1 Chapter 6 The States of Matter 6.8 The Combined Gas Law and Ideal Gas Law

2 The combined gas law uses Boyles Law, Charles Law, and Gay-Lussacs Law (n is constant). P 1 V 1 =P 2 V 2 T 1 T 2 Combined Gas Law

3 A sample of helium gas has a volume of L, a pressure of atm and a temperature of 29°C. At what temperature (°C) will the helium have a volume of 90.0 mL and a pressure of 3.20 atm (n is constant)? 1. Set up Data Table Conditions 1Conditions 2 P 1 = atm P 2 = 3.20 atm V 1 = L (180 mL) V 2 = 90.0 mL T 1 = 29°C = 302 KT 2 = ?? Combined Gas Law Calculation

4 Combined Gas Law Calculation (continued) 2. Solve for T 2 P 1 V 1 =P 2 V 2 T 1 T 2 T 2 = T 1 x P 2 x V 2 P 1 V 1 T 2 = 302 K x 3.20 atm x 90.0 mL = 604 K atm mL T 2 = 604 K = 331 °C

5 A gas has a volume of 675 mL at 35°C and atm pressure. What is the volume(mL) of the gas at -95°C and a pressure of 802 mm Hg (n constant)? Learning Check

6 Solution Data Table Conditions 1Conditions 2 T 1 = 308 K T 2 = -95°C = 178K V 1 = 675 mL V 2 = ??? P 1 = 646 mm Hg P 2 = 802 mm Hg Solve for V 2 V 2 =V 1 x P 1 x T 2 P 2 T 1 V 2 = 675 mL x 646 mm Hg x 178K = 314 mL 802 mm Hg x 308K

7 The ideal gas law uses Boyles Law, Charles Law, and Gay-Lussacs Law, and Avogadros Law in a gas sample. PV = nRT R is the universal gas constant that relates pressure, volume, temperature, and number of moles of gas in the ideal gas law. R (gas constant) = L atm mol K Ideal Gas Law

8 Learning Check A gas system has pressure, volume and temperature of 1.93 atm, 4.31L and o C, respectively. How many moles of gas are present?

9 Solution First, organize the data converting the temperature and volume, if needed: P=1.93atm V=4.31L n=?(in moles) T=692.0C=>965K Rearrange the ideal gas equation to solve for the missing quantity PV=nRT=>n=PV/RT Substitute in the given quantities and solve, using the appropriate ideal gas constant and converting the initial result to the desired dimension, as necessary: (1.93*4.31)/(0.0821*965)=0.105moles

10 Learning Check A gas system has pressure, moles and temperature of 1.77 atm,0.183 moles and o C, respectively. What is the volume in mL?

11 Solution First, organize the data converting the temperature and volume, if needed: P=1.77atm V=?(in mL) n=0.183moles T=62.00C=>335K Rearrange the ideal gas equation to solve for the missing quantity PV=nRT=>V=nRT/P Substitute in the given quantities and solve, using the appropriate ideal gas constant and converting the initial result to the desired dimension, as necessary: (0.183*0.0821*335)/1.77=2.84L=>2840mL