Consider a cube, 10 cm on a side, of He gas at STP. Estimate (order of magnitude) the number of

Consider a cube, 10 cm on a side, of He gas at STP. Estimate...

Key Concepts

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas, allowing one to determine the number density of molecules under standard conditions. This is critical when calculating properties like the collision frequency of gas molecules, as it provides the foundational link between macroscopic measurements and microscopic quantities.

Kinetic Molecular Theory

Kinetic Molecular Theory provides a framework for understanding the behavior of gases on a molecular level, including the motion and collisions of particles. It explains how molecules, moving at various speeds, contribute to properties such as pressure and temperature, and underpins the estimation of quantities like the number of wall collisions in a given time.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann Distribution describes the statistical spread of speeds among molecules in a gas at a given temperature. This concept allows us to estimate an average or most probable speed for the molecules, which is essential when determining the rate at which these molecules collide with the walls of a container.

Molecular Flux

Molecular flux refers to the number of molecules striking a unit area of a surface per unit time. It is directly related to both the molecular speed and the number density derived from the Ideal Gas Law, serving as the bridge between individual molecular motion and the macroscopic observation of collision rates.

Order of Magnitude Estimation

Order of magnitude estimation is a technique used to approximate calculations by focusing on the power of ten rather than precise values. This approach is useful in problems involving gases where exact numbers may not be necessary, and one is primarily interested in determining the scale or approximate frequency of events, such as wall collisions per second.

Transcript

00:01 In this problem, we're asked, we're told that we have a 10 centimeter by 10 centimeter by 10 centimeter box, so a cube of 10 centimeters on each side.

00:12 It contains 0 .010 moles of nitrogen at 20 degree c, and we want to know what is the rate of collisions and collisions per second on one wall of the box.

00:23 We know that we have this moles, and then we have nitrogen and the temperature, and the volume is 10 to the minus.

00:32 3rd to cubic meters and an area of one side is 10 to the minus 2 square meters.

00:40 So to find the collision rate, we need the velocity in any one direction, we can call it x, which is the, and we need the number density of molecules.

00:57 And so this is the rms velocity divided by squared at 3.

01:02 We need a few things here to calculate.

01:04 To get to this.

01:07 So the rms density, the rms velocity, we know the temperature, we know the bolt in the constant, we know what three is, and we need the mass of a nitrogen molecule.

01:22 And so we know the molecular weight of, in kilograms, of nitrogen is two times 12, two times 14, one nitrogen atom is 14, so 28 times 10 to minus 3, 28 grams.

01:41 And then avogadro's number here is we wind up with 4 .65 times 10 to the minus 26 kilograms is the weight of one nitrogen molecule.

02:00 We have the temperature.

02:01 Now we convert that into kelvin...

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