A vacuum system is measured to have a pressure of 0.100 mTorr at 23.0 deg. C. Ho

Question

A vacuum system is measured to have a pressure of 0.100 mTorr at 23.0 deg. C. How many atoms are in a 1 cc volume of this vacuum at this temperature and pressure?

If a container with a volume of 300.00 cc [1 cc = 10-6 m3]. containing 0.21 mol of argon gas has a maximum pressure rating of 10 atm (gauge pressure), what is the maximum safe temperature (in K) that this container can be stored at?

Two rods, one made of pyrex and the other of copper, have the same initial length at 56.00 deg. C? When the temperature drops to 5.00 deg. C the copper rod is 1.900 mm shorter than the pyrex rod. What was the initial length of the rods?

Explanation / Answer

(a) The number of atoms which is given as :

using an equation, we have

P V = N k T

where, P = absolute pressure = 0.1 mTorr = 0.013332237 Pa

V = volume of this vaccum = 1 cc = 1 x 10-6 m3

N = number of atoms in vaccum = ?

k = boltzmann constant = 1.38 x 10-23 J/K

T = temperature = 23 0C = 296 K

then, we get

(0.013332237 Pa) (1 x 10-6 m3) = N (1.38 x 10-23 J/K) (296 K)

(0.013332237 x 10-6 J) = N (408.48 x 10-23 J)

N = (0.013332237 x 10-6 J) / (408.48 x 10-23 J)

N = (3.26 x 10-5) x 1017 atoms

N = 3.26 x 1012 atoms

(b) The maximum safe temperature that this container can be stored at which given as :

using an ideal law, we have

P V = n R T

we know that, Pgauge = Pabs - Patm

(1.013 x 10-6 Pa) = Pabs - (1.013 x 105 Pa)

Pabs = 1.013 x 105 Pa

where, P = absolute pressure = 1.013 x 105 Pa

V = volume of this container = 300 cc = 3 x 10-4 m3

n = number of moles of argon gas = 0.21

R = molar gas constant = 8.314 J/mol.K

(1.013 x 105 Pa) (3 x 10-4 m3) = (0.21) (8.314 J/mol.K) T

(30.39 X 10-10 J) = (1.74594 J/K) T

T = (30.39J) / (1.74594 J/K)

T = 17.4 K

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