Bootcamp: Why does the value of volume equal to the number of moles?

[Bigbirdo]

I understand that at constant temperature and pressure, the volume of the gas is directly proportional to the number of moles. This is the advogadro's law. However, I don't know why the volume is equal to the number of moles. I am confused because direct proportionality does not mean equality. If you can explain this with math, it would be very helpful!

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[DatRav27]

This is one of those properties thats only gases have. If in a chemical reaction, such as the one you were given, includes all gas phases, volume will be proportional in respect to the coefficients in the balanced chemical reaction. This is largely due to the fact that gases occupy the volume they are given. So all of these gasses occupy the same volume. If a solid or liquid were used, this principle is no longer valid.

The volume is not EQUAL to the number of mole. Since liters of each reactant were given, you can approximate the liters of the product. If you wanted moles, divide the volume by 22.4 and you have the moles of product.

Math:

limiting reagent is H2

2L/22.4L/mol = 0.089 mols of H2
(0.o89 mols H2)(2 mols NH3/3 mols H2) = 0.0595 mols NH3

(0.0595 mols NH3)(22.4L/mol) = 1.33 L NH3

Remember that at STP 22.4 L of a gas equals to 1 mol

Hope this helps!

 

[Bigbirdo]

This is one of those properties thats only gases have. If in a chemical reaction, such as the one you were given, includes all gas phases, volume will be proportional in respect to the coefficients in the balanced chemical reaction. This is largely due to the fact that gases occupy the volume they are given. So all of these gasses occupy the same volume. If a solid or liquid were used, this principle is no longer valid. Hope this helps!

The volume is not EQUAL to the number of mole. Since liters of each reactant were given, you can approximate the liters of the product. If you wanted moles, divide the volume by 22.4 and you have the moles of product.

But what happened here? It uses the value of liters directly to do stoichiometry to get the number of moles without dividing it by 22.4 L.

 

[DatRav27]

I edited my previous response. Look at the math, in the beginning you divide by 22.4 and then at the end multiply by 22.4. This is why this principle works

 

[Kend]

well, To make it easier just do the old method which is a little bit longer.
We know that at STP 1 mole of gas = 22.4 L
1st we convert 2 L of H2 to mole of H2,
2 L H2 * (1moleH2/ 22.4L H2)
then convert mole of H2 to mole of NH3.
2 L H2 * (1moleH2/ 22.4L H2) * (2 mole of NH3 / 3 mole of H2)
once we got mole of NH3 we have to covert it back to L since the question ask so
2 L H2 * (1moleH2/ 22.4L H2) * (2 mole of NH3 / 3 mole of H2) * (22.4L NH3/1mole NH3)
notice that along the way, we canceled out 22.4 L. Thus, we can treat the liters of gas same as mols
hope it makes sense

 

[Bigbirdo]

I edited my previous response. Look at the math, in the beginning you divide by 22.4 and then at the end multiply by 22.4. This is why this principle works

I think I know what you are saying. Can I say that at constant temperature and pressure, the values of volume have the same proportionality as the number of moles?

 

[DatRav27]

I think I know what you are saying. Can I say that at constant temperature and pressure, the values of volume have the same proportionality as the number of moles?

Yes