Consider 1 mol an ideal gas at 29 ?C and 1.09 atm pressure. To get some idea how

Question

Consider 1 mol an ideal gas at 29 ?C and 1.09 atm pressure. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube.

Part A
What is the length of an edge of each cube if adjacent cubes touch but do not overlap?

Part B
How does this distance compare with the diameter of a typical molecule? The diameter of a typical molecule is about 10?10m.
Express your answer using one significant figure.

How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart?

Express your answer using one significant figure.

Part C

How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart?

Express your answer using one significant figure.

Exercise 18.26 Part A Consider 1 mol an ideal gas at 29 °C and 1.09 atm pressure. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube What is the length of an edge of each cube if adjacent cubes touch but do not overlap? Submit My Answers Give Up Incorrect, Try Again, 4 attempts remaining Part B How does this distance compare with the diameter of a typical molecule? The diameter of a typical molecule is about 10-10 m. Express your answer using one significant figure Submit My Answers Give Up Part C How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart? Express your answer using one significant figure golid Submit My Answers Give Up

Explanation / Answer

here
temperature , t = 29 C = 273.15 + 29 = 302.15 K
Pressure , p = 1.09 atm
n = 1 mole

from ideal gas law, Pv = nRT

Solving Volume of occupied gas, v

v = nRT/P
v = (1 * 0.08206*302.15) / (1.09)
v = 22.747 litres or 0.02275 m^3

Since 1 mole of gas contains 6.02 * 10^23 molecules,
hence volume occupied by a molecule = (0.02275/6.02*10^23) m^3
vo = 3.779 * 10^-26 m^3

Therefore,
Length of an edge of the cube = cuberoot(3.779*10^-26)
L = 3.355*10^-9 m

Part B:
The distance will be , D
D = L/10^-10
D = (3.355*10^-9)/10^-10
D = 33.55 or 33 times the diameter of a molecule.

Part C:
The Seperation, S = 0.3nm = 3 * 10^-8 m

Comparison = (3.355*10^-9) / (0.3*10^-9)
Comparison = 11.183 or 11 times the atomic spacing in solids.

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