Untitled - Kelly Walsh High School

90 CHEMISTRY FOR THE UTTERLY CONFUSED
Don’t Forget!
The presence of two volumes (or two temperatures) is a very strong indication
that we will need to use the combined gas law. To use this gas law we need
subscripts to differentiate the different volumes and temperatures. Label one
volume V 1 and the other V 2. It does not matter which volume we label 1 or 2 as
long as we label all associated variables with the same subscript.
V1 5.00 L V2 7.50 L
T1 25C 298 K T2 ?C
The combined gas law is (P 1V 1/T 1) (P 2V 2/T 2). It is possible to simplify this
equation in this problem by removing all variables not appearing in the table.
The simplified combined gas law is (V 1/T 1) (V 2/T 2), which is a form of
Charles’ law. After simplification, we need to isolate the variable we are seeking
(the one with the question mark in the table). Isolation of T 2 requires
manipulating the equation. There are various ways of doing this, all yielding the
equation T 2 (T 1V 2/V 1). We now enter the appropriate values from our table
into this equation:
T 2 (T 1 )(V 2 )
(V 1 )
(298 K) (7.50 L)
(5.00 L)
447 K
To finish the problem we must convert this Kelvin temperature to the requested
Celsius temperature (T 2 (447 273)C 174C.
The answer must make sense. In this case, there was an increase in volume, and,
according to Charles’ law, the temperature must also increase.
Let’s try another example: A sample of gas has a volume of 2.50 L at 25C and
745 torr. What will be the volume, in liters, of the sample if we increase the temperature
to 45C and the pressure changes to 0.750 atm? As usual, we begin by
extracting the numbers (and associated units) along with the desired unknown
from the remainder of the problem.
V 1 2.50 L V 2 ? L
T 1 25C 298 K T 2 45C 318 K
P 1 745 torr P 2 0.750 atm