Boyle’s Law Charles’s Law Gay-Lussac Combined Gas Law Gas Laws Boyle’s Law Charles’s Law Gay-Lussac Combined Gas Law

Properties of Gases Gas properties can be modeled using math. Model depends on: V = volume of the gas (liters, L) T = temperature (Kelvin, K) P = pressure (atmospheres, atm) n = amount (moles, mol)

Pressure - Temperature - Volume Relationship P T V P T V P T V Pressure versus volume – At constant temperature, the kinetic energy of the molecules of a gas and the root mean square speed remain unchanged. – If a given gas sample is allowed to occupy a larger volume, the speed of the molecules doesn’t change, but the density of the gas decreases and the average distance between the molecules increases: they collide with one another and with the walls of the container less often, leading to a decrease in pressure. – Increasing the pressure forces the molecules closer together and increases the density, until the collective impact of the collisions of the molecules with the walls of the container balances the applied pressure. Volume versus temperature – Raising the temperature of a gas increases the average kinetic energy and the root mean square speed (and the average speed) of the gas molecules. – As the temperature increases, the molecules collide with the walls of the container more frequently and with greater force, thereby increasing the pressure unless the volume increases to reduce the pressure – An increase in temperature must be offset by an increase in volume for the net impact (pressure) of the gas molecules on the container walls to remain unchanged. Pressure of gas mixtures – If gaseous molecules do not interact, then the presence of one gas in a gas mixture will have no effect on the pressure exerted by another, and Dalton’s law of partial pressures holds. Boyle’s P 1 V a Charles V T a Gay-Lussac’s P T a

Pressure - Temperature - Volume Relationship P T V P n V Boyle’s P 1 V a ___ Charles V T a Gay-Lussac’s P T a

Pressure and Balloons B When balloon is being filled: PA > PB A When balloon is filled and tied: PA = PB When balloon deflates: PA < PB A = pressure exerted BY balloon B = pressure exerted ON balloon

Balloon Riddle A B C When the balloons are untied, will the large balloon (A) inflate the small balloon (B); will they end up the same size or will the small balloon inflate the large balloon? Why? B C

Robert Boyle Robert Boyle, an Irish chemist (1627-1691), performed the first quantitative experiments on gases used a j-shaped tube to study the relationship between the pressure of the trapped gas and its volume.

Boyle’s Law Boyle’s Law states that at constant temperature (and constant number of gas molecules) the volume of a fixed amount of gas is inversely proportional to its pressure. Boyle’s Law: P1V1 = P2V2

Boyle Proves Changes in Pressure cause Changes in Volume As the pressure in a closed system (like a piston) decreases, the volume of the gas inside the system increases. The pressure in the system decreases exponentially. Proving an indirect relationship.

Example: Sulfur dioxide (SO2), a gas, that plays a central role in the formation of acid rain, is found in the exhaust of automobiles and power plants. Consider a 1.53 L sample of gaseous SO2 at a pressure of 5.6 kPa. If the pressure is changed to 15 kPa at a constant temperature, what will be the new volume of the gas?

Solution: P1V1= P2V2 P1= 5.6 kPa P2= 15 kPa V1= 1.53 L V2= ? Rearrange the formula to isolate V2. P1V1 = (5.6 kPa)(1.53 L) = O.571 L P2 (15 kPa)

Does Boyle’s law really work? Since Boyle’s experiments (only three centuries of technological advances!) we have found that his law only holds precisely at very low pressures. We describe a gas that strictly follows Boyle’s law an “ideal gas”.

Jacques Charles In the century following Boyle, a French physicist, Jacques Charles (1746-1823), was the first person to fill a balloon with hydrogen gas and who made the first solo balloon flight.

Charles’s Law Charles’s Law states that at constant pressure (and constant number of gas molecules) the volume of a fixed amount of gas is directly proportional to its absolute temperature. *All gas laws must be calculated with Kelvin temperature!

Volume vs. Temperature: Charles’ Law Notice the linear relationship. This relationship between temperature and volume describes a “direct relationship”. This means when temperature increases, so does the volume.

The importance of 0 Kelvin At temperatures below 0 K, the extrapolated volume of gases would be negative. The fact that a gas can’t have a negative volume tells us 0 K has a special significance. Absolute temperature is measured in Kelvins. At 0 K, all motion of any atom or bond ceases, therefore producing no energy. Temperatures of approximately 0.000001K have been produced in laboratories, but 0 K has never been reached.

Example: A sample of a gas at 15°C and 1 atm has a volume of 2.58 L. What volume will the gas occupy at 38°C and 1 atm? (NOTE: The pressure did not change. So you do not need to worry about it!)

Solution: V1 = V2 Don’t forget to convert °C to K T1 T2 V1= 2.58L V2=? T1 = 15°C=288K T2 = 38°C=311K Rearrange to solve for V2. V1T2 = (2.58L)(311K) = 2.79 L T1 (288K)

Gay-Lussac Joseph Louis Gay-Lussac was a French chemist and physicist. He is known mostly for two laws related to gases, and for his work on alcohol-water mixtures, which led to the degrees Gay-Lussac used to measure alcoholic beverages in many countries. 1778 – 1850 Charles's law, describing how gases tend to expand when heated, was formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to unpublished work by Jacques Charles.

Gay-Lussac’s Gas Law The pressure of a fixed mass and fixed volume of a gas is directly proportional to the gas's temperature. *All gas laws must be calculated with Kelvin temperature!

The Combined Gas Law The combined gas law was derived from Boyle’s and Charles’s work. A direct relationship was observed. As temperature increased, volume increased. As volume increased pressure increased. This resulted in a combined formula to calculate changes observed in a gas due to changes in either temperature, pressure or volume.

Combined Gas Law Equation By combining the equation for Boyle’s Law and Charles’s Law. We derive the Combined Gas Law Equation where:

Example: A sample of a gas at 15°C and 2.0 atm has a volume of 2 mL. What volume will the gas occupy at 38°C and 1 atm?

Solution Rearrange to solve for V2! P1V1 = P2 V2 Don’t forget to convert Temperatures! T1 T2 P1= 2 atm P2= 1 atm V1=2 mL V2=? T1=15°C=288K T2=38°C=311K Rearrange to solve for V2! V2= P1V1T2 = (2 atm)(2 mL)(311K) = 4.32 mL T1P2 (288K)(1 atm)

Summary: Boyle’s Law – Inverse relationship when PV and if PV Charles’s Law -- Direct relationship When VT and if VT Gay-Lussac Law -- Direct relationship When PT and if PT