A mixture of 60 % N2, 30 % argon, and 10 % O2 on a mass basis is in a cylinder at 250 kPa and 31

A mixture of 60 % N2, 30 % argon, and 10 % O2 on a mass...

A mixture of $60 \% \mathrm{N}_{2}, 30 \%$ argon, and $10 \% \mathrm{O}_{2}$ on a mass basis is in a cylinder at $250 \mathrm{kPa}$ and $310 \mathrm{K}$ with a volume of $0.5 \mathrm{m}^{3} .$ Find the mole fractions and the mass of argon.

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation that relates the pressure, volume, temperature, and number of moles of a gas. It is widely used to determine the total amount of gas present in a system and underpins various calculations involving gas mixtures.

Mole Fraction

The mole fraction is a way to express the composition of a mixture by dividing the number of moles of a component by the total number of moles in the mixture. It is a key concept in mixture analysis, allowing for the calculation of the behavior of individual components regardless of the total mass present.

Mass-to-Mole Conversion

When a composition is given in terms of mass, converting these mass fractions to moles involves using the molar masses of the components. This conversion is crucial because many gas laws and chemical calculations, such as the ideal gas law, operate on a mole basis rather than on mass.

Gas Mixtures

Gas mixtures are combinations of different gases where the overall composition can be described in terms of mass fractions or mole fractions. Understanding the properties of each gas and how they interact in a mixture is essential for analyzing and predicting the behavior of the mixture.

Transcript

0:00 Hi, everybody.

00:01 So for this one is find the mole fraction in the massive argon.

00:06 Okay, so for that, we can find here the mole fraction as an i over an total, which equals the ci over mi divided by the epsilon of cimi.

00:28 Okay.

00:28 And for this, we can just do a chart.

00:31 We get into argon, oxygen, okay? and for this, we have the ci.

00:42 Ci here is going to be 0 .6, 0 .3, 0 .1.

00:50 And then we have the mass here, or we put mi.

00:54 Okay.

00:55 And it's going to be 28 .013.

00:58 You can find this on the pr table, okay? so 39 .948, or you can just google it if that helps as well, okay? but just know how to find this on your own for test, okay? and now we can do the cimi, and what you're just going to do is just divide these by each other, okay? so 0 .0214, okay? down here, 0 .07.

01:32 Oops, those two zeros, okay.

01:38 075 and 0 .00312.

01:43 Okay.

01:45 And now we can do the y .i.

01:46 And just remember that this is going to be the top number.

01:49 So this is going to be this top number, okay? and what you're going to do is now the bottom number is add these three for the bottom number, okay? and i'll just go back so that way, there we go.

02:10 It looks nice.

02:11 And because of this, we get 0 .668, 0 .234, and 0 .0974, okay? and i just do a chart because it's easy.

02:25 And this is your answer for the mole fraction.

02:30 Okay...

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