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

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SUMMARY

The discussion focuses on calculating the number density and spacing between molecules of an ideal gas at 25.0 degrees Celsius and 1.00 atm pressure. Using the Ideal Gas Law (pV = nRT), the user derived a number density of 0.041 mol/L, which requires conversion to molecules per unit volume for accuracy. The spacing between molecules was estimated using the cubic root of volume, leading to a result of approximately 4.7 nanometers, which is significantly smaller than the size of a molecule (4 x 10-10 m). The user seeks clarification on the calculations and the relationship between moles and molecules.

PREREQUISITES
  • Understanding of the Ideal Gas Law (pV = nRT)
  • Knowledge of unit conversions (atm to kPa, Celsius to Kelvin)
  • Familiarity with the concept of number density
  • Basic understanding of molecular size and dimensions
NEXT STEPS
  • Learn how to convert moles to molecules using Avogadro's number (6.022 x 1023 molecules/mol)
  • Study the concept of number density in gases and its applications
  • Explore the derivation of molecular spacing from number density calculations
  • Investigate the implications of molecular size on gas behavior and interactions
USEFUL FOR

This discussion is beneficial for students studying chemistry, particularly those focusing on gas laws, molecular theory, and physical chemistry concepts. It is also relevant for educators seeking to clarify these topics for their students.

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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