Gas Laws & Chemical Reactions

Learning Goals

This section puts together the material in the preceding sections and your previous understanding of working stoichiometry problems so that you can apply stoichiometric principles to chemical reactions that involve gases.

Synopsis

Now we are ready to apply our IG EOS and what we learned in Chapters 4 and 5 to chemical reactions. Now we can work stoichiometric problems when some of the reactants and/or products are gases. All the concepts we learned previously including deciding upon the limiting reagent still apply. The only difference is that now we have another tool at our disposal for calculations involving gases. Let's look at a problem:

How do we calculate the number of grams of water formed from the reaction

2H₂(g) + O₂(g) --> 2H₂O(g)

if we have 13.6 liters of O₂(g) at 10 0C and 755 mm Hg mixed with 34.6 liters of H₂(g) at 28 C and 724 mm Hg to produce water?

Now we can calculate the number of moles of the reactants from the ideal gas law. However our units are not what we need for we need pressure in atmospheres and temperature in Kelvin.

For oxygen, T = 10 + 273 = 283 K and P = 755 mm Hg/(760 mm Hg/atm) = 0.993 atm, so for oxygen:

n_oxygen = PV/RT = 0.993 atm*13.6 l/(0.0821 latm/molK)*283K) = 0.581 moles

For hydrogen, T = 28 + 273 = 301 K and P = 724 mm Hg/(760 mm Hg/atm) = 0.952 atm, so for hydrogen:

n_hydrogen = PV/RT = 0.952 atm*34.6 l/((0.0821 latm/molK)*301K)= 1.33 moles.

So the ratio of hydrogen to oxygen that we actually have is 1.33/0.581 = 2.29, but the ratio that we need is given by the ratio of the stoichiometric coefficients which is 2/1 = 2 so we have too much hydrogen and thus oxygen is the limiting reagent. Thus we will use oxygen to calculate how much water the above reaction forms:

0.581 moles oxygen * (2 moles water/mole oxygen) = 1.162 moles of water formed. The gram molecular weight of water is 18.0 grams so the number of grams of water formed is

1.162 moles water * 18.0 grams/mol = 29.916 g = 30. g water

Easy! But you must practice, practice, practice.

To practice the technique involved in working such problems, work Example 12.9 in your text.

Review Question

If in the production of ammonia from nitrogen and hydrogen, 135 liters of gaseous hydrogen at 26.0^oC and 642 mm Hg are combined with excess nitrogen gas how many liters of ammonia measured at 450^oC and 1.00 atm can be theoretically produced.
Work the preceding problem if, instead of in excess nitrogen gas, 144 liters of gaseous nitrogen at 26.0^oC and 732 mm Hg are used.