Average Spacing of Gas Molecules Consider an ideal gas at 27.0 degrees Celsius a

Question

Average Spacing of Gas Molecules

Consider an ideal gas at 27.0 degrees Celsius and 1.00 atmosphere pressure. Imagine the molecules to be uniformly spaced, with each molecule at the center of a small cube.

Part A

Express your answer numerically in meters.

L=_____m

When water freezes into ice it expands in volume by 9.05%. Suppose a volume of water is in a household water pipe or a cavity in a rock.

Part B

If the water freezes, what pressure must be exerted on it to keep its volume from expanding? (If the pipe or rock cannot supply this pressure, the pipe will burst and the rock will split.)

Express your answer using two significant figures.

P=______Pa

Explanation / Answer

a )

given

P = 1.03 X 105 Pa

T = 27 + 273 = 300 K

N = 1

V = N k T / P

V = ( 1.38 X 10-23 ) X 300 / 1.03 X 105

V = 4.019 X 10-26 m3

V = L3

L = ( 4.019 X 10-26 )1/3

L = 3.425 X 10-9 m

b )

Pi = 1.03 X 105 Pa

Vo = 1.0905

dV = - 0.0905 / 1.0905

= - 0.083

B = 0.38 X 1010 N/m2( bulk modulus )

dP = - B ( dV / Vo )

= 6.64 X 108 Pa

P = Pi + dP

P = 1.013 X 105 + 6.64 X108

P = 6.6410 X 108 Pa

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