Question

How many air molecules are in a 13.5 × 12.0 × 10.0 ft room (28.2 L = 1 ft³)? Assume atmospheric pressure of 1.00 atm, a room temperature of 20.0 °C, and ideal behavior.

a) 1.2 × 10²⁴ molecules
b) 2.4 × 10²⁴ molecules
c) 3.6 × 10²⁴ molecules
d) 4.8 × 10²⁴ molecules

Answer 1

To calculate the number of air molecules in the 13.5 × 12.0 × 10.0 ft room, we need to convert the volume to L and use the ideal gas law. The answer is a) 1.2 x 10²⁴ molecules of air in the room.

Step-by-step explanation:

To calculate the number of air molecules in the room, we need to use the ideal gas law. The ideal gas law equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin.

First, we need to convert the volume of the room from ft³ to L. The conversion factor is given as 28.2 L = 1 ft³.

Then, we can use the ideal gas law to calculate the number of moles of air in the room. Given that the room temperature is 20.0 °C, we need to convert it to Kelvin by adding 273.15. Assuming atmospheric pressure of 1.00 atm, and using the values 0.50 L for a normal breath and 295 K for air temperature inhaled, we can calculate the number of moles of air inhaled per breath.

Now, we can calculate the number of moles of air in the room by using the volume of the room and the number of moles per breath. Finally, we can convert the number of moles to the number of molecules by using Avogadro's number, which is approximately 6.02 x 10²³ molecules per mole. With these calculations, the answer is a) 1.2 x 10²⁴ molecules of air in the room