Transcript Slide 1
Molar Mass (M) and Density (d) of Gases PV = nRT Density of CO2: 44.0 g/mol = 1.96 g/L 22.4 L/mol Which gas would be the most dense? N2, CO2, He, or O2 x g/mol d= 22.4 L/mol How Molar Mass (M) and Density (d) are Related: PV = nRT P n = RT V MP = nM =d RT V Hint: always use PV = nRT first and watch your units! Practice An experiment shows that a 0.495 g sample of an unknown gas occupies 127 mL at 98°C and 754 torr pressure. Calculate the molar mass of the gas. Solution (PV = nRT) The molar m as s is equal to t he num ber of gram s of unknown per mole. W e know t he mass s ample, s o we need to compute t he number of moles . To do t his , we rearrange t he ideal gas n p V R T 7 54t orr n 1 27 mL 1 L 1 00 0mL 7 60t orr 1 at m 0 .08 206Lat mK 1 1 mo l 3 71K 3 n 4 .14 1 0 N ow we can det ermine the molar mass . M m n M 0 .49 5g 3 4 .141 0 mo l M 1 20 g mo l mo l Another Example The density of a gas containing chlorine and oxygen has a density of 2.875 g/L at 756 mmHg and 11oC. What is the most likely formula of the gas? 756 mmHg = 0.995 atm 11oC = 284 K 2.875 g/L = 67.3g/mol 0.0427mol/L PV = nRT (0.995atm)(V) = n (0.08206L.atm/mol.K)(284K) (0.995atm) n = 0.0427mol/L = . . (0.08206L atm/mol K)(284K) (V) Dalton’s Law • • • • Gas identity is not important Mixture of gases obeys ideal gas law Dependent only on total number of moles Ptot = P1 + P2 + P3 + … Dalton’s Law of Partial Pressures • For a mixture of gases in a container PTotal = P1 + P2 + P3 + … Mole Fraction • Percentage of moles in a mixture Xi = ni / ntot • Pi = XiPtot (partial pressure = mole fraction x total pressure) Mole Fraction and Partial Pressure C1 = C1 = P1 P1 + P2 + P3 + … n1 nTOTAL = = P1 PTOTAL P1 PTOTAL Mole Fraction Example At 25°C, a 1.0 L flask contains 0.030 moles of nitrogen, 150.0 mg of oxygen, and 4 x 1021 molecules of ammonia. A. What is the partial pressure of each gas? B. What is the total pressure in the flask? C. What is the mole fraction of each? Partial Pressures W e'll st art by det ermining t he number of moles of ox y gen and ammonia. 1 mo l 3 2.0 0g 0mg 00 1 n O 2 1 50 .0mg 1 g 3 n O 2 4 .68 8 1 0 23 0 mo lecu les 6 .02 21 n N H3 4 1 0 mo lecu les 21 1 mo l 3 n N H3 7 1 0 mo l N ow, we us e the ideal gas law to c ompute t he pres sures of eac h gas . PN 2 PO 2 1 l 0 .08 206L at m K 0 .03 0mo (2 98K ) 1 mo l 1 .0 L n O 2 R 2 98 K PN H3 1 .0 L n N H3 R 2 98 K 1 .0 L PO 2 0 .11 5at m PN H3 0 .2at m mo l PN 2 0 .73at m Total Pressure To determ ine t he total pres sure, we add t he part ial press ures Pt ot PN 2 PO 2 PN H3 Pt ot 1 .0at m Mole Fractions W e may det ermine mole f rac tions by us ing m oles or pres sures. I f we us e pres s ures , PN 2 XN 2 Pt ot PO 2 XO 2 Pt ot PN H3 XN H3 Pt ot XN 2 0 .73 XO 2 0 .11 XN H3 0 .2 Mole Fractions U sing moles, we get n t ot n O 2 n N 2 n N H3 nN 2 XN 2 n t ot nO 2 XN 2 n t ot n N H3 XN H3 n t ot XN 2 0 .73 XO 2 0 .11 XN H3 0 .2 n t ot 0 .04 1mo l Practice A sample of KClO3 is heated and decomposes to produce O2 gas. The gas is collected by water displacement at 25°C. The total volume of the collected gas is 229 mL at a pressure of 754 torr. How many moles of oxygen formed? Hint: The gas collected is a mixture so use Dalton’s Law to calculate the pressure of oxygen then the ideal gas law to find the number of moles oxygen. PT = PO2 + PH2O Solution To determine t he press ure of2 ,Owe s ubtrac t t he v apor press ure of water atC25f rom the t ot a press ure. The v apor pres sure of wat er at this t emperat ure is 23. 9 torr. PO 2 7 54t orr 2 3.9t orr PO 2 7 30 .1t orr N ow we us e t he ideal gas law to determine the number of moles. nO 2 ( 7 30 .1t orr) PO 2 V nO 2 R T 3 n O 2 9 .00 1 0 mo l 0 .22 9 L 7 60t orr 1 at m 1 0 .08 206L at m K 1 mo l 2 98 K