Gases and gas laws 45 Complete these tables in your notebook. Assume that it is an ideal gas: a) At a constant temperature. b) At a constant pressure. c) At a constant volume. In each case, state the law you use for the calculations: a) p (atm) 6 24 3 V (L) 4 2 b) V (mL) 1800 1200 900 T (°C) 27 127 c) p (hPa) 1400 1610 T (K) 350 300 230 46 A cylinder with a movable piston contains 5 L of carbon dioxide gas at 1500 hPa when the temperature is 80 °C. a) What volume will the gas occupy in the cylinder if the manometer reads 2 atm and the thermometer reads 0 °C? b) What pressure will it exert if it occupies 7 L at -10 °C? 47 The siphon is an essential piece of equipment in molecular cooking. It is used to make foams. Siphons use 20 cm3 cartridges of dinitrogen monoxide (laughing gas) at 200 atm. The gas is released inside the siphon containing the mixture that will form the foam, and shaken. There is a valve to release the foam and use it in a recipe. a) Assume that the cartridge of N2O is at the same temperature as the kitchen (27 °C) and the siphon (with a capacity of 750 mL) was in the fridge (at 3 °C). What pressure will the gas in the cartridge reach in an empty siphon? b) What volume would the siphon need to have for the N2O to be at a pressure of 1 atm? c h e c k yo u r p r o g r e s s S O LV E D P R O B L E M 1 2 Using a simulator, we obtained these results when the gas was heated at a constant volume: P (atm) T (K) 5.8 300 7.0 358 7.8 399 9.1 469 12.1 621 a) Draw the p-T graph. What shape does it have? Which is the independent variable? b) W rite the relationship between both quantities and the equation that represents it. Calculate p × T. c) D etermine what the temperature will be when the pressure is 4 atm. a) D raw the graph. Use the data from the table shown in the problem. T is the independent variable because we modify its value as we wish, heating or cooling the gas. b) T he graph is a straight line. p and T are directly proportional. When one increases, the other one also increases, and vice versa. The differences in the values are within experimental error. Take the average as the correct value: T p = + + + + = 51 7 51 1 51 2 51 5 51 3 5 51 4 . . . . . . K atm c) Interpolating from the graph, or by calculation: T p T = → = = ⋅ ⋅ 51 4 4 51 4 . . K atm K atm atm 205 K 300 0 T (K) 600 p (atm) 0 4 8 12 p (atm) 5.8 7.0 7.8 9.1 12.1 T (K) 300 358 399 469 621 T/p (K/atm) 51.7 51.1 51.2 51.5 51.3 30
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