At constant pressure the temperature of a 4.00 liter sample of gas is decreased from 400 K to 300 K. ...?
.188 liters
.300 liters
3.00 liters
5.33 liters
Answer:
Assuming the gas behaves as an ideal gas, we have that
P*V = n*R*T
or
P/(n*R) = T/V
In this problem, the pressure (P), number of moles (n), and, of course, the gas constant are all fixed. That means the left hand side of the equation is a constant. If we change the temperature from T1 to T2, then the volume will change from V1 to V2. but in both cases T2/V2 = T1/V1 = P/(n*R), so:
T1/V1 = T2/V2 (this is known as Charles' Law)
400K/4L = 300K/V2
V2 = 4L * 300K/400K
V2 = 3L
---
Note added in response to Norrie's comment that "...until quite recently, all gas pressure, temperature, volume calculations were carried out using the famous 'Ideal Gas Law'. Suddenly, where one parameter is constant, the inverse or direct ratio calculations have come into being."
From a historical viewpoint, Norrie has it backwards; all the "partial" gas laws were discovered *before* the full ideal gas law was formulated. Boyle's Law relating pressure and volume at constant temperature was first articulated in 1662. Charles' Law (see above) was first articulated in 1787. Gay-Lussac's law relating pressure and temperature at constant volume was first articulated in 1809. Avogadro's Law relating the number of moles to the volume of a gas a a given pressure and temperature was first articulated in 1811. These are all special cases of the ideal gas law, which is really just a combination of the preceeding 4 laws, was first formulated by Benoit Clapeyron in 1834.
If one knows the ideal gas law, then one can derive all the other, more restrictive "partial" gas laws as special cases (as I did above in this problem).
Simple use Charle's law---
V1/T1 =V2/T2
put values from question and calculate V2
it comes out to be--- V2= 3.00 L
I say 3 liters. The ratio of temperature and pressure is linear.
V1xT2 = V2xT1
Charle's law = Direct proportion at constant pressure.
300 รท 400 = 3/4 of original volume = 3 litres.
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