GS_Stoichiometry with Gases Lesson

Stoichiometry with Gases

Earlier we learned the concept of molar volume. This means that f or 1 mole of any gas, the volume of that gas at STP is 22.4 L. Let's use this as fact as a conversion and do some stoichiometry problems with gases.

MOLAR VOLUME 1 mol gas = 22.4L used as a conversion 1 mol gas/22.4L 22.4L/1 mol gas

Example Problem What volume of hydrogen at STP can be produced when 6.54 g of Zn reacts with hydrochloric acid, HCI? Zn + 2 HCI → H2 + ZnCl2 Since all the chemicals are at STP, the molar volume fact may be used as an additional conversion. ?LH₂=6.54 g Zn (1molZn/65,4gZn)(1molH₂/1molZn)(22.4 L H₂/1 mol H₂)=2.24 L H₂ Notice that this math could be easily done without a calculator. Remember that calculators are not allowed on certain portions of the AP Exam. So, be on the lookout for situations like this where the numbers can easily be cancelled.

Stoichiometry and Gases Laws Combined

Now, let's combine stoichiometry and the gas laws we have learned. Before you work the problems below, it would be a great idea to go back and make sure that you know all of the equations presented in this module. Note as you work these problems that there is not just one way to approach them or just one type of problem. Gas stoichiometry problems can be extremely varied. The more of them you practice, the better off you will be.

Example Problem When arsenic (III)sulfide is burned in air, it reacts with oxygen to produce arsenic (III) oxide and sufur dioxide. When 89.5 g of arsenic (III)sulfide is burned with the excess oxygen, how many liters of sufur dioxide gas will be procuded. The gaseous product will be measured at 98.0 kPa and 20.0°C? Start by writing the balanced equation. Then, write a list of the data. 2 AS2S3 (s) + 9 O2 (g) → 2 AS2O3(s) + 6 SO2 (g) m = 89.5 g P = 98.0 kPa V = ? mL n = T = 20.0°C Looking at the data and what we want to calculate, we can see that we could calculate V of SO₂ if we knew n. We can do basic stoichiometry to find n of SO2. ?mol SO₂ = 89.5 g As, S₂( 1 mol As₂S₂/245.05 g As,S,2 )(6 mol SO₂)/2molAs₂S₂)=1.09 mol SO₂ Before we calculate V of SO2, we need to convert our pressure and temperature units! P = 98.0 kPa (1atm/101.3 kPa)=0.967atm T= 20.0 + 273=293K Now, we can use PV=nRT to calculate PV=nRT (0.967 atm)(V)-(1.09 mol) 0.0821(Latm/molK) (293K) V = 27.1 L

Let's apply another of our gas laws. Remember that according to the Law of Combining Volumes, the coefficients of a balanced equation of gases also represent the ratio of volumes of those gases.

Example Problem How many liters of hydrogen, measured at STP, are needed to combine exactly with 1.50L of nitrogen, also measured at STP, to form ammonia? All you need to remember here is that since the gases are the same temperature and pressure, the ratio of their volumes is the same as the ratio of moles. ?LH₂ =1.50LN₂ (3LH₂ /1L N₂ )=4.50 LH₂ So, always be on the lookout for gases measured at the same temperature and pressure (STP not required). Recognizing this and remembering that under these conditions, the ratio of their volumes is the same as the molar ratios will save you lots of time!

So, how do you sove a problem like the one above if the gases are not measured at the same temperature and pressure? Watch this video to see how to solve this type of gas problem.

In summary, below is a general procedure for solving gas problems with changing conditions of T and P. Note that this a general procedure and will need to be tweaked for each specific problem

(1) Convert volume to moles using PV = nRT and the initial set of T and P. 
(2) Use the balanced equation molar ratios to determine moles of other substance involved in problem.
(3) Use PV = nRT with new T and P as well as moles of substance from step 2.

Remember to work on the module practice problems as you complete each section of content.  

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