Calculate the Emperical Formula of C-80%, H-20%;
Vapour density -15%. calculate the molecular formula
Answers
Explanation:
use a sample of this compound to help you determine its empirical formula
use the ideal gas law equation, the gas' density, and the known STP conditions for pressure and temperature to find th gas' molar mass
use the empirical formula and the gas' molar mass to find its molecular formula
So, you know that you're dealing with a hydrocarbon that contains
92.3
%
carbon and
7.7
%
hydrogen by mass. To make the calculations easier, select a
100-g
sample of this compound.
You know from the aforementioned percent composition that this sample will contain
92.3 g
of carbon and
7.7 g
of hydrogen.
Use the molar masses of the two elements to figure out how many moles of each you'd get in this sample
92.3
g
⋅
1 mole C
12.011
g
=
7.6846 moles C
7.7
g
⋅
1 mole H
1.00794
g
=
7.6393 moles H
Divide both values by the smallest one to get the mole ratio that exists between the two elements in the compound
For C:
7.6846
moles
7.6393
moles
=
1.006
≈
1
For H:
0.76393
moles
0.76393
moles
=
1
The empirical formula for this hydrocarbon is
C
1
H
1
⇒
CH
Now, STP conditions are characterized by a pressure of
100 kPa
and a temperature of
0
∘
C
. Keep this in mind.
The ideal gas law equation
P
V
=
n
R
T
can be rewritten using the definition of
n
, the number of moles of gas. As you know, the number of moles if equal to the ratio between the mass and the molar mass of a compound
n
=
m
M
M
Plug this into the ideal gas law equation to get
P
V
=
m
M
M
⋅
R
T
Rearrange to get
M
M
isolated on one side of the equation
M
M
=
=
ρ
m
V
⋅
R
T
P
Since density is defined as mass per unit of volume, you can say that
M
M
=
ρ
⋅
R
T
P
Plug in the STP pressure and temperature and solve for
M
M
- do not forget to convert the pressure from kPa to atm and the temperature from degrees Celsius to Kelvin!
Also, convert the density of the gas from grams per milliliter to grams per liter
0.00454
g
mL
⋅
1000
mL
1 L
=
4.54 g/L
M
M
=
4.54
g
L
⋅
0.0821
atm
⋅
L
mol
⋅
K
⋅
(
273.15
+
0
)
K
100
101.325
atm
M
M
=
103.2 g/mol
Now, the molecular formula will always be a multiple of the empirical formula. The molar mass of the empirical formula is
1
×
12./011 g/mol
+
1
×
1.00794 g/mol
=
13.019 g/mol
This means that you have
13.019
g/mol
×
n
=
103.2
g/mol
This will get you
n
=
103.2
13.019
=
7.93
≈
8
Therefore, the molecular formula of the hydrocarbon will be
(
CH
)
8
⇒
C
8
H
8