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Combined Gas Law:
The pressure and volume of a gas are inversely proportional to each
other, but directly proportional to the temperature of that gas.
Mathematically, this can be represented as:Temperature = Volume x Pressure / Constant
Constant x Temperature /
Pressure = Constant x
Temperature / Volume
Pressure x Volume/Temperature =
Substituting in variables, the formula is:PV/T=K
Because the formula is equal to a constant, it is possible to solve for a
change in volume, temperature, or pressure using a proportion:PV/T =
Explanation and Discussion:
The Combined Gas Law is a combination of Boyle's and Charles' Laws. The
Combined Gas Law describes the relationship between pressure, volume, and
temperature. For example, if the pressure increased, wither the volume
would decrease or the temperature would increase.
The Combined Gas Law can be used to solve any Boyle's or Charles' Law
problem. If one of the variables remains constant, disregard that
variable by leaving it out of your equation or setting it to the same
value on either side of the equals sign.
Calculations with the Combined Gas Law:
Let's try a problem with the Combined Gas Law. For example, the pressure
and temperature of a gas are changed to STP
(101.3 kPa/0°C) from 22.0°C and 30.8 kPa. What will be the new
volume if the original volume was 205 mL?
- First, we must convert degrees Celcius to Kelvins. This means that
our original temperature was 295 K and our target temperature is 273 K.
- Estimate and Answer
- It seems that the pressure increases, but the temperature decreases.
Because of their inverse relationship, the increased pressure will
decrease the volume. Because of their direct relationship, the decreased
temperature will decrease the volume, also. If we consider the amount
that the pressure increases, it more than triples. The temperature
decreases only slightly. Therefore, it is safe to assume that the new
volume will be less than a third of its original volume, or less than 68.2
mL (205 x 0.3333 = 68.2).
- Plug values into the formula
- From the problem, we know that, for the original state of the gas,
the conditions were:
Volume (V) = 205 mL
Temperature (T) = 295 K
Pressure (P) =
We also know the target temperature and pressure:Temperature1 (T1) = 273 K
Pressure1 (P1) = 101.3 kPa
The unkown is V1. Our equation is:30.8 kPa x 205 mL / 295 K = 101.3 kPa x V1 / 273
Manipulating the equation, we get:V1 = 30.8 kPa x 205 mL / 295 K x 273 K / 101.3
V1 = 57.68 mL
However, because our problem only was to three digits of precision, the
answer is:V1 = 57.7 mL
- To check our answer, we must compare it to our earlier estimate. We
estimated the value to be less than 68.2 mL. Because 57.7 mL is less
than 68.2 mL, but not incredible much so (like 20 - 30 mL), we can assume
the answer to be correct.
Because the Combined Gas Law is derived from Charles' Law and Boyle's
Law, you can find more information at those pages. You can also test
- Brown, Theodore L., H. Eugene LeMay, Jr. and Bruce E. Burston,
Chemistry: The Central Science, Englewood Cliffs, NJ: Prentice
Hall, Inc., 1994
- Dorin, Henry, Peter E. Demmin, and Dorothy L. Gabel.
Prentice Hall Chemistry: The Study of Matter,
Needham, Massachusetts and Englewood Cliffs, New Jersey: Prentice Hall, Inc.,
Team # 12596
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