A sample of an unknown gas is found to have a density of 2.00 g / L at a pressure of 0.939 atm a

A sample of an unknown gas is found to have a density of...

Key Concepts

Unit Conversion

Accurate application of gas law equations requires proper unit conversion, especially converting temperature from Celsius to Kelvin and ensuring consistency of pressure units. This ensures that all variables are correctly compatible with the gas constant used in calculations, leading to precise results.

Molar Mass Determination Using Density

Molar mass can be determined using the formula M = dRT/P, which is derived from the Ideal Gas Law by relating density (mass per unit volume) to moles. This approach allows one to calculate the molar mass from experimentally measured values of density, pressure, and temperature, making it a useful method in identifying unknown gases.

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is fundamental in describing the behavior of ideal gases. It relates the pressure, volume, temperature, and amount (in moles) of a gas. This law is often used to solve problems involving gas properties and serves as a basis for deriving relationships between measurable quantities like density and molar mass.

Transcript

00:01 Hi there, in this problem, we are trying to solve for the molar mass of an unknown gas, and we are given the density as well as the pressure and the temperature.

00:15 So the equation that it looks like we want to use from this chapter is the one that says that density is equal to molar mass times pressure divided by the universal gas constant r times t.

00:33 Now we are going to have to rearrange this a little bit because we're trying to solve for molar mass.

00:41 So multiplying both sides by rt will give me drt equals molar mass times pressure.

00:53 And then i'm going to divide both sides by p, both sides by pressure, to get molar mass by itself.

00:59 And i'm going to flip the sides just so that i have molar mass over here on the left.

01:04 And then it's going to be density times the universal gas constant, times temperature, all divided by pressure.

01:13 So that's our plan.

01:15 Let's look at the information we're given in this problem.

01:18 We are given a density of 2 .0 grams per liter.

01:30 We are given a pressure of 0 .939 atmospheres.

01:41 We're given a temperature of 40 degrees celsius, knowing this is a gas.

01:50 Law problem, we know that our temperature has to be in kelvin.

01:54 So i'm going to go ahead and convert that by adding 273.

01:57 That gives me a temperature of 313 kelvin.

02:02 And then for r, the universal gas constant, i am going to select the one that has atmospheres in it, since my pressure is in atmospheres.

02:19 All right, so i have laid everything out here.

02:21 I have all of my values from the problem.

02:23 I have my equation.

02:25 Now it's a matter of plugging the values in and using my calculator to solve...

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