what is the difference between the combined gas law and the ideal gas law? are they the same thing?
No, the are not the same.
The Combined Gas Law is:
P1V1/T1 = P2V2/T2
The Ideal Gas Law is:
PV = nRT
Your chemistry textbook should explain the difference. The most importance difference is that in the Combined Gas Law, the amount (moles) of gas are assumed to be constant. In the Ideal Gas Law, the amount of gas is one of the variables.
The combined gas law and the ideal gas law are related, but they are not exactly the same thing. Allow me to explain the difference.
The ideal gas law is a fundamental equation in thermodynamics that describes the behavior of an ideal gas. It states that the product of pressure (P), volume (V), and temperature (T) for a given sample of gas is proportional to the number of gas particles (n) and the ideal gas constant (R). Mathematically, it can be written as:
PV = nRT
Where:
P = Pressure
V = Volume
T = Temperature
n = Number of moles of gas
R = Ideal gas constant
The ideal gas law assumes that the gas behaves ideally, meaning there are no intermolecular forces or volume occupied by the gas particles.
On the other hand, the combined gas law is a rearrangement of the ideal gas law that allows you to compare the initial and final conditions of a gas under the same conditions (same amount of gas particles), but with different values of pressure, volume, and temperature. The combined gas law is useful for solving problems involving changes to these variables. It can be expressed as:
(P₁V₁)/T₁ = (P₂V₂)/T₂
Where the subscripts 1 and 2 represent the initial and final conditions, respectively.
So, in summary, while the ideal gas law describes the behavior of gases in general, the combined gas law is a specific form of the ideal gas law that is used to compare different conditions of the same gas sample.