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It has been said that every breath we take, on average, contains molecules that were once exhaled by Wolfgang Amadeus Mozart (1756-1791). The following calculations demonstrate the validity of this statement. (a) Calculate the total number of molecules in the atmosphere. (Hint: Use the result in Problem 5.106 and $29.0 \mathrm{g} / \mathrm{mol}$ as the molar mass of air.) (b) Assuming the volume of every breath (inhale or exhale) is $500 \mathrm{mL},$ calculate the number of molecules exhaled in each breath at $37^{\circ} \mathrm{C},$ which is the body temperature. (c) If Mozart's life span was exactly 35 years, what is the number of molecules he exhaled in that period? (Given that an average person breathes 12 times per minute.) (d) Calculate the fraction of molecules in the atmosphere that was exhaled by Mozart. How many of Mozart's molecules do we breathe in with every inhalation of air? Round off your answer to one significant figure. (e) List three important assumptions in these calculations.

(a) $1.09 \times 10^{44}$ molecules(b) $1.18 \times 10^{22}$ molecules(c) $2.61 \times 10^{30}$ molecules(d) $2.8 \times 10^{8}$ molecules(e) The assumptions are outlined in the answers.

Chemistry 101

Chapter 5

Gases

Drexel University

University of Maryland - University 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.

04:54

It has been said that ever…

03:22

Assume that an exhaled bre…

11:44

Each time you inhale, you …

08:31

An adult inhales approxima…

03:04

When air is inhaled, it en…

So we're breathing Mozarts molecules. Where are we? Well, let's see. So the first thing that we were asked to do is to calculate how maney, uh, molecules are in the air. And in problem number 106 we had calculated that there were, ah, basically five times 10 to the 18 kilograms of air to using the average atomic mass for air molecules a little greater than nitrogen. We find out how many moles air in the air and then using avocados number how many air molecules air in the entire atmosphere of the earth? That was the first question that we were asked. Then, uh, we could use the ideal gas law solved for end by dividing both sides by rt to calculate how many moles, Uh, and then molecules of air are in each breath. We weren't given the pressure, but we assume that a person's breathing near the near the sea level, roughly one atmosphere. And so that's an assumption that we've made here. I doesn't I did not see any any pressure given, Ah, but reasonable assumption. And so we calculate the number of moles basically point of two moles for every breath but that is a lot of molecules, so also converting that to individual molecules like we did with the atmosphere and then ah, total number of breaths for Mozart. And so in his 35 years each year, with so many days each day, with so many hours each hour, with so many minutes and 12 breaths in every minute, we calculate the total number of breaths again, of course, an estimate that Mozart took and then multiplying that by the number of molecules per breath, we calculate that he breathed in and breathes out 200 or 2.6 times 10 to the 30th molecules. So what fraction of all of the molecules did Mozart free? Then I'll take all of the molecules that we just calculated here and divided by all the molecules in the atmosphere, and you find that he breezed in about 2.4 uh molecules for every 10 to the four teen in the atmosphere. And so taking that and ah, multiplying by the molecules in each breath. That's 10 to the 22 by the way, 1.18 times tended to 28 two molecules for breath we're taking intended to 22 we're getting essentially one out of every 10 to the 14. So we're getting 22 times, 10 to the 8th 2.8 times, 10 to the eighth, uh, molecules that he breathed in in every breath that we take. So, uh, we're assuming that he didn't breathe the same molecule twice and that all the molecules that he did breathe are uniformly distributed. So basically mixing of the atmosphere on both ends and then we're also assuming the atmosphere is constant and unchanging. Uh, and we're assuming ideal behaviour. And as I mentioned, we assumed that we're breathing at one atmosphere. Um, interesting.

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