Gas laws Relationships between variables in the behaviour of gases
Learning objectives Describe physical basis for pressure in a gas Describe the basic features of the kinetic theory Distinguish among and convert common units of pressure Apply gas laws to simple problems in predicting conditions of a gas Apply ideal gas law to simple stoichiometry problems in gases
Gas: no interactions Not rigid Completely fills container Compressible Low density Fast moving molecules
Kinetic theory and car tires a case Molecules have motion Pressure is caused by energetic molecules striking tire wall Pumping up tire increases number of molecules More molecules higher pressure Energy increases with T Higher temperature higher pressure for atoms
Kinetic theory of gases Gases consist of small atoms or molecules in constant random motion Volume occupied by molecules is negligible Molecules are independent of each other no interactions Collisions are perfectly elastic (no energy loss) Average energy is proportional to the temperature
The atmosphere: weight on our shoulders Gases exert pressure on container because of molecular motion Atmosphere exerts pressure because of gravity acting on air molecules mass Air density higher near earth s surface Pressure decreases with elevation The pressure at the top of Everest is much lower than at sea level, adding additional challenges to its would-be conquerors
Atmospheric pressure Pressure is force per unit area The weight of the air supports the same weight of mercury Column is 760 mm high Barometer is used for measuring atmospheric pressure
Units of pressure Atmosphere Atmospheric pressure = 1 atm mm (or cm, or in) of mercury Atmospheric pressure = 760 mm (76 cm/29.9 in) Hg Pascal is SI unit for pressure Atmospheric pressure = 101 000 Pa (N/m 2 ) Pounds/square inch Atmospheric pressure = 14.7 lb/in 2 Torr Atmospheric pressure = 760 torr Bar Atmospheric pressure = 1.01 bar (1 bar = 100,000 Pa)
Standard temperature and pressure (STP) Standard conditions allow direct comparison of properties of different substances Standard temperature is 273 K (0ºC) Standard pressure is 760 mm Hg or 1 atmosphere At STP, 1 mole of any ideal gas occupies 22.414 L
Pressure changes (units) Convert 0.50 atm into a) mm Hg b) Pa
Gas laws: experience in math form The properties of gases can be described by a number of simple laws The laws establish quantitative relationships between different variables They are largely intuitively obvious and familiar
The four variables Pressure (P) Volume (V) Temperature (T in Kelvin) Number of molecules (n in moles)
Variables and constants In the elementary gas laws two of the four variables are kept constant Each law describes how one variable reacts to changes in another variable All the simple laws can be integrated into one combined gas law
Boyle s law The first experimental gas law Pressure increases, volume decreases (T, n constant) 1 P V
Boyle s law problems Initial conditions: P 1 and V 1 Final conditions: P 2 and V 2 PV 1 1 P2 V2 Four variables: three given, one unknown Rearrange equation: P PV ; V PV 1 1 1 1 2 2 V2 P2 Units are not important provided same on both sides
Tank contains 12 L of gas at 4,500 mm Hg. What is volume when pressure = 750 mm Hg?
Charles Law As temperature increases, volume increases (P, n constant) Temperature must be measured in Kelvin V T
Absolute zero Gay-Lussac observed V changed by 1/273 of value at 0ºC Plotted as V = kt (T = ºC + 273): V = 0 at T = 0 Does the gas actually occupy zero volume? No, at lower T the law is not followed
V T V 1 2 T 1 2 Do s and don ts with Charles law
Combined gas law Fold together Boyle and Charles: PV 1 1 2 2 T P V 1 2 Given five of the variables, find the sixth Units must be consistent Temperature in Kelvin T
Example of combined gas law Gas at 27ºC and 2 atm pressure occupies 2 L. What is new volume if pressure becomes 4 atm and temperature is raised to 127ºC?
Gay-Lussac and law of combining volumes When gases react at constant temperature and pressure, they combine in volumes that are related to each other as ratios of small whole numbers His experiments with hydrogen and oxygen had implications for the understanding of the atom and the structures of simple molecules
Avogadro s Law As the number of moles of gas increases, so does the volume (P, T constant) V n V n V 1 2 n 1 2
Dalton s law of partial pressures A mixture of gases exerts a pressure as if all the gases were independent of one another Total pressure is the sum of the pressures exerted by each one P = p 1 + p 2 + p 3 +
Calculations with partial pressures
Molar gas volume The molar volume of a gas is the volume occupied by 1 mole. At STP (standard temperature 273 K, and pressure 1 atm) one mole of gas occupies 22.4 L Gas density is easily obtained from the molar mass and molar volume d = m/v
Ideal Gas Law The particles of an ideal gas have mass but no volume - a fair approximation at low pressures Collisions between the gas molecules are perfectly elastic like superhard billiard balls. Reasonable for smaller molecules or noble gases PV nrt R is the ideal gas constant = 0.0821 L-atmK -1 mol -1 Gases deviate from ideal behaviour as pressure increases closer proximity of molecules molecules are more polar stronger interactions
Calculations with the ideal gas law
Chemical equations with gases Reactions with solids involve masses Reactions with gases involve volumes Volume A n = PV/RT Moles A Mole:mole ratio Moles B V = nrt/p Volume B
Stoichiometry with the ideal gas law
Gas laws and crash safety The airbag represents a fascinating study of chemistry applied in a very practical area Airbags have reduced serious injuries and fatalities by a significant margin compared with seat belts only Chemistry plays a crucial role in the performance of the airbag
Timing is everything The airbag must deploy within about 40 ms of the impact The airbag must not deploy unless there is an impact Inflation depends upon a rapid chemical reaction generating a quantity of gas The bag, once inflated, must then deflate at the point of impact with the driver to prevent injury
Chemistry is involved at many points Chemical reaction to produce gas (nitrogen) Strong N N bond provides driving force Reaction kinetics determine rate must be fast Gas laws provide inflation P proportional to T