12 Gas Laws

Units Pressure is measured in a variety of units. Atmospheres, bars, torrs etc. The standard international unit of pressure is the Pascal (Pa) P179 gives the conversion factors for other units.

S.T.P or standard temperature and pressure T = 273 (0 o C) P = 1 atmosphere R.T.P or room temperature and pressure T = 298 (25 o C) P = 1 atmosphere

Avogadros law Equal volumes of gases at the same temperature and pressure have equal numbers of molecules At STP 1 mol of any ideal gas occupies 22.4L At RTP 1 mol of any ideal gas occupies 24.0L

What volume is occupied by 8g of hydrogen at STP? 1 mol H 2 has a mass of 2g  8g = 8 = 4 mol 2  Volume occupied = 4 x 22.4 L = 89.6 L

250ml of carbon dioxide weighs 0.44g while the same volume of a gaseous oxide of nitrogen weighs 0.46g at the same temperature and pressure. Find the mass of 1mol of this oxide of nitrogen. Moles of carbon dioxide present in 250ml = = 0.01 mol  250ml of nitrogen also contain 0.01mol  0.46g = 0.01 mol  1 mol of the oxide nitrogen weighs 1 x = 46g mol -1

Ideal Gases The following assumptions are made for an ideal gas 1)The gaseous molecules or atoms occupy a volume which is completely negligible compared to the space occupied by the gas. 2)There are no attractive forces between the gaseous molecules or atoms In practice we can treat most gases ideally except at extremes of temperature and pressure.

At low temperature and high pressures the molecules or atoms will be close enough together for Van der Waals forces to be effective. Also the space occupied by the molecules or atoms will no longer be negligible.  At high pressures and low temperatures all gases deviate from ideal behaviour The deviation will be greater for larger molecules.

Boyles Law The volume occupied by a gas is inversely related to its pressure (assuming temperature constant) PV = constant or v  1 P

Charles Law At constant pressure the volume of a gas is directly proportional to its absolute temperature V  T or V = constant T

Combined Gas Laws Combining these 2 laws we get the relationship PV = constant T Which can also be expressed as P 1 V 1 = P 2 V 2 T 1 T 2

Ideal Gas Law Combining Boyle’s law, Charles’s Law and Avogadros’ law we get the ideal gas equation PV = nRT Where n = no of molecules and R = molar gas constant R will have different values depending on its units R = atm L mol -1 K -1

How many moles of gaseous arsine (AsH 3 ) will occupy L at STP? PV = nRT R = atm L mol -1 K -1 P = 1 atm T = 273K V =  n = PV = 1 x = 1.78 x moles RT x 273

The density of a noble gas is 2.71 g/L at 3.00 atm and 0 o C. Identify the gas. PV = nRT P = 3.00 V = 1 L T = 273 n = 3 x 1 = mols x mol = 2.71 g  1 mol = 2.71 = 20  gas is neon 0.133

Krypton has a density of 3.44 g/L at 25 o C and 1 atm. Find its RAM. PV = nRT  n = 1 x 1 = mols x ( ) mols = 3.44 g  1mol = 3.44 = 84.3 g

For the following reaction what volume of hydrogen at 1.01 atm and 225 O C is needed to form 35.5g Cu. CuO (s) + H 2(g)  Cu (s) + H 2 O (g) 35.5 g = 35.5 = mols 63.5 V = nRT = x x 498 = 22.6L P 1.01

A volume of gas collected at 70 O C and 1.04 atms occupies 265ml. What volume would it occupy at STP? P 1 = 1.04 atms T 1 = = 343K V 1 = 265ml P 2 = 1 atms T 2 = 273K V 2 =  P 1 V 1 = P 2 V 2  1.04 x 265 = 1 x V 2 T 1 T V 2 = 219ml

What volume of oxygen is needed for the complete combustion of 100ml of propane? What volume of carbon dioxide is produced? (All gases are measured at the same temp and pressure) C 3 H 8(g) + 5O 2(g)  3CO 2(g) + 4H 2 O 1 molecule of propane reacts with 5 molecules of oxygen to give 3 molecules of carbon dioxide By Avogadros’s Law 100 ml of propane will react with 500ml of oxygen to give 300 ml of carbon dioxide.

1.Correct the following gas volumes to STP a) 205ml at 27 O C and 1 atms b) 355 ml at 310K and 1.23atms 2. A certain mass of ideal gas has a volume of 3.25L at 25 o C and 1 atms. What pressure is required to compress the gas to 1.88L at the same temperature? 3. An ideal gas occupies a volume of 2.00L at 25 O C and 1 atms. What will the volume of the gas be at 40 O C and 2.22 atms? 1 a) 187ml b) 387ml atms L

On strong heating 40ml of ammonia give 20ml of nitrogen and60ml of hydrogen. Derive the equation for the reaction. 40 ml of ammonia gives 30ml of nitrogen and 60ml of hydrogen  2ml ammonia gives 1ml of nitrogen and 3ml of hydrogen  2 molecules of ammonia gives 1 molecule nitrogen and 3 molecules of hydrogen 2 NH 3(g)  N 2(g) + 3H 2(g)