Ideal Gas Law PV=nRT Remember… Boyle’s Law P1V1 P2V2 Charles’ Law: V V 1 2 T1 T2 Combined Gas Law: PV PV (Units MUST Match 1 1 2 2 Temp in Kelvin!!!) T1 T2 A gas with a volume of 350 ml is collected at 15o C and 120 kPa. If the temperature changes to 30o C, what pressure would be required to put this gas in a 300 ml container? 120kPa350ml P 300ml 2 288K 303K P2 147.3kPa A balloon has a volume of 500 ml at a temperature of 22oC and a pressure of 755 mmHg. If the balloon is cooled to 0o C and a pressure of 145 mmHg, what is its new volume? 755mmHg500ml 145mmHgV 2 295K 273K 2409.3ml V 2 Avogadro’s Principle Under similar conditions (same Temperature and Pressure) equal volumes of gases contain equal numbers of particles. 10 L of H2 (g) and 10 L of O2 (g) Both at Standard Temperature and Pressure (STP) contain… The same number of particles! Molar Volume The volume of 1 mole of gas particles at STP is 22.4 L Try this: 1 mole of gas occupies 22.4 L at STP = __________ ml (22400) = ___________ moles of gas (1 mole) = ___________ particles (6.02 x 1023) 44.8L L 22.4 mole How many particles in 11.2 dm3 of gas at STP? 0.5 moles = 3.01 x 1023 particles 3 22,400 cm of NH3 gas at STP weighs? = 22.4 L = 1 mole = 17 grams (add up MW) 44.8 L of NH3 at STP weighs? = 2 moles = 34 grams _____28.00 grams = 1 mole of nitrogen gas = _____22.4 L at STP? How many N2 molecules are in 22.4 dm3 at STP? = 1 mole = 6.02 x 1023 24 What volume will 1.2 x 10 H2 molecules occupy at STP? = 2 moles = 44.8 L at STP Ideal Gas Equation Use when NOT at STP!!! PV= nRT P = Pressure (in kPa) V = Volume (in Liters or dm3) n = number of moles T = Temperature (in Kelvin) R = 8.31 L• kPa mole • K Select the R value carefully R = 0.0821 L * atm/(K*mol) R = 8.3145 J/mol·K R = 8.31 L * kPa/(mol*K) Development of R in kPa L mole K PV 101.3kPa 22.4L kPa L R 8.31 nT 1mole 273K mole K 1. What volume will 2 moles of NO2 occupy at 300 Kelvin and 90 kPa? PV nRT 90kPaV 2moles 8.31300K 28.31300 V 55.4L 90 What will be the temp of 2 grams of 3 H2 if 5000 cm is at 5 atm? PV nRT 506.5kPa5L 1mole8.31T 506.55 T 304.8K 18.31 Finding Molecular Weight of a Gas Remember: MW = grams / moles Converting grams to moles – Divide grams by the molecular weight 1) 5.0 L of a gas weighs 30.00 g at 20o C & 92 kPa. What is the mole weight of the gas? grams 30.00 g MW moles ? mol PV=nRT 92kPa • 5.0 L= n • 8.31 • 293 K n = 0.19 mol 30.00 g MW 158 g/mol 0.19 mol 2)If the mole weight of a gas is 26 g/mol and 18.00 g of the gas is 30 L at 21o C, what is the pressure of the gas? PV= nRT g 18.00 g n 0.69 mol MW 26 g/mol P x 30 L=0.69 mol x 8.31 x 294 K P = 56.2kPa Molar Mass Using Ideal Gas Law Need: Molar mass = dRT/P Temperature D - density Pressure R - gas law constant Correct R value T - temperature (K) density P - pressure Practice Problem A chemist has synthesized a greenish-yellow gaseous compound of chlorine and oxygen and finds that its density is 7.71 g/L at 36°C and 2.88 atm. Calculate the molar mass of the compound. Molar mass = dRT/P (7.71g/L*0.0821 L*atm/(L*mol) * 309K)/ 2.88atm 69.7 g/mol Real Gas The ideal gas makes the assumption that all gas particles are completely independent of each other. The reality is there are some intermolecular forces that lead to the need to reduce of the volume and increase in the pressure. Correcting Pressure 2 2 P ideal = P real + an /V an2/V2 is known as the correction term A is a constant, n is the number of moles and V is the volume The real pressure is smaller then the ideal pressure and it is a function of the ratio between moles and volume. Correcting Volume V –nb b is the constant n is the number of moles As the number of moles increase, the expected real volume occupied by the atoms becomes a factor so the volume of the ideal is larger then the real volume. Corrected Ideal Gas Law (real) (P + an2/V2)(V-nb) = nRT No you do not need to memorize the formula. What you need to know is that gas molecules take up some of the space and intermolecular forces result in some atoms/molecules to stick together. Real Gases Vs Ideal Real Gas Ideal Gas The atoms/molecules The molecules/atoms take actually take up some of the up NO space. volume. The ideal gases have not The real atoms/molecules attraction to each other. have intermolecular forces that stick them together at times. .