The combined gas law: Pressure, volume, and temp.

You can combine Boyle’s Law, Charles’s Law, and Gay-Lussac’s Law into one equation to handle situations in which two or even three gas properties change. Trust me, you don’t want me to show you exactly how it’s done, but the end result is called the combined gas law, and it looks like this:

P₁V₁/T₁ = P₂V₂/T₂

P is the pressure of the gas (in atm, mm Hg, torr, and so on), V is the volume of the gas (in appropriate units), and T is the temperature (in Kelvin). The 1 and 2 stand for the initial and final conditions, respectively. The amount of gas is still held constant: No gas is added, and no gas escapes. There are six For example, suppose that a weather balloon with a volume of 25.0 liters at 1.00 atm pressure and a temperature of 27°C is allowed to rise to an altitude where the pressure is 0.500 atm and the temperature is –33°C. What’s the new volume of the

balloon?

Before working this problem, do a little reasoning. The temperature is decreasing, so that should cause the volume to decrease (Charles’s Law). However, the pressure is also decreasing, which should cause the balloon to expand (Boyle’s Law). These two factors are competing, so at this point, you don’t know which will win out.

You’re looking for the new volume (V₂), so rearrange the combined gas law to obtain the following equation (by multiplying each side by T₂ and dividing each side by P₂, which puts V₂ by itself on one side):

[P₁V₁T₂]/[P₂T₁] = V₂

Now identify your quantities:

P1 = 1.00 atm; V1 = 25.0 liters; T1 = 27°C + 273 = 300. K

P2 = 0.500 atm; T2 = –33°C + 273 = 240. K

Now substitute the values to calculate the following answer: V2 = [(1.00 atm)(25.0 L)(240. K)]/[(0.500 atm)(300. K)] =

40.0 L Because the volume increased overall in this case, Boyle’s Law had a greater effect than Charles’s Law.