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

In summary, in this conversation, the topic of an ideal gas at 25.0 degrees Celsius and 1.00 atm was discussed. The questions focused on determining the number density of the molecules in the gas and the spacing between the molecules. The ideal gas law, pV = nRT, was used to calculate the number density, which was found to be 0.041 mol/L. However, this value does not represent the actual number of molecules, as 1 mole is defined as 6.022 x 10^23 molecules. For the spacing between molecules, the length of one side of a cube was determined using the formula d = (V)^(1/3), which resulted in a value of
  • #1
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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  • #2
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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  • #3
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
 

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

1. What is the ideal gas law?

The ideal gas law is a mathematical equation that relates the pressure, volume, temperature, and number of molecules of an ideal gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

2. How do you calculate number density?

Number density is calculated by dividing the number of molecules in a given volume by the volume itself. It can be expressed as n = N/V, where n is the number density, N is the number of molecules, and V is the volume.

3. What units are used in the ideal gas law?

The units used in the ideal gas law depend on the values given for pressure, volume, temperature, and number of moles. Generally, pressure is measured in atmospheres (atm), volume in liters (L), temperature in Kelvin (K), and number of moles in moles (mol).

4. How do you calculate the spacing between molecules?

The spacing between molecules can be calculated by taking the inverse of number density. This can be expressed as d = 1/n, where d is the spacing between molecules and n is the number density.

5. Can the ideal gas law be used for all gases?

The ideal gas law is most accurate for gases that behave ideally, meaning that their molecules have negligible volume and do not interact with each other. However, it can still be used as an approximation for real gases under certain conditions.

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