Properties of Gases Properties of Gases Three phases of matter solid Definite shape and volume liquid Definite volume, shape of container gas Shape and volume of container Properties of Gases A gas is a collection of molecules that are very far apart on average. Gases exert pressure on the objects in their surroundings. Pressure is caused by collisions between the gas molecules and objects with which they are in contact. Pressure: the force exerted on a unit area P = F A Atmospheric pressure: the pressure exerted by gas molecules in the air on all objects exposed to the atmosphere Pressure Many different units used to report pressure. atmosphere (atm) torr (torr) millimeters of Hg (mm Hg) inches of Hg (in. Hg) pascal (Pa) = SI base unit kilopascal (kpa) pounds per square inch (psi)
Pressure Pressure Relationships between different pressure units: 1 atm = 760 mm Hg = 760 torr = 101.325 kpa = 29.92 in. Hg = 14.7 psi = 1.01325 x 10 5 Pa Convert the pressure 669 torr into pressure in atm? Given: 669 torr Find: P (atm) Conversion factor: 1 atm = 760 torr P (atm) = 669 torr x 1 atm = 0.880 atm 760 torr Four variables are needed to define the physical condition or state of any gas: Temperature (T) Pressure (P) Volume (V) Amount of gas (moles: n) Assume gas molecules are widely separated and non-interacting, thus the equations are independent of the identity of the gas Size, shape, mass of gas molecules don t matter Equations relating these variables are known as the gas laws.
P and V Relationships Boyle s Law: Relates pressure (P) and volume (V) of a fixed amount (i.e. constant number of moles) of gas at constant temperature (T) Pressure of a gas is inversely proportional to its volume at constant temperature and for constant number of moles P 1 V P = k 1 V V and T Relationships Charles s Law: Relates Volume (V) and temperature (T) of a fixed amount of (i.e. constant number of moles) gas at constant pressure (P) Volume of a gas is inversely proportional to its temperature at constant pressure and constant number of moles V T V = k 2 T Behavior at Standard Condition Behavior at Standard Condition Standard Temperature and Pressure (STP) : 0 C (273.15 K) and 1 atm T= 0 C = 273.15 K; P = 1atm = 760 torr Under these condition the volume of 1 mole of an ideal gas is called standard molar volume and is equal to 22.4 L
P, T and V Relationships Boyle s Law and Charle s Law can be merged to give the combined gas law (for a fixed amount of gas): PV = T k P1V T 1 1 P2 V = T 2 2 P, T and V Relationships A sample of gas has a volume of 500. ml at 27 o C and 800. torr. We wish to compress the sample to 250. ml at 900. torr. What temperature is required? If the amount of gas remains constant, we can use this combined gas law to calculate how a gas will respond to changes in T, P and V P, T and V Relationships A sample of Ar gas is confined to a 10.0 L container at P = 1.90 atm and T = 30 o C. What would be the volume at 1.00 atm and 10 o C? Avogadro s Law The combined gas law only works if the number of gas molecules remains constant What if we wish to compare two gases with different numbers of gas molecules? Avogadro s Law states that: Equal volumes of gases measured at the same T and P contain equal numbers of molecules V n or V/n = k (a constant) V 1 V = 2 n1 n2 The law holds because gas molecules don t interact appreciably
Boyle s Law V = k 1 x 1 P Charles Law V = k 2 x T Avogadro s Law V = k 3 x n Three equation can be combined to make a more general gas law: where P = pressure V = volume n = moles PV = nrt T = temperature (K) R = gas constant The value of the gas constant (R) depends on the units of P, V, n, and T. T must always be in Kelvin n is usually in moles Ideal A 2.15 mol sample of SO 2 occupies a volume of 12.6 L at 30 o C. What is the pressure of the gas in atm? If P (atm) and V (L), then R = 0.08206 atm. L mol. K If P (torr) and V (L), then R = 62.36 L. torr mol. K
Ideal A 1.25 g sample of CO 2 is contained in a 750. ml flask at 22.4 C. What is the pressure of the gas in torr? Ideal The reaction of lithium carbonate and nitric acid generates lithium nitrate, CO 2 and water? If 3.00 g of lithium carbonate reacts with 100.0 ml of 0.500 M nitric acid, what volume of CO 2 will form? Ideal A 1.007g sample of an unknown gas exerts a pressure of 715 mm Hg in a 452-ml container at 23 C. What is the molar mass of the gas? The Ideal Gas Law A 6.00 g sample of a Group 13 metal reacts with excess HCl to form hydrogen gas. The gas is collected in a 2.00 L flask at 25.0 o C, giving a final pressure of 1200. torr. What metal was used?