Transcript Chemical Calculations I: Formulas
Chapter 9.
Chemical Calculations I Chemical Formulas
The
Law of Definite Proportions
states that in a pure compound, the elements are always present in the same definite proportion by mass.
This is consistent with Atomic Theory.
It allows us to make useful calculations.
Chemical Formulas
Two samples of NH
3
from different sources: # Mass of Sample Mass of N Mass of H A B 1.840 g 2.000 g 1.513 g 1.644 g 0.327 g 0.356 g A % N = 1.513 g x 100% = 82.23 % 1.840 g B % N = 1.644 g x 100% = 82.20 % 2.000 g
Chemical Formulas
Two samples of N
2
H
4
from different sources: # Mass of Sample Mass of N Mass of H A B 3.245 g 2.950 g 2.836 g 2.578 g 0.409 g 0.372 g A % N = 2.836 g x 100% = 87.40 % 3.245 g B % N = 2.758 g x 100% = 87.39 % 2.950 g
Chemical Formulas
A property of NH
3
(ammonia) is that it always has 82.2% nitrogen, regard less of the source or amount of the sample.
Hydrazine (N
2
H
4
), a different compound than ammonia, always has 87.4% nitrogen, regardless of the source or amount of the sample.
Percent composition is a property of a compound.
Chemical Formulas
If you try to make a compound by combining its elements, you must combine them in the correct mass ratios, or you'll have some of one element left over: Make CaS (calcium sulfide) Mass of Ca 55.6 g 55.6 g Mass of S 44.4 g 50.0 g Mass of CaS 100.0 g 100.0 g Excess S 0.0 g 5.6 g Mass Ratio Ca/S 1.25/1.00
1.25/1.00
Chemical Formulas
What's going on? At the atomic level: 4 atoms of Ca 4 atoms of S 4 units of CaS 4 atoms of Ca 6 atoms of S 4 units of CaS 2 units of S left over
Chemical Formulas
And no matter what happens, the mass ratio of Ca to S in the compound is 1.25 to 1.00. Therefore, the individual atoms of Ca must be 1.25 times the mass of the S atoms.
Experiments with relative masses of elements in compounds were used to determine atomic masses for the Periodic Table.
Chemical Quantities
How many atoms does it take to get meas urable quantities of an element?
A WHOLE LOT!!!
Chemical Quantities
Since we can't see or work with individual atoms, we work with them
en mass,
so to speak. Just like we do with lots of common things: flour, sugar, produce, other staples We also count things in groups: pairs, dozens, scores, gross, reams
Moles
We count atoms in groups called
moles
.
1.000 mole = 6.022 x 10
23
atoms (atoms, or anything else)
Moles
Moles
1 mole = 6.022 x 10
23
atoms (or anything else)
This is huge!
602,200,000,000,000,000,000,000 volume of Earth's oceans in liters age of earth in seconds population of earth, individuals cost of a car, US dollars
Molar Masses
Molar Masses
The
molar mass
6.022 x 10
23
of an element is the mass of atoms of that element.
1.008 g is mass of 6.022 x 10
23
hydrogen atoms 12.01 g is mass of 6.022 x 10
23
carbon atoms 238.0 g is mass of 6.022 x 10
23
uranium atoms The
atomic mass
of an element is the mass of 1 atom of that element.
1.008 amu is mass of one hydrogen atom, etc.
Molar Masses
Relationship between grams and amu's (atomic mass units): 1.000 gram = 6.022 x 10
23
amu 1.000 amu = 1.661 x 10
-22
gram
Molar Masses
6.022 x 10
23
is also called
Avogadro's number
for Amedeo Avogadro, who first deduced a relationship between the number of molec ules of a gas and its volume.
Avogadro's number can be used as a conver sion factor, like "dozen" or "score".
It allows us to "count" atoms by determining the mass of a group of them.
Molar Masses
The molar mass is a conversion factor between moles of a substance and its mass.
Molar mass has units grams mole g mol 12.01 g C mol C 1 mol C 12.01 g C
Molar Masses
Example: In 27.43 grams of iron, (a) (b)
Note:
How many moles of iron are there?
How many atoms of iron are there?
Competency I-2
When working with molar mass, always use enough significant figures in the molar mass to match or exceed the significant figures in other terms. Don't limit the accuracy of your work with molar mass!
Molar Masses
Conversion between molar mass, moles, and atoms (or molecules).
Grams Molar Mass Moles Avogadro's Number Atoms
Use the correct conversion, and don't use one you don't need!
Molar Masses
Examples: (a) What is the mass of 2.500 mol of carbon?
(b) How many atoms of carbon are present?
Molar Masses
Examples: In 1.00 x 10
22
atoms of gold, (a) What mass of gold is present?
(b) How many moles of atoms are present?
Molar Masses of Compounds
At the atomic level, the formula of a compound gives the number of each type of atom that makes up a formula unit or molecule of the compound.
At the macroscopic level, the formula of a com pound gives the number of moles of each type of atom that makes up a mole of for mula units or molecules of the compound.
Molar Masses of Compounds
One molecule of H
2
O contains 2 hydrogen atoms 1 oxygen atom One mole of H
2
O contains 2 moles of hydrogen atoms 1 mole of oxygen atoms 1 mole of water molecules
Molar Masses of Compounds
What is the mass of one mole of water?
2 mol H x 1.01 g H = 2.02 g H mol H 1 mol O x 16.00 g O = 16.00 g O mol O 18.02 g H 2 O
Molar Masses of Compounds
What is the mass of one mole of water?
18.02 g H
2
O mol H
2
O There are 6.022 x 10
23
molecules in there, and you can swallow it in one gulp!
Molar Masses of Compounds
Examples: Find the molar masses of (a) N
2
(b) NaCl (c) CaCO
3
(d) Mg(NO
3
)
2
Percent Composition
The
percent composition
of a compound is the percent of its mass contributed by each element in its formula.
Percent composition can be calculated and checked against an experimental value to confirm the identity of a compound.
Percent Composition
Steps: (a) calculate molar mass of compound, writing out mass contributions of the elements (b) divide mass contribution of each element by molar mass, express result as a percentage.
Percent Composition
Examples: Calculate the percent composition of the following compounds.
(a) H
2
O (b) Mg(NO
3
)
2
Empirical Formulas
Empirical formulas
show the smallest whole-number ratio of the elements found in a compound.
One can obtain a percent composition by experiment, and use it to calculate the empirical formula of a compound.
The calculation is essentially the reverse of determining a percent composition.
Empirical Formulas
Steps: (a) assume 100.00 g of compound, so mass percent of each element can be expressed in grams (b) calculate number of moles of each element present in that mass (c) determine mole ratios of elements (d) write empirical formula
Empirical Formulas
Example: The empirical formula for Freon-12, a refrigerant, is given below. De termine its empirical formula.
9.933 % C 58.63 % Cl 31.44 % F Competency I-3
Molecular Formulas
Molecular formulas
show the number of atoms present in a molecule of a compound. A mol ecular formula is a whole number multiple of an empirical formula.
Empirical Formula NH
2
CH
2
CH
2
O Molecular Formula N
2
H
4
C
2
H
4
, C
4
H
8
, C
6
H
12
C
5
H
10
O
5
, C
6
H
12
O
6
Molecular Formulas
To determine a molecular formula, one needs: (a) The empirical formula of the compound.
(b) The molar mass of the compound.
Steps: (a) Use empirical formula to determine formula mass of compound.
(b) Divide molar mass by formula mass.
(c) Multiply empirical formula by result from (b)
Molecular Formulas
Example: Uracil, a component of ribonucleic acid (RNA), has the empirical formula C
2
H
2
NO. Its molar mass is 112.09 g/mol. What is its molecular formula?
Competency I-4