Chemical
Calculations
The
coefficients in a balanced equation represent the number
of molecules or atoms that are reacting and are produced.
For example, in the
formation of
water, 2 molecules of hydrogen gas react with 1 molecule of oxygen
producing 2
molecules of water. If 4 molecules of hydrogen gas are present, then 2
molecules of oxygen gas will be needed to produce 4 molecules of water.
2H_{2}(*g*)
+ O_{2}(*g*) → 2H_{2}O(*l*)
But
what if there are 400 molecules of hydrogen gas? How much
oxygen gas would be required to use up all the hydrogen gas?
It
can be seen that the ratio of hydrogen
molecules
to oxygen
molecules
required
is always 2:1. But in the laboratory, when a measurable amount of
reactants are
necessary, it is advantageous to use moles to count the molecules. So 2
moles
of H_{2} (representing 1.20 × 10^{24}
molecules) would react
with 1 mole of O_{2} (representing 6.02
×10^{23} molecules) and
produce 2 moles of H_{2}O (representing 1.20
× 10^{24}
molecules).
In
other words, all coefficients in a balanced equation
represent the number of moles of substances as well as the number of molecules, and
can give
a ratio between the compounds and elements in a reaction. In the case
of the
reaction of sodium with chlorine to produce sodium chloride:
2Na(*s*)
+ Cl_{2} (*g*) → 2NaCl(*s*)
The ratio
of moles of Na to moles of Cl_{2} is 2:1, but the
ratio of moles of Na to moles of NaCl is 2:2, and the ratio of moles of Cl_{2} to moles of NaCl is 1:2.
These mole ratios can be developed for any balanced equation and can be
used to
determine how much product is made from a given amount of starting
material.
Sample Problem
How
many moles of Cl_{2} would be required if 5.0
mol of Na was completely reacted?
The mole ratio of Na:Cl_{2 }is
2:1,
so we multiply the 5.0 reacted moles of Na by the mole ratio:
Please note that the mole
ratios used have an infinite
number of significant figures and the number of significant figures in
the
answer will be determined by the number in the starting figure. |