The radius of a xenon atom is 1.3 ×10^-8 cm. A 100 mL flask is filled with Xe at a pressure of

step 1 Hello guys, I'm here to solve question number 120, 120. The question said the radius of the radi

The radius of a xenon atom is 1.3 ×10^-8 cm. A 100 mL...

The radius of a xenon atom is $1.3 \times 10^{-8} \mathrm{~cm}$. A $100 \mathrm{~mL}$ flask is filled with Xe at a pressure of $1.0 \mathrm{~atm}$ and a temperature of $273 \mathrm{~K}$. Calculate the fraction of the volume that is occupied by Xe atoms. (Hint: The atoms are spheres.)

The radius of a xenon atom is $1.3 \times 10^{-8} \mathrm{~cm}$. A $100 \mathrm{~mL}$ flask
is filled with Xe at a pressure of $1.0 \mathrm{~atm}$ and a temperature of $273 \mathrm{~K}$. Calculate the fraction of the volume that is occupied by Xe atoms. (Hint: The atoms are spheres.)

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) is a fundamental equation that relates the pressure, volume, and temperature of a gas with the number of moles present. It provides the basis for determining the amount of gas in a container when given these conditions and is essential for understanding the behavior of gases under different conditions.

Avogadro's Number

Avogadro's Number is a key concept in chemistry, representing the number of particles in one mole of a substance. This constant is crucial for converting between the macroscopic measurement of substances in moles and the microscopic count of individual atoms or molecules.

Volume of a Sphere

The volume of a sphere is calculated using the formula (4/3)?r^3, where r is the radius of the sphere. This geometric formula is important when determining the space occupied by spherical objects, such as atoms, and is used to calculate individual atomic volumes.

Volume Fraction

Volume fraction is a concept that expresses the ratio of the volume occupied by a component (like atoms) to the total volume of the container. It is used to evaluate how much space is taken up by the particles relative to the entire volume, providing insight into the packing efficiency within a given volume.

Unit Conversions

Unit conversions are essential for ensuring that all quantities are expressed in compatible units before performing calculations. This includes converting units of pressure, volume, temperature, and length so that they can be consistently applied in equations and formulas.

Transcript

00:01 Hello guys, i'm here to solve question number 120, 120.

00:16 The question said the radius of the radius of the atom is 1 .3 times 10 to minus 8 centimeter.

00:40 A 100 million flask volume of last is 100 m m .m.

00:53 Is filled with zenium at pressure of one atmosphere and the temperature of 273 carbon calculate the fraction of the volume occupied by xenium atoms i'm trying to explain i'm going to my approach to solving this question this is my container that i said this is a container and the volume of this container is 100 ms it contains zinium like the atom of this gas they are spherical it contains many senile if the total the volume of the container is 100 later we want to know the want to calculate the volume the fraction of the volume that are occupied by the first thing we need we not know the volume of one atom of zeno and the formula we are going to use for that because the asperica we use volume equals to 4 over 3 pi are cube we have the radius this is a volume of sphere the formula for finding volume of sphere.

02:48 Also we need to know the number of atoms that is number of zan atoms.

03:03 Once we know the number of genome atom, we'll calculate volume occupied by xenom atoms or the atoms which is going to be the volume occupied by one atom occupied by the number of atoms, number of atoms, or the by number of atoms, multiply by volume of one atom of synar.

03:45 Now to get the volume of one atom of signal, we need to use the gas law, which is pv equals nrt.

03:56 In this equation, n is the number of mode, that is more of zina, right? but we need the number of atoms.

04:06 You know one mode of any gas will contain apogados number 6 .02 than 10 to 23 atoms.

04:25 So we need to calculate number of more.

04:28 Once we know the number of more, we calculate the number of atoms...

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