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A barometer having a cross-sectional area of 1.00 $\mathrm{cm}^{2}$ at sea level measures a pressure of $76.0 \mathrm{cm}$ of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on $1 \mathrm{cm}^{2}$ of Earth's surface. Given that the density of mercury is $13.6 \mathrm{g} / \mathrm{mL}$ and the average radius of Earth is $6371 \mathrm{km},$ calculate the total mass of Earth's atmosphere in kilograms. (Hint: The surface area of a sphere is $4 \pi r^{2}$ where $r$ is the radius of the sphere.)

$$5.27 \times 10^{18} \mathrm{kg}$$

Chemistry 101

Chapter 5

Gases

Rice University

Drexel University

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.

01:18

A barometer is constructed…

01:45

The height of mercury colu…

03:20

Normal atmospheric pressur…

02:58

The weight of Earth's…

00:54

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01:39

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Determine the atmospheric …

So, um, we have this barometer, and, uh, we're given the density of, uh, the mercury in the barometer and the cross sectional area of the barometer. So, uh, we can multiply the the density. One middle leader, by the way, is one cubic centimeter. So we were given 13.6 grams Springville, but that is 13.6 grams per cubic centimeter and then multiplying by the cross sectional area. We get that. That's 13.6 grams of mercury for each vertical centimeter. Hey, the columnist is 76 centimeters long, and so that is basically a kilogram of mercury that is being pushed up. Ah, by the atmosphere, working on just this one centimeter of the, uh of the barometer. So now we need the surface area of the earth. Ah, in square centimeters. And so we take the formula that is given plug in the, uh, radius of the earth, uh, in kilometers. And then we need this conversion factor in, uh, uh, kilometers two centimeters. Uh, notice that I have K in the denominator and the meaning of kay attended the three kill. Oh, and the numerator and I have sent t in the numerator and the meaning of Centeon the denominator. So that converts kilometers two centimeters. But I have kilometers squared. And so I need to square that factor. And so multiplying out the values I get 5.1 times 10 to the eighth that would be in kilometers squared. And then this conversion factor square it has tended to 10. And so it gives me 5.1 times 10 to the 18th. And now that is Thievy Surface area of the Earth and square centimeters. We found out that the basically a kilogram of the mercury 1.3 kilograms Ah, is ah is supported a column that of that much mercury is supported by the pressure of the atmosphere on one ah, square centimeter. And so we multiply by the, uh, total number of square centimeters that we calculated here and we get ah lot. Uh uh. Atmosphere, uh, tend to the 18 kilograms is a number so very largest to be hard to imagine. A 1,000,000,000 is tend to the nine and so this is basically five billion billions of kilograms

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