Taking a deep breath, a person inhales 5.5 L of air at atmospheric pressure and T=15^∘ C . By v

step 1 So in this example, they give us a lot of information. I think it's best to break it all down be

Taking a deep breath, a person inhales 5.5 L of air at...

Key Concepts

Ideal Gas Law

The ideal gas law relates pressure, volume, temperature, and the number of moles of a gas through the equation PV = nRT. This relationship is fundamental for determining the amount of substance present in a given volume under specific temperature and pressure conditions.

Mole Concept

The mole is a unit used to quantify chemical substances, representing a specific number of entities, typically atoms or molecules. This concept is essential for bridging the gap between the microscopic world of atoms and molecules and the macroscopic amounts measured in the laboratory.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23 particles per mole, is used to convert between the number of moles and the actual number of molecules. It allows one to translate measurable masses and volumes of substances into a count of individual particles.

Molar Mass

Molar mass is the mass of one mole of a substance and is calculated based on the atomic masses of the elements. It is used to convert between the number of moles and the mass of a substance, which is crucial in determining the mass contribution of each component in a gas mixture.

Mole Fraction and Percent Composition in Mixtures

Mole fraction or percent composition provides the relative proportions of each component in a mixture. When dealing with gas mixtures, these values are used to determine how much of each gas is present, either by volume or by moles, which is central to calculating the number of molecules and mass for each component.

Transcript

00:01 So in this example, they give us a lot of information.

00:03 I think it's best to break it all down before actually getting into it.

00:08 So here they tell us that the average breath is 5 .5 liters.

00:15 And it's taken at atp or the atmospheric pressure.

00:21 So i've already converted that to pascal's.

00:24 We're told the temperature is 15 degrees celsius and i've converted that to kelvin.

00:29 The volume of this breath is going to be 5 .5 liters which i've converted to meters cubed.

00:38 The constant or the ideal gas constant is just 8 .315 joules per mole kelvin.

00:48 And they tell us that when we take this breath, when we inhale, 78 % is going to be nitrogen, 21 % is going to be oxygen.

01:03 Then 0 .93 % is going to be argon.

01:08 So i've already kind of converted that into like the total volume.

01:15 Right.

01:15 So if v were to equal our total volume, then nitrogen is going to be 0 .78v.

01:22 Oxygen will be 0 .21v and argon will be 0 .0093v.

01:28 To solve this problem, we're going to need to know a few more things.

01:32 We're going to use the equation, the ideal gas.

01:36 Which is just pv equals nrt.

01:39 We're also going to need to know because what they want to know is the number of molecules per element or compound and then also the mass of each each one.

01:53 So we'll also need to know that the number of molecules will be equal to apakadra's number, which is 6 .022 times 10 to negative or times 10 to the 23.

02:02 3 and then that's multiplied by the number of moles of each one.

02:09 And then to get the mass, which is the other thing they're looking for, we're going to need to know the number of moles times the molar mass of each compound.

02:20 Right.

02:21 So we're going to get started for, we'll start with nitrogen.

02:29 So in order to get the number of moles for nitrogen, which will be n2, we are going to use the equation pv equals an r t and we want to get the number of moles so we're going to rearrange this to solve for n which will give us n equals pv divided by r t we already have all of these values so we'll just plug them in from our information over there v we're just going to take 0 .78 times the 5 .5 times 10 to negative 30 meters cubed.

03:18 All right...

Please give Ace some feedback