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Question: Considering air as a \( 4:1 \) mixture of \( {N_2} \) and \( {O_2} \) , What is the density of air a...

Considering air as a 4:14:1 mixture of N2{N_2} and O2{O_2} , What is the density of air at 28C{28^\circ }C and 1 atm?
A. 1.18 gL11.18{\text{ g}}{{\text{L}}^{ - 1}}
B. 11.62 gL111.62{\text{ g}}{{\text{L}}^{ - 1}}
C. 28.8 gL1{\text{28}}{\text{.8 g}}{{\text{L}}^{ - 1}}
D. 1.29 gL11.29{\text{ g}}{{\text{L}}^{ - 1}}

Explanation

Solution

The ideal gas law is also known as the general gas equation and is the related state variable that describes the state of matter under a given physical condition like pressure, temperature, volume, etc of a hypothetical ideal gas. It is an approximation of behavior under many conditions of many gases. The laws dealing with ideal gases are called ideal gas laws and the laws are intended by the observational work of Boyle and Charles in the seventeenth and eighteenth century respectively.

Complete answer:
The ideal gas equation is PV = nRT
Where n is the ratio of given mass by molecular mass.
n=mMn = \dfrac{m}{M}
So ideal gas equation can be written as PM=mVRTPM = \dfrac{m}{V}RT
Density is equal to mass per unit volume so mV=D\dfrac{m}{V} = D
PM=DRTPM = DRT ….(I)
According to the question 4 parts of N2{N_2} are present in 5 parts of the mixture while 1 part of O2{O_2} is present in 5 parts of the mixture.
So, the effective molar mass of N2{N_2} =45×(14×2)22.4 g/mol= \dfrac{4}{5} \times (14 \times 2) \Rightarrow 22.4{\text{ g/mol}}
(14 is the molecular mass of nitrogen)
Similarly, the effective molar mass of O2=15×(16×2)6.4 g/mol{O_2} = \dfrac{1}{5} \times (16 \times 2) \Rightarrow 6.4{\text{ g/mol}}
Now the effective molar mass of the mixture =22.4+6.4=28.8 g/mol= 22.4 + 6.4 = 28.8{\text{ g/mol}}
From the given information in the question:
T=28CT = {28^\circ }C in kelvin 28+273=301K28 + 273 = 301K
RR (gas constant) =0.0821 L atm/mole K= 0.0821{\text{ L atm/mole K}}
P = 1 atm
M=28.8 g/molM = 28.8{\text{ g/mol}}
Substituting the given values in equation (I)
1×28.8=D×0.0821×3011 \times 28.8 = D \times 0.0821 \times 301
D=28.824.71D = \dfrac{{28.8}}{{24.71}}
D=1.166 1.18g/litreD = 1.166{\text{ }} \approx 1.18{\text{g/litre}}
Therefore the correct answer is option A.

Note:
One should not get confused with molecular mass or a mass number and molar mass. Molar mass or molecular weight is the sum of the total mass of all the atoms that make up a mole of molecules in grams. The mass carried in one mole of a substance is the molar mass. The unit required to measure molar mass is grams per mole.