Question

How many air molecules are in a 11.5

Answer 1

This problem is a pain!.....It's not hard, it's just long and takes a bunch of conversions. Unless your teacher is trying to teach you dimensional analysis and not gas laws I guess it's okay, but if it's supposed to be a gas law problem, then it's a lot of work for nothing. Having got that off of my chest, let me run through the calculations. First you should know that 22.4 liters of any gas at STP equal 1 mole or 6.02 x 10^23 molecules. Since the temperature is 20 degrees and not 0, we've got to convert to an increase in temperature to figure out what volume a mole of gas would be. Since the pressure doesn't change (1 atm), it's Charles law. So:

V/T = V'/T' solving for V' gives us V' = T'V/T = (293)(22.4)/273 = 24 liters.......okay, so know we know that 1 mole of gas is equal to 24 liters at 20 degrees Celsius. The next step is to find out how many liters there are in that dumb room. First, lets find the cubic feet, which is

11.5 x 12 x 10 = 1380 ft3....now we've got to convert cubic feet to liters. This isn't hard, it's just long. I hope you can follow me.

1 ft3 = (30.5cm/1ft)3 =28373 cm3 in 1ft3 1 cm3 = 1 ml so 28373 cm3 = 28373 ml and 1000ml = 1 liter so 1ft3 = 28.373 liters. Now we know the room is 1380 ft3 and there's 28.373 liters in 1ft3 so there's 28.373liters/ft3 x 1380 ft3 = 3.9154 x 10^7 liters.....and since 24 liters equals 1 mole, there's
1mole/24liters x 3.9154 x10^7liters = 1.6314 x 10^6 moles of molecules in the room. Okay...we're almost there. We know that one mole equals 6.02 x 10^23 molecules so there's

6.02 x 10^23 molecules/mole x 1.6314 x 10^6 moles = 9.82 x 10^26 molecules or

982,130,000,000,000,000,000,000,000 molecules......or 982 septillion,130 sextillion molecules......... approximately!