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 radon gas has a volume of 1.53 L, a pressure of 1.15 atm, and a temperature of 305 K. What is the new pressure, if the new volume is 1.78 L and the new temperature is 325 K?
To solve this problem using the combined gas law, we can set up the following equation:
(P1 x V1) / T1 = (P2 x V2) / T2
Plugging in the given values:
(1.15 atm x 1.53 L) / 305 K = (P2 x 1.78 L) / 325 K
Solving for P2:
1.15 x 1.53 / 305 = P2 x 1.78 / 325
1.15 x 1.53 x 325 = P2 x 1.78 x 305
Now, solve for P2:
P2 = (1.15 x 1.53 x 325) / (1.78 x 305)
P2 = 596.20 / 543.90
P2 = 1.096 atm
Therefore, the new pressure of the radon gas is 1.096 atm.