Ideal Gas Problems. 3. What is the pressure (in atmospheres) of a mol sample of helium gas at 20.0ºC if its volume is L? Latm.

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1 Ideal Gas Problems. What are the values of STP (standard temperature and pressure)? Temperature: 7 K. Pressure: atm.. Calculate the volume of mol of an ideal gas under STP. (Memorize this relation!) p = atm T = 7.5 K n = mol V =? pv nrt ; Latm mol K nrt V. 4L (per mol at STP) p atm. What is the pressure (in atmospheres) of a 0.08 mol sample of helium gas at 0.0ºC if its volume is L? p =? T = 0.0ºC + 7 = 9 K n = 0.08 mol V = 0.505L pv nrt ; Latm 0.08mol K p nrt 5. atm V 0.505L 4 4. You are given a problem that has the initial pressure and volume of a gas, and the final pressure of the gas is given too. You are asked to find the final volume. a) What variables could you leave out of the ideal gas law? T and n are constant (not given or mentioned) and will cancel out in the equation. b) How would the ideal gas law equation look like for this problem? pv nrt = constant. pv pv ; p V V. p

2 5. You are given a problem that has the initial pressure and temperature of a gas and the final temperature of the gas is given. You are asked to find the final pressure. a) What variables could you leave out of the ideal gas law? This means that V and n are constant (not given or mentioned) and will cancel out in the equation. b) How would the ideal gas law equation look like for this problem? pv nrt ; p nr p = constant; p p ; T p T V T T T 6. On hot days, you may have noticed that potato chip bags seem to inflate, even though they have not been opened. If I have a 50 ml bag at a temperature of 9, and I leave it in my car which has a temperature of 60, what will the new volume of the bag be? V = 50 ml T = 9 C = 9 K TV V nt nt T V =? T = 60 = K Simplifies to: Answer: (Assume n and P constant.) V V (Boyle's Law) K 50mL V 85mL T T 9K L of a gas at standard temperature and pressure is compressed to 47 ml. What is the new pressure of the gas? V =.00 L P = atm P nt nt V T = 7 K Simplifies to: Answer: L atm.00l V = 47 ml 0.47L P V P V (Charle's Law) P. atm 000mL 0.47L P =? (Consider T and n constant.)

3 8. A flexible container is filled with 8.0 moles of air. How many more moles of gas would you need to introduce in it to change the volume from 5 L to 00 L? V = 5 L Vn n nt nt V n = 8.0 mol Simplifies to: Answer: V V V = 00 L 00L8.0 mol n n n 5L n =? Note that the question is how many more moles, (Consider T and P constant.) so the answer is: n - n = mol - 8 mol = 4 mol 9. A gas has a volume of 40mL at 7ºC and a pressure of 60 mmhg. What volume will it have at STP? pv nrt. The number of moles and R are constants so: pv T p V T nr. The unknown is V :.86atm40 ml7k 0.5K atm pvt V 89mL T p (Don t forget to convert T and p in order to have the appropriate units.) 0. The initial pressure of a gas is 5 atm. Which would the final pressure be if the volume of the gas is doubled and its temperature tripled? Instead of numbers, the data are given in the form of relations. T P = 5 atm P nt nt TV P =? Simplifies to: In the answer we substitute the relations and the values: T V = (V ) 5atmV T 5atm P atm T T TV T V T = (T ) (consider n constant)

4 . A small cylinder of helium gas used to filling balloons has a volume of.0 L and a pressure of 850 atm at 5 C. How many balloons can you fill if each one has a volume of.5l and a pressure of.5 atm at 5 C? (Hint: Notice we were given data for two different containers!) For the cylinder: For the balloons: Latm R = T = 5 C = 98 K T = 5 C = 98 K V =.0 L V =.5 L P = 850 atm P =.5 atm n =? n =? We need to calculate the number of moles of helium in the cylinder and then the number of moles that each balloon can hold. If we get the ration of the number of moles, we ll now how many balloons we can fill. Equation: Rearranging the equation: = nrt; n RT Moles in the cylinder: Moles in each balloon: (850 atm)(.0 L) (.5 atm)(.5 L) n = = 74 mol n = = L atm (98 K) ( mol K ) L atm mol (98 K) ( mol K ) 74 mol # ballons = = 67 ballons 00 ballons mol. Blast furnaces give off many unpleasant and unhealthy gases. If the total pressure is 0.99 atm, the partial pressure of carbon dioxide is 0.05 atm, and the partial pressure of hydrogen sulfide is 0.0 atm, what is the partial pressure of the remaining air? Equation: Answer: P TOT 0. 99atm PT PCO PH S P Air P Air 0.99atm 0.05atm 0. 0atm P CO 0. 05atm P atm Air 0. 9 P H S 0. 0atm Rearranging the equation:? P P P P Air Air T CO H S P. A metal tank contains three gases: oxygen, helium, and nitrogen. If the partial pressures of the three gases in the tank are 5 atm of O, 5 atm of N, and 5 atm of He, what is the total pressure inside of the tank? Equation: Answer: P TOT? PT PO P N PHe P T 5atm 5atm 5atm 65atm P O 5atm P T 65atm P N 5atm P He 5atm 4

5 4. In the Haber process, nitrogen reacts with hydrogen to produce ammonia (NH ). a. Write the balanced chemical equation. N + H NH b. If.0 L of nitrogen gas at STP is combined with 5.0 L of hydrogen gas also at STP. Is there a limiting reagent? If so, which one? mol molnh.0ln 0. 79molNH.4L STP moln mol molnh 5.0LH 0. 49molNH.4L STP molh Hydrogen is the limiting reactant. c. If L of nitrogen gas at 00.0 psi and.0 C is combined with 00.0 L of hydrogen gas at 40.0 psi at.0 C, what mass (in grams) of ammonia can theoretically be produced? [ atm = psi; R = L atm/mol K] pv nrt ; pv n. RT n N n H atm 00.0 psi 50.0L psi 8.09molN Latm K atm 40.0 psi 00.0L psi 67.4molH Latm K Find the limiting reactant: molnh 8.09molN 56. 8molNH moln molnh 67.4molH molNH molh Hydrogen is the limiting reactant. 7.0g 44.95molNH 766gNH molnh 5