Gas Laws - Chapter Kinetic-Molecular Theory of Matter Boyle’s Law Charles’s Law Gay-Lussack’s Law Avogadro’s Law Combined Gas Law Ideal Gas Law Dalton’s Law of Partial Pressures

The Kinetic Molecular Theory of Ideal Gases 1. All matter is composed of tiny, discrete particles (molecules or atoms). 2. The average kinetic energy of a gas particle depends on the temperature of the gas. 3. These particles are in rapid, random, constant straight line motion. They therefore possess kinetic energy. 4. There are no forces of attraction or repulsion between gas molecules or between molecules and the sides of the container with which they collide. 5. Energy is conserved in these collisions, they are perfectly elastic.

Ideal Gases vs. Real Gases Ideal gases are imaginary gases. Ideal gases follow the gas laws perfectly. Real gases actually do have attractive forces between them and therefore, deviate from ideal gas behavior. Real gases can only approach ideal gas conditions.

The Four Gas Law Variables: Temperature Pressure Volume Moles

Converting Temperature between Celsius and Kelvin (gas law problems must all be solved in Kelvin degrees, not celsius) Absolute Zero = C, the point at which all motion stops. Degrees Kelvin = Degrees Celsius ex. 20 O c = = K

Robert Boyle and His Data This 36K GIF is of Robert Boyle. Just to be safe, that's not his real hair. Wigs were the fashion in his day. The next table shows the values Boyle collected. The titles of each column are rather wordy and so are given below the table. All measurements are in inches. It was published in "A Defence of the Doctrine Touching the Spring And Weight of the Air....," published in 1662.

The 28K GIF just below is a photo of the page typeset in 1662 in which Boyle announced his discovery. His notes below the table are reproduced below the image.

The graph just below is of Robert Boyle's data.

Boyle’s Law (Constant Temperture) His law gives the relationship between pressure and volume if temperature and amount are held constant. If the volume of a container is increased, the pressure decreases. If the volume of a container is decreased, the pressure increases. Pressure x Volume = Constant P 1 x V 1 = K P 1 x V 1 = P 2 x V 2 P 2 x V 2 = K

Charles’s Law (Constant Pressure) V 1 V 2 T 1 = T 2 (Volume) V 1 (Temp.) T 1 = K (Constant) V 2 T 2 = K This law gives the relationship between volume and temperature if pressure and amount are held constant. If the volume of a container is increased, the temperature increases. If the volume of a container is decreased, the temperature decreases.

Gay-Lussac’s Law (Constant Volume) Gives the relationship between pressure and temperature when volume and amount are held constant. If the temperature of a container is increased, the pressure increases. If the temperature of a container is decreased, the pressure decreases. (Pressure) P 1 (Temp.) T 1 = K (Constant) P 2 T 2 = K P 1 P 2 T 1 = T 2

Avogadro’s Law (Constant Volume) Gives the relationship between volume and amount when pressure and temperature are held constant. If the amount of gas in a container is increased, the volume increases. If the amount of gas in a container is decreased, the volume decreases. (Volume) V 1 (moles) n 1 = K (Constant) V 2 n 2 = K V 1 V 2 n 1 = n 2

The Combined Gas Law “putting it all together” To derive the Combined Gas Law, do the following: Step 1: Write Boyle's Law: P 1 V 1 = P 2 V 2 Step 2: Multiply by Charles Law: P 1 V 1 2 / T 1 = P 2 V 2 2 / T 2 Step 3: Multiply by Gay-Lussac's Law: P 1 2 V 1 2 / T 1 2 = P 2 2 V 2 2 / T 2 2 Step 4: Take the square root to get the combined gas law: P 1 V 1 P 2 V 2 T 1 = T 2

PV = nRT: The Ideal Gas Law This is just one way to derive the Ideal Gas Law: For a static sample of gas, we can write each of the six gas laws as follows: –PV = k 1 –V / T = k 2 –P / T = k 3 –V / n = k 4 –P / n = k 5 –1 / nT = 1 / k 6 PV = nRT When you multiply them all together, you get: P 3 V 3 / n 3 T 3 = k 1 k 2 k 3 k 4 k 5 / k 6 Let the cube root of k 1 k 2 k 3 k 4 k 5 / k 6 be called R. Resuming, we have: PV / nT = R or, more commonly:

Dalton's Law of Partial Pressures This law was discovered by John Dalton in Dalton's Law of Partial Pressures: each gas in a mixture creates pressure as if the other gases were not present. The total pressure is the sum of the pressures created by the gases in the mixture. P total = P 1 + P 2 + P P n

Graham's Law Consider samples of two different gases at the same Kelvin temperature. Since temperature is proportional to the kinetic energy of the gas molecules, the kinetic energy (KE) of the two gas samples is also the same. In equation form, we can write: KE 1 = KE 2 Since KE = (1/2) mv 2, (m = mass and v = velocity) we can write the following equation: m 1 v 1 2 = m 2 v 2 2 Note that the value of one-half cancels. The equation above can be rearranged algebraically into the following: the square root of (m 1 / m 2 ) = v 2 / v 1