Estimating the spacing between gas molecules

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To estimate the average spacing between gas molecules in 1 mol of an ideal gas at 1 atm and 300K, the ideal gas law (PV=nRT) is used to calculate the volume occupied, which is approximately 0.0246 m^3. The next step involves determining the volume per molecule by dividing the total volume by the number of molecules, which is Avogadro's number (approximately 6.022 x 10^23). However, the discussion highlights the uncertainty in this estimate due to the unknown size of the molecules, raising concerns about whether this calculation accurately reflects the actual separation distance. The volume per molecule only provides a rough estimate of the distance between centers of molecules, not accounting for their physical size. Ultimately, while the approach is valid, the size of the molecules must be considered for a more accurate representation of spacing.
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Homework Statement



Estimate the average spacing between molecules of 1 mol of an ideal gas at a pressure of 1atm and a temperature of 300K.


Homework Equations



PV=nRT


The Attempt at a Solution



I was able to calculate the volume occupied by the gas (0.0246m^3). Using the ideal gas law. So we know how many molecules there are in what volume. But without further information how can I calculate the spacing?

Thanks a lot.
 
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whats the volume per molecule
 
granpa said:
whats the volume per molecule

That would be the volume divided by the total number of molecules. I did think of that but is that an estimate of separation? We don't know the size of each molecule. The volume per molecule would just be the distance from the centre of one molecule to another. What if the molecules are really large?
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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