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2. (**) modern vacuum pumps make it easy to attain pressures of the order of 10-13 atm in the laboratory. consider a volume of air and treat the air as an ideal gas. a. at a pressure of 9.00 * 10-14 atm and an ordinary temperature of 300.0 k, how many molecules are present in a volume of 1.00 cm3 ? b. how many molecules would be present at the same temperature but at 1.00 atm instead?

Answer :

The number of air molecules in a volume of 1.00 cm3 under the conditions of the vacuum pump is 3.65 * 10-15 moles and those that would be present at the same temperature but at 1.00 atm would be 0, 04 moles

The vacuum pump is a device that extracts gas molecules from a sealed volume, to create a partial vacuum, and is frequently used in industry, especially food.

To perform both calculations considering air as an ideal gas, the equation PV = nrt is used, in which

P = Pressure

V = Volume

n = number of moles

R = Gas constant

t = temperature

Calculation of the number of air molecules in a volume of 1.00 cm3 under the conditions of the vacuum pump

Data

t = 300K

V = 1L

P = 9.00 * 10-14 atm

R = 0.082 L Atm / mol °K .

n = ?

PV = nrt

n = PV/rt

n = 9.00 * 10-14. 1 / 0.082 . 300

n = 9.00 * 10-14 / 24.6

n = 3.65 * 10-15 moles

Calculation of the number of molecules present at the same temperature but at 1.00 atm

Data

t = 300K

V = 1L

P = 1 atm

R = 0.082 L Atm / mol °K .

n = ?

PV = nrt

n = PV/rt

n=1. 1 / 0.082 . 300

n = 1 / 24.6

n = 0.04 mole

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