(a) Compute the densities of each of the noble gases...

(a) Compute the densities of each of the noble gases (elements in the last column of the periodic table, starting with helium) at $T=25^{\circ} \mathrm{C}$ and $P=1 \mathrm{~atm} .(\mathrm{b})$ Which are lighter than air?

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) is fundamental for relating the physical properties of gases, such as pressure, temperature, and volume. In problems involving gas density, the law is rearranged (often yielding ? = PM/RT) to connect a gas's molar mass with its density under specified conditions, making it essential for computations with any gaseous substance.

Gas Density Calculation

Gas density is determined by dividing the mass of gas by its volume, and for ideal gases, this can be calculated using the modified ideal gas law. By expressing moles in terms of molar mass, it allows for the calculation of density based on temperature, pressure, and molar mass, which is especially useful when determining whether one gas is lighter or heavier than another such as air.

Noble Gases in the Periodic Table

The noble gases comprise the group of elements in the far right column of the periodic table. They are characterized by their full electron shells, which make them chemically inert. Their unique properties and low reactivity make them ideal for experiments and applications where predictable behavior under varying conditions is required.

Comparison with Air Density

Comparing the calculated densities of gases to that of air, which has a density of about 1.2 g/L at standard conditions, is a key concept. This comparison helps in determining whether a gas will rise or fall in the atmosphere. The idea is crucial in various applications, including gas buoyancy, environmental monitoring, and safety assessments.

Transcript

00:01 So in this example, they want us to calculate the densities of all the renewable gases on the periodic table.

00:07 And then in part b, they just want us to determine which ones will float in air.

00:12 Now, they do tell us that the temperature is 25 degrees celsius, which i've already converted to kelvin, and the pressure is 1 atm, which have already converted to pascal's.

00:25 So to find the density, we know that the density is equal to the mass of.

00:32 Over the volume.

00:34 We know that the mass could be found by multiplying the number of moles times the molar mass of each element.

00:44 So i already went ahead and found the molar masses for each element or for each noble gas to make this go a little quicker.

00:55 We also note that the pressure times the volume is equal to the number of moles times our gas constant times the temperature, which can be rearranged so that we get the moles per volume, per unit volume, is equal to the pressure over our constant times t.

01:27 Now, we already have all the information here to solve for this.

01:32 We can put in our pressure, we can put in our temperature, and then we can put in our constant, which is right here.

01:41 So we'll know that the moles per unit volume is is equal to 40 .9 moles per meters cubed.

01:56 All right.

01:58 So we can plug both of these, this and this, and our density equation...

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