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## The Gas Laws

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**The Gas Laws**• Describe HOW gases behave. • Can be predicted by the theory. • The Kinetic Theory • Amount of change can be calculated with mathematical equations.**The effect of adding gas.**• When we blow up a balloon we are adding gas molecules. • Doubling the number of gas particles doubles the pressure (of the same volume at the same temperature).**4 things**• In order to completely describe a gas you need to measure 4 things • Pressure • Temperature • Volume • Number of particles**Pressure and the number of molecules are directly related**• More molecules means more collisions • Fewer molecules means fewer collisions.**If you double the number of molecules**• You double the pressure. 2 atm**4 atm**• As you remove molecules from a container**2 atm**• As you remove molecules from a container the pressure decreases**1 atm**• As you remove molecules from a container the pressure decreases • Until the pressure inside equals the pressure outside • Molecules naturally move from high to low pressure**Changing the size of the container**• In a smaller container molecules have less room to move • Hit the sides of the container more often • As volume decreases pressure increases.**1 atm**• As the pressure on a gas increases 4 Liters**As the pressure on a gas increases the volumedecreases**• Pressure and volume are inversely related 2 atm 2 Liters**Temperature**• Raising the temperature of a gas increases the pressure if the volume is held constant. • The molecules hit the walls harder. • The only way to increase the temperature at constant pressure is to increase the volume.**300 K**• If you start with 1 liter of gas at 1 atm pressure and 300 K • and heat it to 600 K one of 2 things happens**600 K**300 K • Either the volume will increase to 2 liters at 1 atm**600 K**300 K • Or the pressure will increase to 2 atm. • Or someplace in between**Ideal Gases**• In this chapter we are going to assume the gases behave ideally • Does not really exist • makes the math easier • close approximation. • Assume particles have no volume • Assume no attractive forces between molecules**Ideal Gases**• There are no gases for which this is true. • Real gases behave this way at high temperature and low pressure.**Graph**Boyle’s Law • At a constant temperature pressure and volume are inversely related • As one goes up the other goes down • P x V = K (K is some constant) • Easier to use P1 x V1= P2 x V2**P**V**Example**• A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm what is the new volume?**Example**• A balloon is filled with 73 L of air at 1.3 atm pressure. What pressure is needed to change to volume to 43 L?**Graph**Charles’ Law • The volume of a gas is directly proportional to the Kelvin temperature if the pressure is held constant. • V = K xT(K is some constant) • V =KT • V1 = V2T1 T2**V**T**Example**• What is the temperature of a gas that is expanded from 2.5 L at 25ºC to 4.1L at constant pressure.**Example**• What is the final volume of a gas that starts at 8.3 L and 17ºC and is heated to 96ºC?**Gay Lussac’s Law**• The temperature and the pressure of a gas are directly related at constant volume. • P = K xT(K is some constant) • P =KT • P1= P2T1 T2**P**T**Examples**• What is the pressure inside a 0.250 L can of deodorant that starts at 25ºC and 1.2 atm if the temperature is raised to 100ºC? • At what temperature will the can above have a pressure of 2.2 atm? Animation**Putting the pieces together**• The Combined Gas Law Deals with the situation where only the number of molecules stays constant. • P1 x V1 = P2 x V2T1 T2 • Lets us figure out one thing when two of the others change.**The combined gas law contains all the other gas laws!**• If the temperature remains constant. P1 V1 P2 x V2 x = T1 T2 Boyle’s Law**The combined gas law contains all the other gas laws!**• If the pressure remains constant. P1 V1 P2 x V2 x = T1 T2 Charles’ Law**The combined gas law contains all the other gas laws!**• If the volume remains constant. P1 V1 P2 x V2 x = T1 T2 Gay-Lussac’s Law**Examples**• A 15 L cylinder of gas at 4.8 atm pressure at 25ºC is heated to 75ºC and compressed to 17 atm. What is the new volume?**Examples**• If 6.2 L of gas at 723 mm Hg at 21ºC is compressed to 2.2 L at 4117 mm Hg, what is the temperature of the gas?**The Fourth Part**• Avagadro’s Hypothesis • V is proportional to number of molecules at constant T and P. • V is proportional to moles. • V = K n ( n is the number of moles. • Gets put into the combined gas law • P1 x V1 = P2 x V2n1 x T1 n1 x T2 = K = R**The Ideal Gas Law**• P x V = n x R x T • Pressure times Volume equals the number of moles times the Ideal Gas Constant (R) times the temperature in Kelvin. • This time R does not depend on anything, it is really constant**The Ideal Gas Constant**• R = 0.0821 (L atm) (mol K) • R = 62.4 (L mm Hg) (K mol) • R = 8.31 (L kPa) (K mol)**The Ideal Gas Law**• PV = nRT • We now have a new way to count moles of a gas. By measuring T, P, and V. • We aren’t restricted to STP. • n = PV/RT • Nothing is required to change, • No 1’s and 2’s**Example**• How many moles of air are there in a 2.0 L bottle at 19ºC and 747 mm Hg?**Example**• What is the pressure exerted by 1.8 g of H2 gas exert in a 4.3 L balloon at 27ºC?**Density**• The Molar mass of a gas can be determined by the density of the gas. • D= mass = m Volume V • Molar mass = mass = m Moles n • n = PV RT**Molar Mass = m (PV/RT)**• Molar mass = m RT V P • Molar mass = DRT P**At STP**• At STP determining the amount of gas required or produced is easy. • 22.4 L = 1 mole**Not At STP**• Chemical reactions happen in MOLES. • If you know how much gas - change it to moles • Use the Ideal Gas Law n = PV/RT • If you want to find how much gas - use moles to figure out volume V = nRT/P • Use the equation in place of 22.4 L**Example**• HCl(g) can be formed by the following reaction • 2NaCl(aq) + H2SO4 (aq) → 2HCl(g) + Na2SO4(aq) • What mass of NaCl is needed to produce 340 mL of HCl at 1.51 atm at 20ºC?**Example**• 2NaCl(aq) + H2SO4 (aq) → 2HCl(g) + Na2SO4 (aq) • What volume of HCl gas at 25ºC and 715 mm Hg will be generated if 10.2 g of NaCl react?