Estimating Total Air Molecules in a Room | Help with Homework Statement

[Teenytiny1991]

Homework Statement

Estimate to 1 significant figure the total # of air molecules in this room (l=20ft, w=14ft, H= 8ft) Find molecules/room

Homework Equations

1 mole = 22.4 liters
6.02 x 10^23 molecules = 1 mole

The Attempt at a Solution

volume of room = 2240 ft^3 or approx 683 m^3

6.02x10^23 Molecules / 1 mole x 1 mole/ 22.41 liters = 6.02 x10^23 molecules/ 22.41 liters... I am stuck here. how do i figure out how many liters are in the room?

 

[tiny-tim]

Welcome to PF!

Hi Teenytiny1991! Welcome to PF!

(oooh, you're even smaller than i am! )

… volume of room = 2240 ft^3 or approx 683 m^3

how do i figure out how many liters are in the room?

(try using the X² tag just above the Reply box )

How many cm³ to a litre?

How many cm to a foot?

 

[kerimek]

I would approach this problem by first converting the given dimensions of the room from feet to meters, as the volume of the room is typically measured in cubic meters. This can be done by using the conversion factor 1 ft = 0.3048 m.

So, the length (l) of the room would be 20 ft x 0.3048 m/ft = 6.096 m, the width (w) would be 14 ft x 0.3048 m/ft = 4.2672 m, and the height (H) would be 8 ft x 0.3048 m/ft = 2.4384 m.

Next, I would calculate the volume of the room by multiplying the three dimensions together: 6.096 m x 4.2672 m x 2.4384 m = 62.8 m^3.

Now, using the given conversion factor of 1 mole = 22.4 liters, I would convert the volume of the room from cubic meters to liters: 62.8 m^3 x 1000 liters/m^3 = 62,800 liters.

Finally, I would use the Avogadro's number (6.02 x 10^23 molecules/mol) to calculate the total number of air molecules in the room: 6.02 x 10^23 molecules/mol x 62,800 liters/22.4 liters/mol = 1.7 x 10^27 molecules.

Therefore, the estimated total number of air molecules in the room is approximately 1.7 x 10^27 molecules. It is important to note that this is only an estimate, as the actual number may vary due to factors such as temperature, pressure, and humidity in the room.