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