This problem is another quick calculation, just to get a...

This problem is another quick calculation, just to get a sense for the numbers of molecules in ordinary matter that we encounter. Part A According to Sec. 12.5 in Knight, Jones and Field, a mole of gas molecules takes up a volume of 22.4 liters at \"Standard Temperature and Pressure,\" that is, a pressure of one atmosphere and a temperature of 0 Celsius, the freezing point of water. Under those conditions, how many molecules are there in 1 $cm^3$ of air? One or two significant figures is enough for this problem. View Available Hint(s) Hint 1.

Transcript

0:00 Hi there.

00:01 So for this problem we need to consider for part a of this problem um that we have one more of an ideal gas that is at a temperature of 285 calvin and at a pressure of one atmosphere.

00:28 And we need to imagine that the multiples are and evenly spaced at the center of identical cubes.

00:40 So using the apple graduates constant in taking the diameter of the molecule.

00:46 So we are given the diameter of the molecule to be equal to three times 10 to the -8 cent immature.

00:58 We need to find the length of an edge of such a cube and calculate the ratio of this length to the diameter of the molecules.

01:07 So what we need to do if we call that length.

01:10 Elt what we need to calculate is the ratio of yeah, the ratio of the over held.

01:28 We need to find that ratio.

01:32 So um we are given the baldy um and we know that the volume per particle is going to be be over end because and is the number of particles in that gas.

01:50 And because this is an ideal gas, this is equal to bold woman constance times the temperature or over the pressure.

02:00 So we just need to simply substitute those values in order to find the volume per particle.

02:07 So, and we know that bald zeman constant is equal to 1.38 times 10 to the -23 jules.

02:20 Berg calvin.

02:22 The temperature is 285 kelvin and the pressure and the pressure is equal to 1.01 times 10 to the five possible because that corresponds to one atmosphere.

02:48 And from this we obtain about you of 3.89 times 10 to the -26 cubit meters.

03:01 Now as the problem states this is the volume of the cube in which the molecule is at.

03:14 So we will have that, this is the cube and this is the molecule right here at the center.

03:21 So what we need to obtain is the length of this.

03:26 Because we are given we we obtain the volume to obtain that length because this is a perfect cube.

03:33 We just need to simply uh take the the cube root of that value.

03:46 So that is the cube root of the volume over.

03:50 And so from this taking the square root of that value that we obtain, that is equal to 3.39 times 10 to the -9 meters.

04:07 So what we need to do now is to obtain the ratio between this length and the diameter of the particle.

04:15 Um sorry i forgot in here, the ratio that we need to obtain is the length l over the diameter.

04:22 So the diameter is in centimeters...

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