An experiment shows that a 113 -mL gas sample has a mass of 0.171 g at a pressure of 721 mm Hg a

An experiment shows that a 113 -mL gas sample has a mass of...

An experiment shows that a 113 -mL gas sample has a mass of $0.171 \mathrm{g}$ at a pressure of $721 \mathrm{mm}$ Hg and a temperature of $32^{\circ} \mathrm{C} .$ What is the molar mass of the gas?

Key Concepts

Ideal Gas Law

The ideal gas law is a fundamental concept in chemistry that relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This equation allows the calculation of one property when the others are known, making it essential for understanding and predicting the behavior of gases under various conditions.

Molar Mass Determination

Molar mass determination involves finding the mass of one mole of a substance. In the context of gases, once the number of moles in a sample is calculated using the ideal gas law, the molar mass can be found by dividing the measured mass by the number of moles. This concept is important for identifying gases and understanding their properties at the molecular level.

Unit Conversion

Accurate gas calculations require converting units to maintain consistency, such as converting volume from milliliters to liters, temperature from degrees Celsius to Kelvin, and pressure from millimeters of mercury to atmospheres or another consistent pressure unit. These conversions are critical to correctly apply the ideal gas law and obtain valid results.

Transcript

00:01 In this question, we have 113 millimeters of gas with a mass of 0 .171 grams.

00:08 And we're told that the pressure is 721 millimeters of mercury and the temperature is 32 degrees celsius.

00:13 And we're asked to find the molar mass of the gas.

00:16 So what we're going to do is use the ideal gas equation and solve for n, which is the number of moles.

00:22 And then we'll use that number and this mass that we're given to find the molar mass.

00:26 So that equation is pv equals n r t.

00:32 P is the pressure, v is the volume, n is the number of moles, that's what we're going to solve for.

00:38 R is a constant, r is 0 .0821, liter, atmosphere over mole, kelvin, and then t is the temperature.

00:48 So here we have v, p, t, and we know r, so we're solving for n.

00:53 But before we can do that, we have to make sure all of our units are correct.

00:57 So because r has units of liter atmosphere over mole kelvin, we have to make sure that everything else is in those same units.

01:05 So volume needs to be in liters.

01:07 So there's 1 ,000 milliliters and 1 liter.

01:10 So we'll divide 113 by 1 ,000 to get 0 .113 liters.

01:17 The pressure needs to be in atmospheres.

01:19 In one atmosphere, there are 760 millimeters of mercury.

01:23 So 721 divided by 760 is 0 .949 atmospheres.

01:31 That's what we're gonna use for pressure...

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