Chapter 13 The Gas Laws

Robert Boyle studied how gas volume varied with changes in pressure.

 Boyles Law - The volume of a fixed mass of gas varies inversely with the pressure at constant temperature. P 1 V 1 = P 2 V 2 Demo soda can, vacuum jar, marsh-mellow man, spud gun, ete

How is this related to Boyles’ Law ?

Jacques Charles studied the variation of gas volume with changes in temperature.  Charles found that the volume of a gas changes by 1/ 273 of the original volume for each Celsius degree, at constant pressure.

 Using this information he was able to predict the value of absolute zero, the point where all motion stops C

 Charles’s Law- The volume of a fixed mass of gas at constant pressure varies directly with the Kelvin temperature.

Charles Law Math V 1 = V 2 or V 1 T 2 = V 2 T 1 V 1 = V 2 or V 1 T 2 = V 2 T 1 T 1 T 2 T 1 T 2

Lord Kelvin ak Sir William Thompson  Kelvin didn’t like negative numbers, so he created a system that started at the coldest possible temperature.  - 273°C became 0° K

 To convert celsius to kelvin,  Add 273  To covert kelvin to celsius  Subtract 273 All temperatures in all gas law problems must be in degrees Kelvin

Joseph Gay-Lussac studied the variation of gas pressure with changes in temperature.

Gay-Lussac Law – The pressure of a fixed mass of gas at constant volume varies directly with the Kelvin temperature. P 1 = P 2 or P 1 T 2 = P 2 T 1 T 1 T 2

Unknown math guy Combined the above three equations in to the Combined Gas Law  P 1 V 1 = P 2 V 2 or P 1 V 1 T 2 = P 2 V 2 T 1  T 1 T 2

Daltons law of Partial pressure – The total pressure of a mixture of gases is equal to the sum of the partial pressures of the component gases.

 Math P T = P 1 + P 2 + P 3 + ……..

Avogadro’s Law - Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.  Thus Molar Volume - The volume occupied by one mole of a gas at STP is known as the standard molar volume of a gas, it is 22.4 liters. 1 Mole of a gas = 22.4 STP.

Ideal Gas law - The ideal gas law is the mathematical relationship of pressure, volume, temperature and the number of moles of a gas. ( Combined gas law and Avogadro’s law, combined )

 Math PV = nRT  P is pressure in ATM, V is volume in Liters, T is temperature in degrees K  And r is a gas constant, which varies according to the units of pressure used.  When P is ATM r =.0821  mmHg r = 62.4  Kpa r = 8.31  For any other pressure convert the pressure to one of the three above.

Molar mass and density with the Ideal gas law PV = nRT substitute n = m PV = mRT M M mass / molar mass = moles To find molar mass rearrange to M = mRT PV

Density substitute m = D V M = mRT PV M = DRT P

Rearrange this to solve for density D = MP RT

Grams X 1 mole X moles looking for (from equation) X FW of looking for Given FW of given moles given (from equation) 1 mole of looking for Grams X 1 mole X moles looking for (from equation) X FW of looking for Given FW of given moles given (from equation) 1 mole of looking for  Remember –mass/mass problems Now we can use 1 mole = 22.4 to find moles given, or convert moles to volume at STP. If the given information about the gas is not at STP, we can use PV = nRT to do the same thing. Instead of calling them just mass / mass problems we can call them Gas / mass and mass / gas problems

Also have to divide the water level difference by 13.6 to convert it to mm Hg