Question

The densities of gases a, b, and c at stp are 1.25 g/l, 2.86 g/l and 0.714 g/l, respectively. calculate the molar mass of each substance. identify each substance as ammonia (nh₃), sulfur dioxide (so₂), chlorine (cl₂), nitrogen (n₂) or methane (ch₄).

Answer 1

The  molar  mass  of    a, b and  c at  STP is calculated  as  below

At  STP  T  is always=   273 Kelvin and ,P= 1.0 atm 

by  use of  ideal  gas  equation  that  is  PV =nRT
n(number   of moles) = mass/molar mass  therefore  replace   n  in  the  ideal   gas  equation

that  is Pv = (mass/molar mass)RT
multiply  both side  by molar  mass  and  then  divide  by  Pv  to  make  molar mass the  subject of the  formula

that is  molar  mass =  (mass x RT)/ PV

 density is always = mass/volume

therefore  by  replacing  mass/volume  in   the equation  by  density the equation
molar  mass=( density  xRT)/P  where R  =  0.082 L.atm/mol.K

the  molar mass  for  a
= (1.25 g/l  x0.082 L.atm/mol.k  x273k)/1.0atm = 28g/mol

the molar  mass of b
=(2.86g/l  x0.082L.atm/mol.k   x273  k) /1.0  atm  = 64  g/mol

the molar  mass of c

=0.714g/l  x0.082  L.atm/mol.K  x273 K) 1.0atm= 16 g/mol

therefore  the 
   gas  a  is  nitrogen N2   since 14 x2= 28 g/mol
   gas b =SO2  since  32 +(16x2)= 64g/mol
  gas c =   methaneCH4  since  12+(1x4) = 16 g/mol