± The Ideal Gas Law The ideal gas law describes the relationship among the press

Question

± The Ideal Gas Law The ideal gas law describes the relationship among the pressure P, volume V, number of moles n, and absolute temperature T of an ideal gas. Here is the relationship expressed mathematically: PV=nRT where R is a proportionality constant. The units of R are determined by the units of pressure and volume used in the equation. When atm is used for pressure and L for volume, the appropriate R value is 0.0821 Latm/molK.

Part A

How many air molecules are in a 11.0×12.0×10.0 ft room? Assume atmospheric pressure of 1.00 atm, a room temperature of 20.0 C, and ideal behavior. Volume conversion:There are 28.2 liters in one cubic foot.

Explanation / Answer

Volume of room = 11.0 × 12.0 × 10.0 = 1320 cubic foot

Volume in litres = 1320 × 28.2 = 37224 L

Using the ideal gas equation pV = nRT,

T = 20 + 273.15 = 293.15 K

Putting all the values in the equation

1 x 37224 = n × 0.0821 × 293.15

n = 1546.64 moles

Now 1 mole ideal gas has 6.022 x 1023 molecules

So 1546.64 moles will have 1546.64 × 6.022 × 1023

= 9.314 × 1026 molecules

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