EXAMPLE 2.1
Mass Ratios
The gas methane (CH4), the main component of the fuel natural gas, can be decomposed to give carbon (C)
and hydrogen (H) in a ratio of 3.00 parts by mass of carbon to 1.00 part by mass of hydrogen. How much
hydrogen can be made from 90.0 g of methane?
Solution
We can express the parts ratio in any units we choose—pounds, grams, kilograms—as long as it is the same
for both elements. Using grams as the units, we see that 3.00 g of C and 1.00 g of H would mean 4.00 g CH 4
at the start. To convert g CH4 to g H, the conversion factor we need includes 1.00 g H and 4.00 g CH 4.
We start with the
given quantity.
90.0 g CH4 x
We multiply by the ratio,
expressed in grams.
1.00 g H
4.00 g CH4
= 22.5 g H
the number
the unit
Exercise 2.1A
The gas ammonia can be decomposed to give 3.00 parts by mass of hydrogen and 14.0 parts by mass of
nitrogen. What mass of nitrogen is obtained if 1.27 g of ammonia is decomposed?
EXAMPLE 2.1
Mass Ratios continued
Exercise 2.1B
Nitrous oxide, sometimes called “laughing gas,” can be decomposed to give 7.00 parts by mass of nitrogen
and 4.00 parts by mass of oxygen. What mass of nitrogen is obtained if enough nitrous oxide is decomposed to
yield 36.0 g of oxygen?
EXAMPLE 2.2
Atom Ratios
Hydrogen sulfide gas can be decomposed to give sulfur and hydrogen in a mass ratio of 16.0:1.00. If the
relative mass of sulfur is 32.0 when the mass of hydrogen is taken to be 1.00, how many hydrogen atoms are
combined with each sulfur atom in the gas?
Solution
We start with the
relative mass of a
sulfur atom
3.2.0 units S
1 atom S
We multiply by
the given mass
ratio
x
1.00 unit H
16.0 units S
Then we multiply by
the relative mass of a
hydrogen atom
x
1 atom H
1 unit H
=
2 atoms H
The answer:
a ratio of 2 atoms H
to 1 atom S
1 atom S
Exercise 2.2
Arsine gas can be decomposed to give arsenic and hydrogen in a mass ratio of 25.0:1.00. If the relative mass
of arsenic is 74.9 when the mass of hydrogen is taken to be 1.00, how many hydrogen atoms are combined
with each arsenic atom in the gas?