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Chapter 3: Q23E (page 611)

Modern vacuum pumps make it easy to attain pressures of the order of10-13atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 9.00脳10-14atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of1.0cm3? (b) How many molecules would be present at the same temperature but at 1.00 atm instead?

Short Answer

Expert verified
  1. 2.201脳106molecules are present in a volume of1.00cm3
  2. 2.446脳1019 molecules are present at temperatures of 300K and 1.00atm pressure.

Step by step solution

01

Ideal Gas Equation

Given data:

P=9脳10-14脳1.013脳105V=1脳10-6m3R=8.314J/molT=300K

The ideal gas equation is

PV=nRTn=PVRTn=9脳10-14脳1.013脳105脳1脳10-68.314脳300n=3.665脳10-18mol

02

No. of moles

No. of moles

N=nNA=3.665脳10-18脳6.022脳1023=2.201脳10-18脳6.022脳1023=2.201脳106molecules

Therefore,2.201脳106molecules are present in a volume of 1.00cm3.

03

Step 3:

Molecules present at the same temperature but at 1.00atm pressure;

Assumingp1V=n1RTas the first case and p2V=n2RTas the second case

Comparing both the cases:

p1Vp2V=n1RTn2RTp1p2=n1n2p1p2=N1NAN2NA=N1N2

Now the equation and putting the values for no. of molecules

N2=N1p2p1=2.201脳106脳19脳10-14=2.446脳1019molecules

Hence, 2.446脳1019molecules are present at temperatures of 300K and 1.00atm pressure.

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