Stoichiometry V = 9.98 L CO ml H 2 SO 4 soln 6.0 mol H 2 SO ml H 2 SO 4 soln. 2 mol CO = mol CO 2 1 mol H 2 SO 4

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1 Stoichiometry We cannot count molecules so instead we weigh them; however, it is etremely inconvenient to weigh gases. So, when adding gases to a reaction how do we measure the amount of gas? We use the Ideal Gas Law. How ml of a 6.0 M sulfuric acid solution is spilled on the floor Sodium hydrogen carbonate is poured on top of the spill to neutralize the acid. What is the volume, in L, of the carbon dioide which is released? The gas being released is at 5 C and 1 atm. H SO 4 (aq) + NaHCO 3 (s) Na SO 4 (aq) + H O(l) + CO (g) so how many moles of acid are neutralized ml H SO 4 soln 6.0 mol H SO ml H SO 4 soln which which produces how many moles of CO ml H SO 4 soln 6.0 mol H SO ml H SO 4 soln mol CO mol CO 1 mol H SO 4 which is how many liters? PVn (1 atm) V (0.408 mol CO )( L atm K -1 mol -1 ) (98.15 K) V 9.98 L CO

2 At constant temperature and pressure volumes of gas can be related directly to each other. e.g. If L of H, which are at the same temperature and pressure as the Cl, are combined with 3 L of Cl, how many liters of HCl will form? H (g) + Cl (g) HCL(g) Without knowing the temperature and pressure we cannot determine the number of moles of either H or Cl present. Since the temperature and pressure are constant we can relate volumes of gas as though they are moles of gas...watch. So, (P H )( L) (n H ) and (P Cl )(3 L) (n Cl ) n H ( L) P H and n Cl (3 L) P Cl Normally, to relate H to Cl we must convert to moles... ( L) P H mol H mol HCl 1 mol H () P L HCl HCl 1 mol HCl 4 P H P HCl L HCl Since the temperatures and pressures of the gases are the same, the pressure of H equals the pressure of HCl, so the numbers needed to perform the conversion from moles to L and L back to moles cancel out! There is enough H to produce 4 L of HCl, but what about the Cl? This is really a limiting reagent problem hidden in a gas problem! There is enough Cl to make 6 L HCl, but there is only enough H to make 4 L of HCl. Only 4 L of HCl can be made in this reaction.

3 We just found that "At constant temperature and pressure volumes of gas can be related directly to each other." A similar statement can be made about pressure and moles! At constant temperature and volume, the pressure of gases can be related directly to each other. Hydrogen reacts with acetylene to form ethane. A reactor is charged with 3 atm of acetylene, CH, and 10 atm of H. Determine the pressure inside the reactor after the reaction has finished. C H (g) + H (g) C H 6 (g) There is enough acetylene to make 3 atm C H 1 atm C H 6 3 atm C H 6 1 atm C H There is enough oygen to make 10 atm H 1 atm C H 6 5 atm C H 6 atm H So, 3 atm CH6 will form. All of the CH will be consumed, but only 3 atm C H atm H 1 atm C H 6 atm H consumed So, the total pressure is P P + P tot H C H 6 leaving 4 atm of H. P tot 4 atm H + 3 atm C H 6 P 7 atm

4 Partial Pressure In the previous eample, the total pressure inside the "bomb" was 7 atm. We calculated that the pressures of the CO and the O were 3 and 4 atm respectively. The pressures of CO and the O are called partial pressures, because the pressures of the CO and the O add up to the total pressure. P tot P O + P CO The partial pressure, Pa, is related to the mole fraction of "a", and the total pressure. Mole fraction is a means of measuring concentration and is defined as follows: χ a n a and χ b n b The mole fraction of a, χa, is defined as the number of moles of a, na, divided by the total number of moles of stuff present, na + nb. The partial pressure, Pa, of a is a result of all the "a" molecules present. P a V n a The total pressure, Ptot, is a result of all the molecules present. P tot V ( ) Divide one equation by the other...

5 P a V P tot V n a ( ) P a P tot n a P a P tot χ a Incidentally, since a and b are both parts of the whole the mole fractions, χa and χb, must add up to 1. χ a + χ b n a + n b χ a + χ b χ a + χ b 1 A balloon is filled with air at a pressure of atm. Air is actually a miture of gases, approimately 80% nitrogen and 0 % oygen (by volume). What is the pressure of the nitrogen in the balloon? 1.6 atm NOT atm...how come? Because the total pressure is.0 atm, and the total pressure is the sum of the partial pressures.

6 P N P tot χ N P N atm 0.8 P N 1.6 atm P O 0.4 atm P tot atm Collecting gases over water Often a gas produced by a reaction can be collected over water; that is, a gas can be used to displace the water from and inverted container of water. A graduated cylinder was filled with water and inverted in a tub of C water. H produced from the reaction of Zn with HCl. With the water level inside and outside of the cylinder at the same level 90.0 ml H were produced. The barometric pressure was 761 torr. How many moles H were collected? To determine moles of gas we need to know P, V, and T... V 90.0 ml T C 95 K P? Level inside being equal to the level outside means the pressure inside is the same as the pressure outside... P 761 torr

7 This is the pressure of what? Is 761 torr the pressure of the H which was collected? Wait...why not... NO! What gases are present in the graduated cylinder? H is present, but so is HO! HO evaporates, right? So, the HO in the cylinder will evaporate. So, there is HO vapor mied with the H. Therefore, P tot P H + P H O 761 P H + 1 torr P H 740 torr Now that the pressure of the H is known, the problem is just a PV n problem torr (0.090 L) n R (95 K) 760 torr atm n mol H