(a) What fraction of the space in a tank of hydrogen gas at 0^∘ C and 1 atm is occupied by the h

(a) What fraction of the space in a tank of hydrogen gas at...

(a) What fraction of the space in a tank of hydrogen gas at $0^{\circ} \mathrm{C}$ and 1 atm is occupied by the hydrogen molecules themselves? Assume each hydrogen atom is a sphere with diameter 0.100 $\mathrm{nm}$ and a hydrogen molecule consists of two such spheres in contact. (b) What fraction of the space within one hydrogen atom is occupied by its nucleus, of radius 1.20 $\mathrm{fm}$ ?

Key Concepts

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, provides a relationship between pressure, volume, and temperature for a gas in thermal equilibrium. It allows for the determination of the number of molecules (or moles) present in a given volume when temperature and pressure are known, which is crucial for estimating the total amount of material in a system.

Spherical Volume Calculations

Calculating the volume of a sphere using the formula V = (4/3)?r³ is fundamental when approximating atoms or molecules as spherical objects. This approach is used to compute the volume occupied by individual atoms or groups of atoms, which is essential for determining spatial occupancy within a larger container.

Volume Fraction Concept

The concept of volume fraction involves determining the ratio of the cumulative volume of a collection of objects (such as atoms, molecules, or nuclei) to the entire volume they inhabit. This aids in understanding how much of the overall space is actually taken up by the material itself, versus the empty space in between.

Atomic and Nuclear Structure

Atomic and nuclear structure refers to the organization of matter at the microscopic level, distinguishing between the relatively large electron cloud that defines the size of an atom and the much smaller, denser nucleus at its center. This distinction is key when calculating and comparing the proportions of space occupied by the nucleus versus the whole atom.

Transcript

00:01 The first part of this question we want to find what is the fraction of volume occupied by the molecules.

00:07 Hydrogen molecules, we are given this pressure and we're given the temperature.

00:11 So we're going to use the equation pv equals to nrt to find what is the number of molecules.

00:23 Well, we don't know what is the volume of the tank, so we're going to leave it as an unknown for now.

00:30 The n over here is the number of most of the gas molecule they were looking at.

00:42 So n is equal to p over r t times v.

00:51 It is substituted in the values.

00:53 So one atmospheric pressure is in other units 1 .013 times 10 power 5 newtons.

01:02 R is the constant, right? 8 .34.

01:13 And the temperature that we're actually looking at is 273 kelvin, since it's 0 degrees.

01:27 So putting the values, we should get about 44 .6 moles.

01:53 Most times the volume v which we don't know yet right now we know the we can find the volume of one molecule by assuming it to be a sphere and since we have two hydrogen gas exists as a two atom molecule right h2 can assume it to be like two spheres.

02:33 The typical radii of this sphere of an atom is about 10 to power of minus 10 meters.

02:49 Sorry the diameter actually it's about 10 to power of minus 10.

02:57 Therefore this entire volume of a h2 molecule is about 4 third pi down to 10 minus 10 this is the volume of one sphere times 2.

03:19 Since you have two spheres...

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