Air pollution in the Mexico City metropolitan area is among the w...

Question

Air pollution in the Mexico City metropolitan area is among the worst in the world. The concentration of ozone in Mexico City has been measured at 441 ppb (0.441 ppm). Mexico City sits at an altitude of 7400 feet, which means its atmospheric pressure is only 0.67 atm. (b) How many ozone molecules are in 1.0 L of air in Mexico City? Assume T = 25 °C.

Accepted Answer

Hey everyone today, we're being asked to calculate the number of carbon dioxide molecules present in 2021 in 1.5 liters of air at 5000 m above sea level where the atmospheric pressure is 0.53 and has a temperature of 1 15 degrees Celsius. So we can see right off the bat that we're going to utilize volume pressure and temperature in order to find the a number of carbon dioxide molecules. So we're going to need to utilize the ideal gas law, which is PV is equal to N our T. And to find the number of molecules, we can find that from the number of moles. So we can rearrange the ideal gas law for N, which is the number of moles. And that will be P. V over R. T. So let's keep this to the side for now. And first focus on finding the pressure because we have every other value more or less. So we're given the parts per million ppm of carbon dioxide and we know that the partial pressure of a gas or anything is equal to D parts per million, which will denote X. So the parts per million of c. 0 2 times the atmospheric pressure. And the parts per million that were given is 412 parts per million. So, what this essentially means. And let's write this out 4, 12 pp. M of CO2, which means That we have 412 moles of CO C 02 for every one million or 10 to the sixth moles of air Moles cancel Latin. We will be left with the value of 4.12 times to the -14. Or start to the -4. So this is the value that we need to plug back in over here. So let's do that and we will do this in green. This will equal 4.12 Times 10 to the -4, which is our PPM times the atmospheric pressure. Which in this case is given in the problem, It is 0.5380 M. So times 0.53 a. t. m. Which gives us a final value for the partial pressure of carbon dioxide as 2.1836 times 10 to the negative 4 80 M. So with that in hand we can go ahead and start solving for the number of moles. Alright, this in red. So N is equal to P V by R T. And we have these values. It will be 2.1836 times 10 to the negative four A. T. M. The volume is 1.5 L. Has given him the problem. R is the universal gas constant, which has a value of 0.8206 M. Leaders per mole kelvin times the temperature in kelvin, which would just be 15 plus 73.15 Calvin since 15° is the temperature at a Atmospheric pressure of 0.53. And finalizing all this, we get a value of 1.38, 5 Times 10 to the -5 moles of carbon dioxide. Let's not forget however, that we're being asked how many molecules of CO2 there are present in this volume at this temperature at this pressure. And to do this, we need to utilize avocados number. So avocados number states that we have 6.22, 02, two times 10 to the 23 molecules molecules Per mole of one substance. So, with this in mind and let's just rewrite this over here Permal. So with this in mind, if we want to convert molds to molecules, we have to multiply by avocados number. So If we have one 38, that's right, that's a little higher. 1.38, 5 times 10 to the negative 5th moles times 6.02, 2 times 10 to the 23rd Molecules molecules per one more. We get a final answer of 8. Times 10 to the 18th molecules to the 18th molecules Of CO two. Thus, at a volume of 1.5 L with a pressure of 0. 80 M and 15°C. In the conditions in 2021, the number of carbon dioxide molecules will be 8.34 times 10 to the negative 10 to the 18th molecules. I hope this helps. And I look forward to seeing y'all in the next one.

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