U NIT 5: G ASES AND A TMOSPHERIC C HEMISTRY Combined Gas Laws

Combining the Gas Laws So far we have seen three gas laws: Jacques CharlesRobert Boyle P1V1P1V1 =P2V2P2V2 V1V1 T1T1 = V2V2 T2T2 These are all subsets of a more encompassing law: the combined gas law P1P1 T1T1 = P2P2 T2T2 P 1 V 1 P 2 V 2 T 1 T 2 = Joseph Louis Gay-Lussac

Combined Gas Law = P 1 V 1 P 2 V 2 T 1 T 2

Sandra is having a birthday party on a mild winter’s day. The weather changes and a higher pressure (103.0 kPa) cold front (-25°C) rushes into town. The original air temperature was –2.0 °C and the pressure was kPa. What will happen to the volume of the 4.2L ballons that were tied to the front of the house? V 1 = 4.2L T 1 = -2.0 °C T 2 = -25 °C =271K =248K P 1 = kPa P 2 = kPa

P 1 V 1 P 2 V 2 T 1 T 2 (100.8kPa)(4.2L)(103.0 kPa)(V 2 ) 271K248K (100.8kPa)(4.2L)(248K) (271K)(103.0kPa) V 2 = 3.76 L = 3.8 L = = = V 2

In an analysis of 39.8 mg of caffeine, 10.1 mL of N 2 gas is produced at 23°C and 746 torr. What must the new temperature of nitrogen be, in °C, if the volume is increased to 12.0 mL and the pressure is increase to 780 torr? V 1 = 10.1 mL V 2 =12.0 mL T 1 = 23 °CT 2 =? °C =296K P 1 = 746 torr P 2 = 780 torr

T 1 P 2 V 2 P 1 V 1 (296K)(780 torr)(12.0 mL) (746 torr)(10.1 mL) T 2 = 368 K T 2 = 368 –273 = 95°C = T 2

Since the space between the particles in a gas is very large, the individual gases in a mixture of gases can be thought to each act independently. Therefore the total pressure exerted by a mixture of gases is the sum of the pressure of each gas when measured alone. P total = P 1 + P 2 + P 3 + ….. For example the partial pressures in the atmosphere are: P N2 = 79 kPa, P O2 = 21 kPa, P Ar = 1 kPa, P total = 101 kPa

Using Dalton’s Law with Combined Gas Law Problems Many experiments involve collecting gases over water using chemical reactions. Even if only a single gas was produced in the chemical reaction, water vapour (H 2 O (g)) will also be present. Since: i) The total pressure in the cylinder (P total ) is equal to the current atmospheric pressure (P atm ). ii) The partial pressure of the water vapour (P H2O ) depends on the temperature that the water is at (see the table Vapour Pressure of Water at Various Temperatures). Thus we can use Dalton’s law to determine the partial pressure of the dry gas. Since:P atm = P dry gas + P H2O Therefore:P dry gas = P atm - P H2O

Temperature o C Pressure kPa Temperatur e o C Pressure kPa Temperatur e o C Pressure kPa VAPOUR PRESSURE OF WATER

1. A volume of 400 mL of oxygen is collected over water at a temperature of 27 o C and an atmospheric pressure of kPa. What is the volume of the dry oxygen at STP?

2. What volume of gas must be collected over water at 21 o C and kPa to give 4.00 L of dry hydrogen at STP?

C LASSWORK /H OMEWORK - Work on Combined Gas Law Problems and Dalton’s Law of Partial Pressure Problems - Use Vapour Pressure of Water Table if needed