(a) Calculate the number of molecules in a deep breath of air whose volume is 2.25 L at body temperature, 37 °C, and a pressure of 97.99 kPa.

Question

Accepted Answer

Hey everyone for this problem, it says approximately .04 of the Earth's atmosphere is made up of carbon dioxide. How many carbon dioxide molecules would be in a 3.4 liter sample collected from the atmosphere at sea level on a warm day. So here we're given pressure. Were given volume and were given temperature so we can use the ideal gas law equation to solve this problem and that is PV equals N. R. T. And we can go from moles to molecules and we'll do that by solving for moles in our ideal gas law equation and we can divide both sides by R. T. And we're left with and is equal to PV over R. T. So now let's go ahead and plug in what we're given. We're told that the pressure is at sea level. So N. Is equal to 1 80 M. And our volume given is the volume of the entire sample. But we're told that the Earth's atmosphere is .04% carbon dioxide. So we need to solve for the volume of carbon dioxide, not use the volume that's given here, which is the entire sample. So here we are told that we have 0. And we'll divide that by 100 is equal to will say Ex Leaders Over the whole sample which is 3.4 L. So let's go ahead and solve for R. X. leaders. We will Move that over to the left and multiply both sides by 3.4 L. So are 0.04% over Is going to be multiplied by R 3.4 leaders and when we do that, we get that our leaders Is equal to 1.36 Times 10 to the -3 leaders. Now this is the volume of just our carbon dioxide, which is what we're looking for. So let's plug that in for our volume. So we have 1.36 times to the -3 leaders. Now, our is our gas constant, Which is 0. 206 leaders atmosphere over more Calvin. And our temperature, they gave it to us in degrees Celsius and we need to convert that to kelvin because our gas constant unit has kelvin and we'll do that by adding 0.15 And we get a temperature of .15 Kelvin. So let's plug that in and we'll make sure all of our units cancel. Our atmosphere's canceled. Our leaders cancel and our kelvin's cancel. And we're left with moles. So we get and Is equal to 5.47 times To the negative five moles of carbon dioxide. And were asked for molecules so to go from most two molecules we can use avocados number and in one More of CO Avocados number is 6.02, 2 times 10 to the molecules. Okay, so we'll go ahead and cancel out our moles and will be left with our molecules. Once we do that, plug it in, we get 3.3 times 10 to the molecules Of CO two. And that is our final answer, and that is the end of this problem. I hope that this was helpful.

(a) Calculate the number of molecules in a deep breath of air whose volume is 2.25 L at body temperature, 37 °C, and a pressure of 97.99 kPa.

Verified Solution

Key Concepts

Ideal Gas Law

Molar Volume of a Gas

Avogadro's Number