14.1 Answers How many molecules are there in 1 L of air at T1 = 0 ºC and at T2 = 25 ºC? 1. Write out what you have and see if you need to convert anything to SI units V= 1 L (not SI) = 0.001 m3 T1 = 0 ºC (not SI) = 0 ºC + 273 = 273 K T2 = 25 ºC (not SI) = 25 ºC + 273 = 298 K NA = 6.022 x 1023 mol (we need this because we are looking for the number of molecules!) kB = 1.38 x 10-­‐23 J/K (Boltzmann’s constant) P = 1.01 x 105 Pa (atmospheric pressure) 2. Determine the equation you need to use PV =NkBT 3. Solve for molecules (N) N = PV/kBT 4. Plug in the values! Solve separately for each temperature N1 = ((1.01 x 105 Pa)( 0.001 m3)) / ((1.38 x 10-­‐23 J/K)(273 K)) N1 = 2.687 x 1022 molecules N2 = ((1.01 x 105 Pa)( 0.001 m3)) / ((1.38 x 10-­‐23 J/K)(298 K)) N2 = 2.461 x 1022 molecules Express these numbers in moles! N1 = 2.687 x 1022 molecules x (1 mol/ 6.022 x 1023 molecules) = 0.04462 mol (we divide by avagadro’s number to find the number of moles) N2 = 2.461 x 1022 molecules x (1 mol/ 6.022 x 1023 molecules) = 0.0409 mol How many Liters would each mole take up at these temperatures?! As long as the gas is ideal, 1 mole = 22.4L. You can double check this with our numbers. 1L / 0.04462 mol = 22.4L