3.8.12 A 2.07 L cylinder contains 2.88 mol of Helium gas at 22 C. What the pressure in atmospheres of the gas in the cylinder? How could we find the density of this gas? HW solve the density of the above question TYGAGT Experimentally determine the volume of a gas at room temp (not STP) produced from a reaction of Magnesium and HCl
Look ahead first Tomorrow probably a green book day Monday probably a wrap up and last little topic (Graham s law and diffusion/ effusion which we will not be going into extensively) Tuesday quiz/test on Gas laws
density For gases, it s simply formula/molecular weight divided by 22.4 L (for solids, d is usually reported as g/ml, for gases we use g/l why should this make sense?) Can we substitute the density formula into the ideal gas expression?
substitution Ideal gas law already includes the basic information Volume is explicitly part of it From n, number of moles, we can determine mass Rearranging will give us density OR, the molar mass of an unknown gas! Rearrangement solving for n/v Convert n to MASS (m) by multiplying BOTH sides by molar mass (M) d = m/v If d is known we can determine molar mass M
today More fun with Magnesium and Hydrochloric acid We ve done this a few times already we know it produces gas (hydrogen), but we want to measure the VOLUME of the gas, not just simply know that gas is produced
Lab notes This is essentially a Dalton s Law and Avogadro s Law lab We will be determining pressure of the gas by subtracting the vapor pressure, then Determining number of moles of gas from the volume of the gas We are skipping part i and will just wing that step Goggles are mandatory!
Turn in to me Brief summary sheet showing me: Your calculations and all relevant work A neat presentation of your data in a table Clearly indicate BOTH the volume of your gas produced AND the number of moles of gas produced
3.9.12 What is the density of HBr(g) at 3.10 atm and -5 C? HW finish WS from green book Today review density of gases Also, finish analysis/journals, etc. from labs
Density problems What is the density of silicon tetrafluoride gas at 72 C and a pressure of 144.5 kpa? At what temperature will nitrogen gas have a density of 1.13 g/l at a pressure of 1.09 atm?
solutions 5.24 g/l 329 K (56 C)
3.12.12 Say you have two containers of different gases: one contains Helium and the other contains Xenon. You open equal size holes in each container: which gas escapes the container the fastest? HW p 388 1-5 TYGAGT use Graham s law to explain rates of effusion of gases
Effusion and diffusion Diffusion the gradual mixing of gases due to spontaneous, random motion Effusion the process whereby the molecules of a gas confined in a container pass through a tiny opening in the container Can be used to estimate the molar masses of gases
Kinetic energy The kinetic energy of gases is a function of their mass since molecules in gas do not attract each other when we say mass we mean molar mass Kinetic energy depends only on temperature, expressed as ½ mv2 For two different gases A and B at the same temperature, the following is true: ½ M A v A 2 = ½ M B v B 2
Recall: KE A = ½ m A v A 2 KE B = ½ m B v B 2 Gases at the the same temperature have same kinetic energy, so KE A = KE B Therefore ½ M A v A 2 = ½ M B v B 2
Kinetic energy Just because KE is same for gases A and B, it doesn t mean their velocity s are the same What if you hit a bowling ball and a golf ball with the same force: which travels farther/ faster? Which has more kinetic energy? Because the only difference is their mass, if we know the energy is the same then we can work out mass from the proportionality of their velocities
The ratio of effusion rates of two gases at equal temperature and pressures will be inversely proportional to the square roots of the molar masses rearrangement
summary Gases diffuse become more spread out due to their constant and random motion Different gases will have different rates of effusion Under equal conditions of temperature and pressure, the effusion rates of different gases will be a function of the molar mass
practice Compare the rates of effusion of hydrogen and oxygen at the same temperature and pressure. Molar mass ratio = ratio of rates of effusion (Square root molar mass of O)/(square root molar mass of H) Square root molar mass of O/molar mass of H) = square root ~15.99 = 3.98 Explanation H 2 will effuse about four times as fast O 2
More practice Compare the rate of effusion for Carbon dioxide with that of hydrogen chloride at the same temperature and pressure Nitrogen gas effuses through a pinhole 1.7 times as fast as another gaseous element at the same temperature and pressure. Estimate the other gas s molar mass and determine its probable identity.