Some gas basics…. Describe the properties of gases? Describe the arrangement of particles in a gas? Describe the movement of particles in a gas? How does a gas exert a pressure? Can you compress gases? Why? What is diffusion? What is kinetic theory as applied to ideal gases?

kPa → Pa multiply by 1000 dm3 → m3 divide by 1000 cm3 → m3 divide by 1000,000 and °C → K add 273 Volume of gases- SI Unit is m 3 1 mole occupies 22.4 dm 3 at STP and 24dm 3 in room conditions Temperature- SI unit is K Kelvin scale 0 o c is 273k. So to convert from o c to Kelvin, add 273 (and vice versa). Pressure- SI unit is Pa 1 atmosphere = 101kPa= Pa= 760mm Hg A Pascal is 1 Nm -2 Standard temperature and pressure (STP) is 273K and 101kPa. Room conditions are 298K and 101kPa.

Avogadro’s Law- molar gas volumes Avogadro's Law states that equal volumes of gases under the same conditions of temperature and pressure contain the same number of particles. One mole of any gas (or the formula mass in g), at the same temperature and pressure occupies the same volume. This is 24dm 3 (24 litres) or cm 3, at room temperature and pressure or 22.4 dm 3 at standard temperature and pressure Avogadro’s law can be restated: the volume of a gas is directly proportional to its amount at constant temperature and pressure- see later

moles= volume/ molar volume 1.How many moles of carbon dioxide in 48dm 3 ? 2.What is the volume of 3.5g hydrogen? 3.Given the equation MgCO 3 (s) + H 2 SO 4 (aq) => MgSO 4 (aq) + H 2 O(l) +CO 2 (g) What mass of magnesium carbonate is needed to make 6 dm 3 of carbon dioxide? (assume room conditions) Why does the volume vary according to the conditions?

Boyle’s Law p x V = constant For a fixed mass of gas, the pressure is inversely proportional to the volume if the temperature remains constant.

(for fixed amount of gas at constant temperature) p1 x V1 = p2 x V2 p2 = p1 x V1/V2 or V2 = p1 x V1/p2 Ensure the units are the same! If a gas is compressed to half its original volume the concentration or density of the gas is doubled. There will be twice as many collisions with the surface causing twice the impact effect i.e. double the pressure. If the volume of a gas is increased by a factor of three, the concentration is reduced by the same factor, so the chance of particle collision with the container walls is similarly reduced, so the pressure decreases by a factor of three.

Boyle's Law calculations ( at constant temp) 240cm3 of air at a pressure of 100kPa in a bicycle pump is compressed to a volume of 150cm3. What is the pressure of the compressed air in the pump? p1 x V1 = p2 x V2, rearranging to scale up for the new higher pressure p2 = p1 x V1/V2 = 100 x 240/150 = 160 kPa 10 m3 of butane gas at 1.2 atm was required to be stored at 6 atm pressure. To what volume must the gas be compressed to give the required storage pressure? p1 x V1 = p2 x V2, rearranging to scale down for the new lower volume V2 = p1 x V1/p2 = 1.2 x 10/6 = 2.0 m3

Charles’ Law V/T= constant For a fixed mass of gas, the volume is proportional to the absolute temperature if the pressure remains constant.

Pressure Law p/T= constant The pressure of a gas is directly proportional to the absolute temperature (K) at constant volume p1/T1 = p2/T2 for constant volume

These three laws can be summarised: pV= constant V/T = constant p/T = constant. And they can be combined: pV/T = constant So….. p1V1/T1 = p2V2/T2 therefore the three permutations for problem solving are... p2 = (p1 x V1 x T2)/(V2 x T1) or V2 = (p1 x V1 x T2)/(p2 x T1) or T2 = (p2 x V2 x T1)/(V1 x p1)

Because pressure, volume, temperature, and moles are the only variables, if three of the variables are known, the other can be determined. The relationship between these variables is called the ideal gas law. Remember pV/T = constant The constant depends on the amount of gas, measured in moles (n). Therefore the constant may be written as nR, where R is the molar gas constant, which has the approximate value of 8.314JK -1 mol -1

pV = nRT The units must be SI. P = Pa or Nm -2 V = m 3 n = moles R = JK -1 mol -1 T = K Practice moving between units Practice identifying which variables are changing and which are constant. p?chapter=chapter_08&folder=ideal_gas_law

Finding the Relative Molecular Mass (Mr) of a gas: n= mass (g)/ Mr or n= mass (g)/ molar mass (gmol -1 ) R eplace n in the equation with mass/ Mr : Mr = m RT/PV

Questions and answers. The pressure exerted by a gas in sealed container is 100kPa at 17 o C. It was found that the container might leak if the internal pressure exceeds 120kPa. Assuming constant volume, at what temperature in o C will the container start to leak? 17 o C = 290K (convert to correct unit) p1/T1 = p2/T2 (apply) rearranging to scale up to the higher temperature T2 = T1 x p2/p1 T2 = 290 x 120/100 = 348 K or = 75 o C when the container might leak

Practice questions 25 cm3 of a gas at 1.01 atm. at 25 o C was compressed to 15 cm3 at 35 o C. Calculate the final pressure of the gas. p1 = 1.01 atm, p2 = ?, V1 = 25 cm3, V2 = 15 cm3, T1 = = 298 K, T2 = = 308 K (p1 x V1)/T1 = (p2 x V2)/T2 p2 = (p1 x V1 x T2)/(V2 x T1) p2 = (1.01 x 25 x 308)/(15 x 298) = 1.74 atm

What is the volume of 6g of chlorine at 27 o C and 101kPa (approx. 1 atm)? pV = nRT, V = nRT/p T = = 300K, n = 6/71 = mol chlorine, Mr(Cl2) = 2 x 35.5 = 71 and p = 101 x 1000 = Pa. V = x x 300/ = m 3 What is the volume of the chlorine in dm 3 and cm 3 ? Practice moving between units! 1 m 3 = 1000 dm 3 = 10 6 cm 3 V = x 1000 = dm 3 V = x 106 = 2087 cm 3