Question

If the mixing ratio of carbon dioxide is 404 ppmv and the number density of air is 2.69x10²⁵ molecules m^-3, determine the mass density.

Question 24 options: show work

	8 x 10-4 kg m-3
	4.7 x 10-3 kg m-3
	0.18 ppm
	793 kg m-3

Answer 1

We have CO₂ molecule is

it has carbon atom having mass = 12g/mole
it has oxygen atom having mass = 16g/mole

total mass of 1 mole CO₂ contains 1 mole carbon atoms and 2 moles oxygen atoms

mass of 1mole CO₂ is = 1*12g + 2*16g = 44g

in kg = 0.044kg

now 6.023*10²³ molecues in 0.044kg =

mass of one molecule = 0.044kg/6.023*10²³molecule
7.3 * 10-²⁶ kg/molecule

404 ppm(parts per million) means

404 volume of CO₂ in total volume of 10⁶ volume

lets take volume in m³

so 404m³ volume of CO₂ are in 10⁶ m3 volume

in 1m³ volume ------> 404m³/10⁶ = 4.04 * 10^-4m³ volume of CO₂

given 1 m³ air contains 2.69x10²⁵ molecules

4.04*10^-4 m³ CO₂ contains = 2.69x10²⁵molecules/m³ *4.04*10^-4
   = 10.86x10²¹ molecules/m³

now
density = mass/volume = kg/molecule * molecules/m³

here kg will cancel out and we will get kg/m³

hence density = 7.3 * 10-26 kg/molecule * 10.86x10²¹ molecules/m3
   7.93 * 10^-4Kg/m3
   = 1kg = 10⁶mg
= 793 mg/m³
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