The gas laws describe the behavior of gases under specific conditions of temperature, pressure, and volume. Three gas laws show the relationship between two variables when all others are held constant: Boyle’s law (pressure and volume are inversely proportional), Charles’s law (volume and temperature are directly proportional), and Gay-Lussac’s law (temperature and pressure are directly proportional).
The three laws can be combined into one law, called the combined gas law.
pressure times volume over temperature under conditions 1 equals pressure times volume over temperature under conditions 2
A sample of helium gas has a temperature of 298 K and a pressure of 3.60 atm, under a constant volume. What is the new temperature, if the pressure is increased to 3.80 atm?
Using the combined gas law:
P1V1/T1 = P2V2/T2
Given:
P1 = 3.60 atm
V1 = constant (not given)
T1 = 298K
P2 = 3.80 atm
V2 = constant (not given)
Now we can plug in the values and solve for T2:
(3.60 atm) / (298 K) = (3.80 atm) / T2
(3.60 * T2) = (3.80 * 298)
3.60T2 = 1132.4
T2 = 1132.4 / 3.60
T2 = 314.22 K
Therefore, the new temperature of the helium gas when the pressure is increased to 3.80 atm is 314.22 K.