A 2.94 -gram sample of an unknown gas is found to occupy a...

A 2.94 -gram sample of an unknown gas is found to occupy a volume of $2.06 \mathrm{L}$ at a pressure of 1.16 atm and a temperature of $46^{\circ} \mathrm{C}$. What is the molar mass of the unknown gas?

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Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation in chemistry that relates the pressure, volume, and temperature of a gas to the number of moles present. This relationship is crucial for predicting how gases behave under different conditions.

Unit Conversion

Accurate application of the ideal gas law requires converting all measurements into appropriate units, such as converting temperatures from Celsius to Kelvin. Consistent units ensure that the gas constant (R) is applied correctly, maintaining the integrity of the calculations.

Molar Mass Calculation

Molar mass is calculated by dividing the mass of a sample by the number of moles derived from the ideal gas law. This approach is essential for identifying an unknown gas by comparing its molar mass to known values, tying together experimental data with theoretical predictions.

Transcript

00:01 Hi there.

00:03 In this problem, we are trying to determine the molar mass for an unknown sample of gas.

00:10 From the chapter, we were given an equation that says molar mass is going to be equal to the mass times universal gas constant times temperature in kelvin divided by pressure times volume.

00:29 So that's the equation that we are going to need to solve this problem.

00:32 So let's go through and see what things we are given in this problem.

00:38 We are given a mass of 2 .94 grams.

00:44 We are given a volume of 2 .06 liters.

00:52 We have a pressure of 1 .16 atmospheres and a temperature of 46 degrees celsius.

01:10 We know this is a gas law problem.

01:13 And for all gas law problems, our temperature has to be in kelvin.

01:16 Units.

01:17 So to convert this to kelvin, i'm going to add 273, and that will give me 319 kelvin as the temperature.

01:29 Finally, i need to select a value for the universal gas constant.

01:33 We were given a couple of choices in the chapter.

01:37 I'm going to select the one that uses atmospheres in it, so that atmospheres will cancel when i do my equation.