A 2 -kg mixture of 25 % N2, 50 % O2, and 25 % CO2 by mass is at 150 kPa and 300 K. Find the mixt

A 2 -kg mixture of 25 % N2, 50 % O2, and 25 % CO2 by mass is...

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = mRT for mass-based formulations) is fundamental for describing the state of gases. It relates pressure (P), volume (V), temperature (T), and mass (m) through the gas constant (R). It is used to calculate any one of these variables when the others are known, making it essential for determining the properties of gas mixtures under given conditions.

Universal and Specific Gas Constants

The universal gas constant (R_u) is a fixed value used in the ideal gas law when the amount of substance is expressed in moles. The specific gas constant (R) for a particular gas, however, is derived by dividing the universal constant by the gas's molecular weight. This concept is key when transitioning from a general to a substance-specific form of the ideal gas law, especially in the context of mixtures.

Mixture Gas Constant Calculation

For a gas mixture, the effective specific gas constant is determined by first calculating the average molecular weight using the mass fractions and the molecular weights of each component gas. The mixture gas constant is then obtained by dividing the universal gas constant by this averaged molecular weight. This process allows accurate application of the ideal gas law to mixtures, enabling further calculations such as total volume.

Transcript

00:01 Hi, everybody.

00:01 So for this one, it's asking us, find the mixture gas constant and the total volume.

00:08 So the mixture of gas constant, i'm just going to call it r mix because it's fun to say r mix, okay? and for that, what we need to do is, is have the r in two.

00:27 So let's see, we have the r in two.

00:28 So let's see, we have the r in two.

00:32 Nitrogen 2.

00:33 You could be of nitrogen 2 at 25%.

00:36 So before i begin the r mix here, i'm just going to write these out so you guys know what they are.

00:44 And you can find these numbers.

00:47 They're a table or in your book.

00:49 Okay.

00:49 So your book should have this in a chart.

00:52 So do not worry.

00:53 That's where i got them from.

00:55 Okay.

00:58 And i'm just going to write them out just so before i do anything.

01:02 So that's that way you guys have them written down and you just know what they are.

01:08 Okay, you do not have to write them out yourself.

01:12 You do not feel like it.

01:13 You have the chart, do not worry about it.

01:16 If you don't, this is the numbers, okay? and i got this from a chart.

01:22 Okay, so now we can do the r mix, because it's just fun to say r mix, but it's the mixture gas, it's the gas constant mixture, okay? so we got 25 % for the n2.

01:34 Nitrogen two okay so 2968 i'm not complaining units on it right now it's just easier that we know all the units are gonna be this okay so it's not a big deal so and the next one was it looks like 50 % so we got 0 .5 times 0 .298 for the oxygen and the next one was .25.

02:08 So we had 0 .25.

02:11 Me, it was 25%.

02:12 0 .25.

02:13 There we go.

02:14 I said it weird...

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