∙A 20.0 L tank contains 0.225 kg of helium at 18.0^∘ C . The molar mass of helium is 4.00 g / mo

step 1 This is chapter 15 problem number four. We have a tank of helium gas, whose volume is 20 liters.

∙A 20.0 L tank contains 0.225 kg of helium at 18.0^∘ C . The...

$\bullet$ A 20.0 $\mathrm{L}$ tank contains 0.225 $\mathrm{kg}$ of helium at $18.0^{\circ} \mathrm{C}$ . The molar mass of helium is 4.00 $\mathrm{g} / \mathrm{mol} .$ (a) How many moles of helium are in the tank? (b) What is the pressure in the tank, in pascals and in atmospheres?

Key Concepts

Mole Concept

The mole is a fundamental unit in chemistry that represents a specific number of particles (Avogadro's number). It is used to convert between the mass of a substance and the number of constituent particles by dividing the given mass by the substance's molar mass.

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, number of moles, and temperature of a gas. It is essential for calculating any one of these variables when the others are known, assuming the gas behaves ideally.

Temperature Conversion

For calculations involving the ideal gas law, the temperature must be expressed in Kelvin. This involves converting temperatures from Celsius to Kelvin by adding 273.15 to the Celsius temperature.

Pressure Unit Conversion

Pressure can be expressed in various units. In many gas law problems, it is necessary to convert between units such as pascals and atmospheres to ensure consistency and to interpret the results in familiar terms.

Transcript

00:01 This is chapter 15 problem number four.

00:02 We have a tank of helium gas, whose volume is 20 liters.

00:06 The total mass of this gas is 0 .2 to 5 kilograms, so it means 225 grams.

00:14 And the temperature at which it's capped at is 18 celsius, which means if we convert it to kelvin, 273 plus 18, right? which is 291, 291 kelvin.

00:30 Now we're asked to calculate the number of moles that we have of this gas.

00:36 So we're after n.

00:38 As you remember, the total mass of the gas equals to the number of moles of gas that we have times the molar mass.

00:44 So if we divide both sides by the molar mass, we can calculate the number of moles.

00:49 Then it's going to be equal to m over molar mass.

00:54 So m is 225 grams divided by molar mass.

01:00 Let's remember it's given to us in a problem.

01:02 You can also look it up if it's not given to us in the problem on the textbook, right? 4 grams per mole.

01:08 So 4 grams per mole for the healing gas.

01:13 So the number of moles that we have is 56 .25 moles.

01:18 In part b, we're asked to calculate the pressure.

01:23 So how are we going to get to pressure is by applying ideal gas law? as you know, it's p times v.

01:29 The pressure of the gas times the volume of the gas equals to the number of moles on the gas times the ideal gas constant times the temperature of that particular gas.

01:38 Now, if you divide both sides by the volume, then we have our pressure on the left -hand side.

01:45 So number of moles and rt over v equals the pressure...

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