Gases Chemistry Worksheet - Chapter 13, An Introduction To Chemistry Page 18

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Chapter 13
Gases
When Properties Change
Another useful equation, derived from the ideal gas equation, can be used to calculate
changes in the properties of a gas. In the first step of the derivation, the ideal gas
equation is rearranged to isolate R.
PV
= R
nT
In this form, the equation shows that no matter how the pressure, volume, moles of
gas, or temperature of an ideal gas may change, the other properties will adjust so that
the ratio of PV/nT always remains the same. In the equations below, P
, V
, n
, and
1
1
1
T
are the initial pressure, volume, moles of gas, and temperature, and P
, V
, n
, and
1
2
2
2
T
are the final pressure, volume, moles of gas, and temperature.
2
P
V
1
1
P
V
= n
RT
= R
so
1
1
1
1
n
T
1
1
P
V
2
2
P
V
= n
RT
= R
so
2
2
2
2
n
T
2
2
Therefore,
P
V
P
V
1
1
2
2
=
O
18
bjeCtive
n
T
n
T
1
1
2
2
The equation above is often called the combined gas law equation. It can be used to do
calculations such as Example 13.4 and Exercise 13.2, which follow the sample study
sheet below.
Sample Study
T
-
– The problem requires calculating a value for a gas property that has
ip
off
changed. In other words, you are asked to calculate a new pressure, temperature,
Sheet 13.2
moles (or mass), or volume of gas given sufficient information about the initial and
Using the
other final properties.
Combined Gas
G
S
eneral
TepS
Law Equation
Step 1 Assign the variables P, T, n, and V to the values you are given and to
O
18
the unknown value. Use the subscripts 1 and 2 to show initial or final
bjeCtive
conditions.
Step 2 Write out the combined gas law equation, but eliminate the variables for any
constant properties. (You can assume that the properties not mentioned in the
problem remain constant.)
Step 3 Rearrange the equation to isolate the unknown property.
Step 4 Plug in the values for the given properties.
Step 5 Make any necessary unit conversions and cancel your units.
Step 6 Calculate your answer and report it with the correct units and with the
correct significant figures.
e
See Example 13.4.
xample

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