The pressure a gas exerts on a container depends on the number of particles in the container. This is related with the mass of a gas. General ideal gas equation : p V T ⋅ =constant. For 1 mol of any gas at 105 Pa and 0 °C: p V T R ⋅ ⋅ ⋅ = → 0.082 atm L mol K . In general , for n moles: p V T n R ⋅ = ⋅ . Ideal gas equation of state It relates the p, V and T of a gas and the amount of substance, n. p × V = n × R × T 6. The ideal gas equation of state 18 Two equal gas cylinders are at the same temperature and hold the same mass of gas. One contains helium and the other carbon dioxide. Will they be at the same pressure? Why? At 105 Pa and 0 °C a mole of a gas occupies a volume of 22.7 L. The units of R determine that p is measured in atm, V in L and T in K. SOLVED PROBLEM 6 A 2 L bottle contains 11 g of carbon dioxide gas. What pressure will it exert if the temperature is -10 °C? 1. Relate the p, V and T of a gas to its mass. We must use the ideal gas equation of state. p × V = n × R × T • Calculate the amount of substance for the gas. (Look for the atomic mass of the elements in the periodic table in the annex.) M(CO2) = 12 + 16 × 2 = 44 g/mol n= ⋅ = 11 g CO 1 mol CO 44 g CO mol CO of of of of 2 2 2 2 0.25 • Express the temperature in kelvin: T (K) = T (°C) + 273 = -10 °C + 273 = 263 K 2. Make p the subject and substitute the data: p n R T V = ⋅ ⋅ ® p = ⋅ ⋅ ⋅ ⋅ = 0.25 mol 0.082 atm L mol K 263 K 2 L 2.7 atm 19 A 2 L bottle contains 11 g of helium gas. What pressure will it exert if T = -10 °C? Compare the result with the one in the solved problem. 20 What mass of helium gas must be put into a 2 L bottle, at a temperature of -10 °C, for it to exert a pressure of 2.7 atm? A C T I V I T I E S The mole The mass of one mole of a substance is the molar mass, M. It is equal to the sum of the mass of all the atoms in its formula , expressed in grams. Mass of a substance (m) = Amount of substance (n) × Molar mass (M) m = n × M Chemistry often measures the amount of substance (n) in mol in the SI. One mole is equal to 6.022 × 1023 particles (atoms, molecules or ions). Avogadro's number, NA CHALLENGE 20
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