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The Chemistry in Action essay on p. 208 describes the cooling of rubidium vapor to $5.0 \times$ $10^{-8} \mathrm{K} .$ Calculate the root-mean-square speed and average kinetic energy of a Rb atom at this temperature.

$$\begin{array}{l}u_{r m s}=3.9 \times 10^{-3} \mathrm{m} / \mathrm{s} \\K E=1.08 \times 10^{-30} \mathrm{J} / \text { atom }\end{array}$$

Chemistry 101

Chapter 5

Gases

Carleton College

University of Toronto

Lectures

05:03

In physics, a gas is one of the three major states of matter (the others being liquid and solid). A gas is a fluid that does not support tensile stress, meaning that it is compressible. The word gas is a neologism first used by the early 17th-century Flemish chemist J.B. van Helmont, based on the Greek word ("chaos"), the simplest of all the elemental forms of matter.

04:46

In physics, thermodynamics is the science of energy and its transformations. The three laws of thermodynamics state that energy can be exchanged between physical systems as heat and work; that the total energy of a system can be calculated by adding up all forms of energy in the system; that energy spontaneously flows from being localized to becoming dispersed, spread out, or uniform; and that the entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.

03:09

The Chemistry in Action es…

01:17

Calculate the root-mean-sq…

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00:34

The average kinetic energy…

02:47

Determine the root-mean-sq…

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01:56

Suppose that the average v…

01:37

(a) What is the average ki…

02:19

(a) What is the average k…

01:39

Calculate the temperature …

02:06

Calculate the root mean sq…

04:23

At $20^{\circ} \mathrm{C}$…

03:21

An oxygen molecule with ma…

So how fast do molecules move as we get close to absolute zero? This is five times 10 to the minus eight Calvins. That's pretty close to zero Kelvin's at this molecule. These rubidium atoms really slowed down. So the first of all the root, mean square speed is going to be given I, uh this equation. And so, uh, and for our here, uh, we're using Ah, the same ideal gas constant, but with a different set of units. Ah ah! To, uh, get into units of motion. We would speed here. Um, so let's see. Now let's see what's gonna happen with their units. The, uh, Permal is going to cancel. Um, so that's first to some Multiply. So that is in the numerator. Okay, 1.25 Essentially one point to 47 times 10 to the minus six now, OK, And the Kelvin's we're gonna cancel also. Now Jewell is a kilogram meter squared per second squared, and we're dividing here by Teoh uh, 0.8547 kilograms And okay, so that is the square root of essentially 1.5 times 10 to the minus five. Okay. And then square to that, uh, 3.8 times 10 to the minus three. And now our kilograms cancel. And we've got the square two meters squared per second squared. That's meters per second. So that's essentially 3.8 millimeters per second. So it's still moving, um, air molecules at room temperature moving at the speed of rifle bullets, couple 1000 meters per second. So we've got him slowed down quite a bit, but they're still moving even at that very, uh, most speed. And now the average kinetic energy again, uh, using the equation from your chapter and looking in our and the kelvin temperature. And that would be per mole. And so we want to cancer the d Permal and do it for each rubidium, uh, Adam, and crunching the numbers gives us one times 10 to the minus 30 jewels.

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