Question #a334f

1 Answer
Jun 3, 2015

Think of the ideal gas law as being a general model that encompasses all the other gas laws.

For example, you know that the ideal gas law looks like this

PV = nRT, where

P - the pressure of a gas;
V - the volume it occupies;
n - the number of moles of gas present in that volume;
T - the temperature of the gas.

Let's say that a have number of moles of gas that occupies a volume V_1 under conditions P_1 and T_1. The ideal gas law equation for this gas would be

P_1V_! = nRT_1 " "color(blue)((1))

If I keep the number of moles of gas unchanged, i.e. I don't add or remove any molecules of gas from my sample, but change the volume to V_2 and the conditions to P_2 and T_2, the ideal gas law equation would be

P_2V_2 = n RT_2 " "color(blue)((2))

If I want to express the number of moles of gas I have using the ideal gas lw equation, I can write

n = (P_1V_1)/(RT_1) -> from equation color(blue)((1))

and

n = (P_2V_2)/(RT_2) -> from equation color(blue)((2))

This means that I get

(P_1V_1)/(cancel(R) * T_1) = (P_2V_2)/(cancel(R) * T_2) <=> underbrace((P_1V_1)/T_1 = (P_2V_2)/T_2)_(color(green)("combined gas law"))

Both the ideal gas law and the combined gas law can be used to describe the behavior of an ideal gas under certain conditions for pressure and temperature.

However, the ideal gas law still stands if all the parameters change, whereas the combined gas law can only be used when the number of moles of gas is constant when going from one set of conditions to another.

Each of the gas laws describes the behavior of an ideal gas when at least one parameter of the ideal gas law equation is constant

and so on.