The maximum mass of phosphane
(
PH
3
)
that can be produced under the conditions stated in the question is
6.8 g
.
Explanation:
Start with a balanced equation.
P
4
+
6H
2
→
4PH
3
This is a limiting reactant problem. The reactant that produces the least
PH
3
determines the maximum number of grams of
PH
3
The process will go as follows:
given mass P
4
→
mole P
4
→
mol PH
3
→
mass PH
3
and
given mass H
2
→
mole H
2
→
mol PH
3
→
mass PH
3
The molar masses of each substance is needed. Molar mass is the mass of one mole of an element, molecule or ionic compound in g/mol.
Molar Masses
Multiply the subscript for each element by its atomic weight on the periodic table in g/mol. If there is more than one element, add the molar masses together.
P
4
:
(
4
×
30.974
g/mol P
)
=
123.896 g/mol P
4
H
2
:
(
2
×
1.008
g/mol H
)
=
2.016 g/mol H
2
PH
3
:
(
1
×
30.974
g/mol P
)
+
(
3
×
1.008
g/mol H
)
=
33.998 g/mol PH
3
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now you need to determine the mass of phosphane,
PH
3
, produced individually by
6.2 g P
4
and by
4.0 g H
2
. I'm going to start with
P
4
since it is first in the equation.
Moles of Phosphorus
Multiply the given mass of
P
4
by the inverse of its molar mass.
6.2
g P
4
×
1
mol P
4
123.896
g P
4
=
0.05004 mol P
4
Moles of Phosphane
Multiply mol
P
4
by the mole ratio,in the balanced equation, between
P
4
and
PH
3
that will cancel
P
4
.
0.05004
mol P
4
×
4
mol PH
3
1
mol P
4
=
0.20016 mole PH
3
Mass of Phosphane
Multiply mol
PH
3
by its molar mass.
0.20016
mol PH
3
×
33.998
g PH
3
1
mol PH
3
=
6.8 g PH
3
(rounded to two sig figs due to 6.2 g and 4.0 g)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Now you need to determine the mass of phosphane that
4.0 g H
2
can produce. I'm going to put the steps together into one equation, but it will contain all of the steps required.
4.0
g H
2
×
1
mol H
2
2.016
g H
2
×
4
mol PH
3
6
mol H
2
×
33.998
g PH
3
1
mol PH
3
=
45 g PH
3
Phosphorus is the limiting reactant, which means the maximum amount of phosphane that can be produced is
6.8 g
sorry its so long.