Imagine you are sitting in a room with a volume of 25,000 liters and a temperature of 72^∘ F. Th

Imagine you are sitting in a room with a volume of 25,000...

Key Concepts

Unit Conversion

Unit conversion is a critical skill in applying the gas laws since measurements must be in consistent units. This includes converting temperature to the Kelvin scale, pressure to appropriate units (e.g., atm), and converting any other units so that calculations using the gas constant can be correctly performed.

Mole Concept and Molar Mass

The mole concept is a way to count particles in chemistry and links the microscopic scale to the macroscopic via Avogadro's number. Combined with the molar mass (the mass of one mole of a substance), it allows for the conversion from the number of moles of a gas (calculated using the ideal gas law) to the mass in grams.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, temperature, and amount of a gas in moles. It is a fundamental principle in thermodynamics that allows one to calculate any one of these variables if the others are known, assuming the gas behaves ideally, which is a good approximation under many conditions.

Dalton’s Law of Partial Pressures

Dalton’s Law states that in a mixture of non-reacting gases, the total pressure is equal to the sum of the partial pressures of the individual gases. This concept is essential for determining the contribution of a single gas (such as oxygen) to the overall pressure when it forms only a fraction of the gas mixture.

Transcript

00:03 So in this question, we have a room that is 4 meters by 5 meters by 2 .5 meters.

00:09 And we know that it contains a mixture of gases at stp, at stp, excuse me, stp that is 20 .95 % oxygen.

00:18 So it's probably just air, but to any extent, it's 20 .95 % oxygen.

00:24 And the question is how many grams of oxygen are in the room? so the first thing we're going to do is we're going to use our ideal gas law, pv equals nr t we're trying to find the amount of oxygen in grams and you'll notice that there are no grams in here so what we're going to try to solve for first is n n is going to be moles of oxygen and then once we have that we can we can figure out how many grams of oxygen using some basic stoichiometry so the first thing i'm going to do is i'm going to rearrange this to get n by itself so pv over rt is equal to n.

01:07 And then if we look at our known information, so p is at stp, it is going to be one atmosphere.

01:21 V, now this is where we have to be careful.

01:23 So we want our volume to be in liters.

01:28 And right now our units are in meters, and of course that would be cubic meters in terms of volume.

01:34 But a liter is not equal to a cubic meter.

01:38 There are actually a thousand liters in a cubic meter.

01:43 A liter is the same as a cubic decimeter.

01:45 So i'm going to convert these all into decimeters.

01:47 So i'm going to say that v equals 25 times 40 times 50.

01:55 So i'm converting all of those measurements into decimeters so that when i multiply them together, i get a volume in liters.

02:03 And that volume comes out to 50 ,000 liters.

02:11 R is a constant.