mol N
7.00 : 7.01 : 1.00 : 2.00
The empirical formula of PABA is C7H7NO2. This is the simplest formula for the compound.
3 b. compound.
2 b. The molecular formula is either the same as, or a multiple of the empirical formula. To find the multiple, one must compare the molar mass (MM) of the actual compound to the empirical formula weight (EFW). It is not necessary to use many significant figures to find this multiple.
Calculate the EFW of PABA: 7(12 g/mol) + 7(1 g/mol) + 1(14 g/mol) + 2(16 g/mol) = 137 g/mol
The molar mass of PABA is given to be 137 g/mol.
Determine the multiple:
MMEFW = 137 g/mol137 g/mol = 1
The molecular formula for PABA is the same as the empirical formula: C7H7NO2.
4 a. Assume exactly 100 grams of potassium ferricyanide. As result, 35.62 % K becomes 35.62 g K, 16.96 %Fe becomes 16.96 g Fe, 21.89 %C becomes 21.89 g C and 25.53 %N becomes 25.53 g N. Convert each of these masses to moles:
35.62 g K x 1 mol K39.10 g K = 0.9110 mol K
16.96 g Fe x 1 mol Fe55.85 g Fe = 0.3056 mol Fe
21.89 g C x 1 mol C12.01 g C = 1.823 mol C
25.53 g N x 1 mol N14.01 g N = 1.823 mol N
Divide through by the smallest moles to find the ratio of K:Fe:C:N :
0.9110 mol K0.3056 mol Fe : .3056 mol Fe.3056 mol Fe : 1.823 mol C.3056 mol Fe : 1.823 mol N.3056 mol Fe
3.000 : 1.000 : 6.000 : 6.000
The empirical formula for potassium ferricyanide is K3FeC6N6. This is the simplest formula for this compound.
4 b. The molecular formula is either the same as, or a multiple of the empirical formula. To find the multiple, one must compare the molar mass (MM) of the actual compound to the empirical formula weight (EFW). It is not necessary to use many significant figures to find this multiple.
Calculate the EFW for potassium ferricyanide:
3(39 g/mol) + 1(55.85 g/mol) + 6(12 g/mol) + 6(14 g/mol) = 329 g/mol
The molar mass of potassium ferricyanide is given to be 329 g/mol.
Determine the multiple:
MMEFW = 329 g/mol329 g/mol = 1
The molecular formula is the same as the empirical formula: K3FeC6N6
5 a. Assume exactly 100 g of lindane. As a result, 24.78 %C becomes 24.78 g C, 2.08 %H becomes 2.08 g H and 73.14% Cl becomes 73.14 g Cl. Convert each of these masses to moles:
24.78 g C x 1 mol C12.01 g C = 2.063 mol C
2.08 g H x 1 mol H1.08 g H = 2.063 mol H
73.14 g Cl x 1 mol Cl35.45 g Cl = 2.063 mol Cl
Divide through by the smallest moles to find the ratio of C:H:Cl :
2.063 mol C2.063 mol C : 2.063 mol H2.063 mol C : 2.063 mol Cl2.063 mol C
1.000 : 1.000 : 1.000
The empirical formula for lindane is CHCl. This is the simplest formula for the compound.
5 b. The molecular formula is either the same as, or a multiple of the empirical formula. To find the multiple, one must compare the molar mass (MM) of the actual compound to the empirical formula weight (EFW). It is not necessary to use many significant figures to find this multiple.
Calculate the EFW: 1(12 g/mol) + 1(1 g/mol) + 1(35.5 g/mol) = 48.5 g/mol
The molar mass of lindane is given to be 290 g/mol.
Determine the multiple:
MMEFW = 290 g/mol28.5 g/mol = 6
The molecular formula of lindane is found by multiplying the subscripts of the empirical formula by the multiple of 6:
C1 x 6H1 x 6Cl1 x 6 = C6H6Cl6
