Modern vacuum pumps make it easy to attain pressures of the order of 10-13 atm in the laboratory. Consider a volume of air and treat the air as an ideal gas. (a) At a pressure of 9.00 X 10-14 atm and an ordinary temperature of 300.0 K, how many molecules are present in a volume of 1.00 cm3? (b) How many molecules would be present at the same temperature but at 1.00 atm instead?
Solution 24E Introduction We will use the ideal gas equation to calculate the number of atoms. Step 1 The ideal gas equation is PV = NkT Here k is the boltzmann constant and N is the number of atoms. Using, so we have PV N = kT In the first problem we have 14 9 P = 9.00 × 10 atm = 9.12 × 10 Pa V = 1.00 cm = 1.00 × 10 6 m3 T = 300 K 23 We also know that k = 1.38 × 10 J/K So, from the above equation we have (9.12×10Pa)(1.00×10m ) N = 23 = 2.20 × 106 (1.38×10 J/K)(300 K) 6 Hence there will be 2.20 × 10 number molecules.