A 784 -mL hydrogen lecture bottle is left with the valve...

A 784 -mL hydrogen lecture bottle is left with the valve slightly open. Assuming no air has mixed with the hydrogen, how many moles of hydrogen are left in the bottle after the pressure has become equal to an atmospheric pressure of 752 torr at a temperature of $22^{\circ} \mathrm{C} ?$

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is widely used to predict the behavior of gases under various conditions, assuming the gas behaves ideally.

Unit Conversions

Accurate application of the ideal gas law requires consistency in the units used. This includes converting pressure units (from torr to atmospheres or pascals if necessary), converting volumes into liters or cubic meters, and converting temperature to Kelvin, ensuring that all units match the gas constant being used.

Temperature Conversion

Temperature must be converted from Celsius to Kelvin when using the ideal gas law. This conversion is done by adding 273.15 to the Celsius temperature, as Kelvin is the absolute temperature scale used in gas law calculations.

Transcript

00:01 Hi there.

00:03 This problem is an ideal gas equation problem.

00:07 So that means we're going to be using the ideal gas law, pv, equals nrt.

00:17 Reading through the problem, we see that we are trying to find the number of moles of hydrogen.

00:29 We are given a volume, and the volume that they give us is in millimeters.

00:35 It is 784 milliliters.

00:39 When we get to our gas constant, the ideal gas constant, we know that all of our options have liters in them.

00:47 So we are going to have to convert this milliliters to liters so that the units will cancel when we work our problem.

00:56 So we know that there are 1 ,000 milliliters of anything and one liter.

01:02 So in other words, we're dividing by 1 ,000 and we get 0 .784 liters.

01:13 We are also given a pressure of 752 tour.

01:19 We're going to use that unit tour to determine which universal chaos constant we're going to use here in a moment.

01:27 And we have a temperature provided to us in celsius of 22 degrees.

01:34 We know that temperature to use the ideal gas equation, temperature has to be in kelvin.

01:40 So i'm going to go ahead and add 273 to that, giving me 295 kelvin.

01:48 Finally, the universal gas constant.

01:51 This is a constant so i can select from the values they gave us in the chapter.

01:56 The one that i want to use is the one that has tor in it.

02:00 So that is 62 .4 liters times tor over mole kelvin.

02:11 Don't forget to carry along all of your units.

02:15 We will cancel them when we actually work the problem...

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