The lowest pressure achieved in a laboratory is about 1.0 X 10^-15 mm Hg. How many molecules of gas are present in a 1.00-L sample at that pressure and a temperature of 22.0 degrees C?

Expert Answers

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In this question, we have to use the ideal gas law, which can be written as:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant and T is the temperature (in K).

In this question, P = 1 x 10^-15 mm Hg

1 atm of pressure is equal to 760 mm Hg. Thus the given pressure can also be converted to the units of atm.

Thus, P = 1 x 10^-15 mm Hg x 1 atm / 760 mm = 1.3158 x 10^-18 atm

V = 1 l

T = 22 degrees C = 22 + 273 K = 295 K

and R: universal gas constant = 0.0821 l atm/mol/K

Substituting all the values in the equation, we get:

1.3158 x 10^-18 atm x 1 l = n x 0.0821 l atm/mol/K x 295 K

or, n = 5.378 x 10^-20 moles

Since each mole of a substance contains 6.023 x 10^23 molecules, the number of molecules in the current case are:

Number of molecules = 5.378 x 10^-20 x 6.023 x 10^23

= 3.24 x 10^4 molecules or 32,392 molecules.

Hope this helps.

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