Ideal Gas Law Homework: Calculating Number Density and Spacing Between Molecules

AI Thread Summary
The discussion focuses on calculating the number density of an ideal gas at 25.0 degrees Celsius and 1.00 atm pressure. The user initially calculated the number density as 0.041 mol/L but expressed confusion over the units and the conversion from moles to molecules. For the spacing between molecules, they derived a length of 101.5 of an unspecified quantity, leading to a cubic root calculation that resulted in a value of 4.7, which they suspect should be in nanometers. The user seeks clarification on the relationship between moles and molecules, emphasizing the need for proper unit conversion in their calculations. Accurate understanding of these concepts is crucial for solving ideal gas law problems effectively.
Matt Armstrong

Homework Statement



Consider an ideal gas at 25.0 degrees Celsius and with a pressure of 1.00 atm.

a) What is the "number density" of the molecules, expressed as molecules per unit volume? (Cubic meter, cubic centimeter or liter)

b) What is the typical spacing between molecules in the gas? Of course they are rapid in motion and some will be closer than others at any point in time, but to get an idea of the spacing, imagine the molecules are uniformly spaced like a cubed lattice. What is the length of one side of the cube?

c) How does the spacing compare to the size of a molecule, about 4 x 10^(-10) m?[/B]

Homework Equations



pV = nRT

d = (V)^(1/3)

The Attempt at a Solution



I attempted A by setting n/V = p/RT after having converted pressure to kPa and temperature to Kelvin. I got .041 mol/L, which felt weird but since I hadn't done a problem like this before I kept going. For part b, I solved for L, which I got as 101.5 of an unknown quantity, then put that in a cubic root to get 4.7, still unknown quantity, although I would assume at the molecular level I should be getting a nanometer answer. However, in compared to the size of molecules which are even smaller than a nanometer, I am not doubting my calculations. Can somebody help me? Nothing about number density or the space between molecules has been covered either by the book or by my professor's notes.

Thank you for any information you can provide.
 
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Show your work, but make sure to write the units for each step. There is no reason to ever have any unknown units or mysterious quantities.
 
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Matt Armstrong said:

Homework Equations



pV = nRT

d = (V)^(1/3)

The Attempt at a Solution



I attempted A by setting n/V = p/RT after having converted pressure to kPa and temperature to Kelvin. I got .041 mol/L, which felt weird
n is the number of moles, but it is not the number of molecules. How is 1 mol defined? how many molecules is it?
http://whatis.techtarget.com/definition/mole
 

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