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Question: If the components of air are\({{N}_{2}}\) \(78%\), \({{O}_{2}}\) \(21%\), \(Ar\) \(0\cdot 9%\) and \...

If the components of air areN2{{N}_{2}} 7878%, O2{{O}_{2}} 2121%, ArAr 0⋅90\cdot 9% and CO2C{{O}_{2}} 0⋅10\cdot 1% by volume, the molar mass of air would be (nearest integer):

Explanation

Solution

To find the molar mass of air, we can multiply the given percentage of constituent elements with their respective molar masses. Molar mass is the mass of all the atoms of a molecule in grams per mole.

Complete step by step answer:
For N2{{N}_{2}}, we have molar mass = 28 g/mole where we have calculated it as follows: For one single atom of nitrogen we have atomic no. 7 which is the no. of protons and mass no. is 14 which is the no. of protons and the no. of neutrons.
So, for N2{{N}_{2}} we will simply multiply the atomic mass no. of single atom by 2 i.e. 14×2=2814\times 2=28 g/mole
Similarly for O2{{O}_{2}}: For one single oxygen atom we have atomic mass no. =16, the molar mass for O2=16×2=32{{O}_{2}}=16\times 2=32 g/mol.
Molar Mass for Argon (Ar)(Ar) =40=40g/mol.
For CO2C{{O}_{2}} we have one carbon and two oxygen atoms, the mass no. for Carbon =12=12 and mass no. for Oxygen =16=16, so molar mass of O2{{O}_{2}} =16×2=32=16\times 2=32g/mole and molar mass of CO2C{{O}_{2}} =12+32=44=12+32=44g/mol.
So, the molar mass of air== component % ofN2×{{N}_{2}}\times ×\times molar mass of N2+{{N}_{2}}+ component % of O2×{{O}_{2}}\times molar mass of O2+{{O}_{2}}+ component % of Ar×Ar\times molar mass of Ar+Ar+ component % of CO2×C{{O}_{2}}\times molar mass ofCO2C{{O}_{2}}
⇒78×28+21×32+0⋅9×40+0⋅1×44100\Rightarrow \dfrac{78\times 28+21\times 32+0\cdot 9\times 40+0\cdot 1\times 44}{100}
⇒2184+672+36+4⋅4100\Rightarrow \dfrac{2184+672+36+4\cdot 4}{100}
⇒2896⋅4100\Rightarrow \dfrac{2896\cdot 4}{100}
∴28⋅964\therefore 28\cdot 964
So, the nearest integer value will be 29.
If we have a digit greater than 55 after the decimal then we go for the next integer value. Here, in the above question, we have 28⋅96428\cdot 964 i.e. 9 after the decimal to nearest integer value will be 29 i.e. next to 28.

Note:
Molar mass is given by the mass of the chemical element/compound divided by the amount of substance. So, molar mass of a compound can be calculated by simply adding the standard atomic masses of the constituent atoms.
Atomic masses are given in amu(atomic mass unit) because each proton and each neutron weigh one amu.