How Close Together Are Gas Molecules? Consider an ideal gas at 27o C and 1.00 atm. To get some idea how close these molecules are to each other, on the average, imagine them to be uniformly spaced, with each molecule at the center of a small cube. (a) What is the length of an edge of each cube if adjacent cubes touch but do not overlap? (b) How does this distance compare with the diameter of a typical molecule? (c) How does their separation compare with the spacing of atoms in solids, which typically are about 0.3 nm apart?
Solution 28E Step 1 of 4: (a) What is the length of an edge of each cube if adjacent cubes touch but do not overlap From ideal gas equation, PV =NkT Where P, V and T are the pressure ,volume and temperature of gas, N is number of molecules. Since here it is given that, for each cube, N= 1 molecule Volume of one such cube, V=l 3 5 Pressure, P=1 atm =1.01× 10 pa 0 Temperature, T= 27 c= 300 k boltzmann constant, k=1.38× 10 23m kg / K.s 2 Step 2 of 4: Substituting in above equation, (1.01× 10 pa)(l ) =(1)(1.38× 10 23m kg / K.s 2 )(300 k) l =409.9 m 3 3 18 3 l = 09.9 × 10 m 9 l = 3.5 × 10 m 9 Using 1nm=10 m l = 3.5 nm Therefore, the length of an edge of each cube is found to be 3.5 nm.