How do mole ratios compare to volume ratios?

Answer 1

I'm assuming you're talking about ideal gas reactions, where it's easy to find the relationship between mole ratios and volume ratios.

Avogadro's law states that equal volumes of ideal gases contain the same number of moles at the same temperature and pressure. This implies that one mole of any ideal gas will occupy the exact same volume if temperature and pressure are held constant.

#V_("molar") = V/(n)# for #n=1 "mole"#. (1)

The molar volume of a gas at STP, or Standard Temperature and Pressure, is the most widely used application of this principle. Under STP conditions, which entail a temperature of 273.15 K and a pressure of 1 atm, one mole of any ideal gas occupies precisely 22.4 L.

Suppose, for example, that you have an ideal gas reaction at STP.

#N_(2(g)) + 3H_(2(g)) -> 2NH_(3(g))#
The mole ratio between #N_2#, #H_2#, and #NH_3# is #1:3:2#; that is, 1 mole of #N_2# reacts with 3 moles of #H_2# to produce 2 moles of #NH_3#.
Let's assume we have #0.25# moles of #N_2# that react completely with #H_2# to produce #NH_3#. Since we are a STP, we know that 1 mole of each of these gases occupies 22.4L. According to (1), this means that
#V_(H_2) = n_(H_2) * V_("molar") = 3 * 0.25 * 22.4L = 16.8L# #V_(N_2) = n_(N_2) * V_("molar") = 0.25 * 22.4L = 5.6L# #V_(NH_3) = n_(NH_3) * V_("molar") = 2 * 0.25 * 22.4L = 11.2L#
The volume ratio between #N_2#, #H_2#, and #NH_3# will be #5.6 : 16.8 : 11.2#, which is of course equal to #1:3:2#, the mole ratio between the gases.

Therefore, the mole ratio and the volume ratio are equal for gaseous reactants and products that are at the same pressure and temperature.

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Answer 2

Mole ratios compare the number of moles of substances in a chemical reaction, while volume ratios compare the volumes of gases involved in a reaction, typically at constant temperature and pressure.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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