EART6
Balancing chemical equations
Worksheet 6
Because atoms are neither created nor destroyed in any chemical reaction, a chemical equation must have an equal number of atoms of each element on each side. An equation is balanced when this occurs.
• Subscripts should never be changed, since they represent identity
• Coefficients need to be changed. For most purposes, a balanced equation should contain the smallest possible whole-number coefficients
• It is usually best to balance first those elements that occur in the fewest chemical formulae on each side of the equation.
Eg . Combustion of methane:
CH
4
CH
4
CH
4
+ O
2
+ O
2
+ 2O
2
!
CO
2
!
CO
2
!
CO
2
+ H
2
+ 2H
O
( unbalanced
2
+ 2H
O
( unbalanced
2
O
( balanced
)
)
)
Molar mass
The molar mass of an element is the atomic weight in grams per mole.
Q: How many moles of water are in a liter of water, if 1 liter = 1 kilogram water.
A: Atomic weights:
Hydrogen: 1.008 amu
Oxygen: 16.00 amu
Formula weight = 1.008 amu + 1.008 amu + 16.00 amu = 18.016 amu
Molar mass:
1 H
2
O molecule has a mass of 18.0 amu ↔ 1 mol H
2
O has a mass of 18.0 g
1000 g
!
"#
1 mol
$
18.0 g %&
= 55.55 moles of water
Q: If a new corn-based fuel called ethanol-XP has the following characteristics:
• 1 km 2 of land yields 27200 bushels of corn
• 1 bushel of corn can produce 10 liters of ethanol-XP
• Density of liquid ethanol-XP = 790 kg/m 3
How much ethanol-XP can be produced on 1 km 2 of land (units of kg/km 2 )

A:
!
"#
27200 bushels
1 km
2
$
%&
!
"#
10 liter bushel
$
%&
!
"#
1 m
3 $
1000 liter
%&
!
"#
790 kg m
3
$
%&
=
!
27200 bushels
"# 1 km 2
$
%&
!
10 liter
"# 1 bushel
$
%&
!
"
1 m 3
1000 liter
$
%
!
"#
790 kg
$ m
3 %&
= 214880 kg km 2
!
"
!
"#
Conversions: 1 km2 = 247 acre
Q: If the molecular weight of ethanol-XP is 32 g/mol, and 215,000 kg of ethanol-XP can be produced on 1 km 2 of land, how many moles of ethanol-XP can be grown per 1 km 2 ?
A:
215,000 kg
1 km 2
$
%&
!
"#
1 mol
$
32 g
%&
=
215,000 kg
1 km
2
$
%
!
"
1 mol
0.032 kg
$
%
=
6.71875
'
10 6 mol km
2
Q: Solar panels under development at NASA are ~30% efficient. If a panel receives 400
W/m 2 of solar radiation, how much power [W/m 2 ] is available for use?
400
W
m 2
!
( ) = 120
W
m 2
Q: If the energy requirement of Texas and surrounding states is ~10 12 W, how much land [km 2 ] would be necessary to develop for solar power using the above panels?
10
12
W
= 8.33
!
10 9 m 2
120 W m –2
Q: If Europe’s annual energy consumption were 6.2
!
10 19 J , how many kg of uranium would be required to produce it by nuclear power alone? 1 gram of uranium yields ~ 5.0 x 10 7 kJ
"
6.2
!
10 19 J
5.0
!
10 7 kJ
%
= 6.2
!
10 19 J
"
#$
1 g
5.0
!
10 7 kJ
%
&'
= 6.2
!
10 19 J
"
#$
1 kJ
1000 J
%
&'
"
#$
1 g
5.0
!
10 7 kJ
%
&'
=
#$ g &'
1.24
!
10 9 g
"
#$
1 kg
1000 g
%
&'
= 1.24
!
10 6 kg