A gas mixture composed of helium and argon has a density of 0.670 g / L at 755 mm Hg and 298 K .

A gas mixture composed of helium and argon has a density of...

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental equation in thermodynamics that relates the pressure, volume, temperature, and number of moles of a gas. It is widely used to connect the measurable properties of gases, such as density and molar mass, and serves as the basis for calculating other gas properties in both pure gases and mixtures.

Average Molar Mass of a Gas Mixture

The average molar mass of a gas mixture is a weighted mean of the molar masses of the individual gases, with the weights corresponding to their mole fractions. This concept allows the determination of an overall property (such as density) of the mixture by considering the contribution of each gas based on its proportion in the mix.

Gas Density and Molar Mass Relationship

The density of a gas is directly related to its molar mass and the conditions of temperature and pressure through the relation derived from the Ideal Gas Law. This relationship enables the calculation of a gas’s molar mass when its density is known and, in mixtures, facilitates the determination of the mixture's composition by comparing the expected and observed densities.

Mole Fraction and Volume Fraction Equivalence in Ideal Gases

For ideal gases, the mole fraction of each component in a gas mixture is equivalent to its volume fraction. This property simplifies the analysis of gas mixtures, as it allows the composition to be expressed interchangeably in terms of moles or volumes, a key concept when determining the makeup of a mixture.

Transcript

00:01 Solution for the given problem here, given information to solve the problem here.

00:18 We have pressure is equal to 0 .755 millimeter of mercury.

00:29 And here we will convert millimeter of mercury into atm.

00:33 So the conversion matter is 0 .755 millimeter of mercury.

00:42 Into 180m divided by 760 millimeter of mercury is equal to we have 0 .99m.

01:11 And here other information are here.

01:17 We have partial pressure for argon and helium.

01:24 Argon and helium is equal to we have 0 .67 gram per liter and here step one to solve the given problem is we have step one step one is by using ideal guess law we will find amounts in mall amount in malls so here we will take one liter of the mixture.

02:55 Mixure to solve the problem easily.

02:57 Here volume is constant.

02:59 That is why we take here one letter of the mixture.

03:03 So by using ideal guess equation we have ideal guess equation is here pv is equal to nrt.

03:14 Here p is pressure, v is volume and n is number of molds.

03:18 R is generally constant and t is kelvin temperature.

03:22 So here we can convert this equation.

03:26 Here number of moles is equal to pv divided by rt is equal to by putting values here.

03:39 Value for pressure 0 .993 atm and volume is 1 litre we have taken here one liter and next here we have value for general gas constant is 0 .0826 later atm per mole per kelvin and next is kelvin temperature is 298 kelvin is equal to the calculated value for the number of malls here is 0 .0406 mall.

04:33 So here we will cancel the same units.

04:36 Atm can sell with atm, later cancel with later.

04:40 And k, kelvin, cancel with kelvin, and the left it here is small...

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