Calculate length of side of cube

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Discussion Overview

The discussion revolves around calculating the length of a side of a cubic simulation box containing 500 molecules, given a molar volume of 0.6 l/mol. The focus is on the mathematical relationships and conversions necessary to derive the side length in Ångstrøm.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant inquires about the calculation of the side length L of a cube with 500 molecules and a specified molar volume.
  • Another participant suggests determining the number of moles from the number of molecules and using the volume formula V = l² to find the side length, emphasizing the importance of unit consistency.
  • A participant clarifies that 1 mole corresponds to approximately 6.002e+23 molecules, leading to the calculation of moles from 500 molecules as 8.3e-22 moles, but expresses confusion about the volume calculation.
  • There is a correction regarding the volume being cubed rather than squared, with a participant questioning the volume formula used.
  • One participant confirms the calculation of moles and suggests multiplying the molar volume by the number of moles to find the cube's volume in liters, followed by conversion to cubic meters.
  • A later reply provides a formula for calculating the side length in meters and mentions the need to convert the final result to Ångstrøm.
  • Some participants express uncertainty about the calculations and the steps involved in deriving the side length.

Areas of Agreement / Disagreement

Participants generally agree on the method of calculating the number of moles and the relationship between volume and side length. However, there remains confusion regarding the specific calculations and unit conversions, indicating that the discussion is not fully resolved.

Contextual Notes

There are unresolved questions about the correct application of volume formulas and unit conversions, particularly in transitioning from liters to cubic meters and then to Ångstrøm.

Who May Find This Useful

This discussion may be useful for students or individuals interested in molecular simulations, volume calculations, and unit conversions in the context of chemistry and physics.

Omsin
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How can I calculate the length L of each side of a cubic simulation box with 500 molecules (in Ångstrøm) when I want molar volumes of V1 = 0.6 l/mol?
 
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How many molecules in 1 mol? What fraction of 1 mol is 500molecules? That gives you the volume of the cube in l.
V=l2 will give you the length of a side of the cube.
All you need to do is the Arithmetic -get the units right, of course,
 
1 mole is 6.002e+23 molecules. 500 molecules have 8.3e-22 moles. I am not really sure what you meant after that. Volume = (liter)^2? Isn't Volume[m^3] = [1000* Liter]
 
Omsin said:
1 mole is 6.002e+23 molecules. 500 molecules have 8.3e-22 moles. I am not really sure what you meant after that. Volume = (liter)^2? Isn't Volume[m^3] = [1000* Liter]
My bad. Of course volume is cubed. But the sums are easy, no?
 
sophiecentaur said:
My bad. Of course volume is cubed. But the sums are easy, no?
Sorry, but I am not really sure how to do this.
 
You have already calculated how many moles will be in your cube (8.3e-22 moles as you previously said).

You want molar volume of 0.6 Liters/mol, so if you multiply this number with the moles, you will get the volume of the cube (V) in Liters. Then you can divide by one thousand to get the Volume in m3.

So, your cube's side will have length ## l = \sqrt[3] V ## meters.

The last step is to change meters to Angstroms.
 
Omsin said:
Sorry, but I am not really sure how to do this.
Sorry. I was busy and couldn't get back to you quickly. But @DoItForYourself has sorted you out I think.
 
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