Gas Variable Relationships

Gas Variables Pressure Volume Temperature Number of moles

Pressure & Volume As P (h) increases V decreases

Boyle’s Law P a 1/V Constant temperature P x V = constant Constant amount of gas P x V = constant

Pressure & Volume As T increases V increases

Charles’s Law 𝑉 𝑇 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 **Temperature must be in Kelvin 𝑉∝𝑇 Constant pressure Constant amount of gas

Pressure & Temperature Constant volume Constant amount of gas 𝑃∝𝑇 𝑃 𝑇 =𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 **Temperature must be in Kelvin As T increases P increases

Gay-Lussac’s Law

Avogadro’s Law

*video: gas laws

Combined Gas Law P1V1 T1 P2V2 T2 = P1V1 n1T1 P2V2 n2T2 = n1=n2 Boyle’s law: PV = c (at constant n and T) Charles’s law: V = c (at constant n and P) T Gay-Lussac’s law: P = c (at constant n and P) T Avogadro’s law: V = c (at constant P and T) n c = PV nT P1V1 T1 P2V2 T2 = P1V1 n1T1 P2V2 n2T2 = n1=n2

Example 1 A gas at 110 kPa and 30.0˚C fills a flexible container with an initial volume of 2.00L. If the temperature is raised to 80.0˚C and the pressure increased to 440 kPa, what is the new volume?

Example 2 An unopened bottle of soda contains 46.0 mL of gas confined at a pressure of 1.30 atm and temperature of 5.00˚C. If the bottle is dropped into a lake and sinks to a depth at which the pressure and temperature changes to 1.52 atm and 2.90˚C, what will be the volume of gas in the bottle?

Ideal Gas Law PV constant = nT PV (1 atm)(22.414L) = nT (1 mol)(273.15 K) R = 0.082057 L • atm / (mol • K) PV = nRT The conditions 0 0C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.