Using the data in Table 20.12, calculate the mass of argon...

Using the data in Table 20.12, calculate the mass of argon at $25^{\circ} \mathrm{C}$ and $1.0$ atm in a room $10.0 \mathrm{~m} \times 10.0 \mathrm{~m} \times 10.0 \mathrm{~m}$. How many $\mathrm{Ar}$ atoms are in this room? How many Ar atoms do you inhale in one breath (approximately $2 \mathrm{~L}$ ) of air at $25^{\circ} \mathrm{C}$ and $1.0 \mathrm{~atm}$ ? Argon gas is inert, so it poses no serious health risks. However, if significant amounts of radon were inhaled into the lungs, lung cancer is a possible result. Explain the health-risk differences between argon gas and radon gas.

Using the data in Table 20.12, calculate the mass of argon at $25^{\circ} \mathrm{C}$ and $1.0$ atm in a room $10.0 \mathrm{~m} \times 10.0 \mathrm{~m} \times 10.0 \mathrm{~m}$. How many $\mathrm{Ar}$
atoms are in this room? How many Ar atoms do you inhale in one breath (approximately $2 \mathrm{~L}$ ) of air at $25^{\circ} \mathrm{C}$ and $1.0 \mathrm{~atm}$ ? Argon gas is inert, so it poses no serious health risks. However, if significant amounts of radon were inhaled into the lungs, lung cancer is a possible result. Explain the health-risk differences between argon gas and radon gas.

Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) serves as a fundamental relation in physical chemistry to connect pressure, volume, temperature, and the number of moles of a gas. It allows the calculation of any one variable when the others are known, which is critical in understanding and predicting gas behavior under varying conditions.

Mole Concept

The mole concept is vital for transitioning between the microscopic scale of atoms and molecules and the macroscopic amounts we measure in the laboratory. It establishes a standard counting unit that enables quantitative comparisons and computations in chemical reactions and gas calculations.

Avogadro's Number

Avogadro's number, approximately 6.022 × 10^23, defines the number of particles in one mole of a substance. This fundamental constant is used to directly relate the number of atoms or molecules to the amount in moles, facilitating the calculation of particle counts in various chemical processes.

Gas Density and Molar Mass

Understanding gas density and molar mass is important for converting between the mass of a gas and its volume under specific conditions. This concept is used to determine the mass of a gas from its measured volume, or vice versa, by employing the ideal gas law together with the molar mass.

Health Risk Assessment of Gases

Assessing the health risks of gases involves differentiating between chemical inertness and radioactivity. While inert gases like argon do not chemically react and are non-toxic, radioactive gases such as radon emit harmful radiation that can lead to lung cancer, thereby requiring distinct safety considerations.

Transcript

00:01 So for the first part of this question, we're trying to calculate the mass of argon at a specific temperature, pressure, and volume.

00:07 So if we further calculate the volume, it's going to be 1000 meters cubed.

00:20 But if we want to put it into our ideal gas equation, which is pressure times volume equals n the moles times r the gas constant times t the temperature, we need to convert that meters cubed into liters.

00:36 And that's because r, our gas constant, is in the units liters times atmospheres over kelvin times moles.

00:45 So the gas constant tells us what each part of the equations units need to be.

00:51 So volume needs to be in liters, and one cubic meter is equal to 1000 liters.

01:01 So there's 1000 liters for every one cubic meter.

01:06 Cubic meters cancel out, and your answer is 1 times 10 to the 6th liters.

01:15 So now we have liters and atmospheres, but our temperature is in celsius and it needs to be in kelvin.

01:20 So to convert celsius into kelvin, we just add 273.

01:26 So our new temperature is going to be 298 kelvin.

01:29 So now we can plug these values into our ideal gas equation to solve for n the moles, which if we rearrange that to get n by itself, it's going to be pressure times volume divided by r the gas constant times t the temperature.

01:45 So it's going to be our pressure at 1 atmosphere times our volume, which is 1 times 10 to the 6th liters, divided by our gas constant, liters times atmospheres over kelvin times moles, times our temperature, which was 298 kelvin.

02:06 So our liters cancels out, our atmospheres cancel out, our kelvins cancel out, so we're left with moles.

02:13 So type this into your calculator, and you should get 4 .18 times 10 to the 4th moles.

02:27 So now we know how many moles of argon there are, but we want to know the mass of argon.

02:33 So when we convert moles into grams, we take it times its molar mass.

02:40 So we take it times the molar mass of argon, which is 39 .95 grams per mole.

02:51 Moles cancel out.

02:53 Type that into your calculator.

02:54 You should get 1 .67 times 10 to the 6th grams of argon...

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