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Question: If \({10^{21}}\) molecules are removed from \({\text{200}}\) mg of \({\text{C}}{{\text{O}}_{\text{2}...

If 1021{10^{21}} molecules are removed from 200{\text{200}} mg of CO2{\text{C}}{{\text{O}}_{\text{2}}}, the number of moles of CO2{\text{C}}{{\text{O}}_{\text{2}}} left is:
A. 2.88 × 10−32.88\, \times \,{10^{ - 3}}
B. 28.8 × 10−328.8\, \times \,{10^{ - 3}}
C. 0.288 × 10−30.288\, \times \,{10^{ - 3}}
D. 1.66 × 10−31.66\, \times \,{10^{ - 3}}

Explanation

Solution

To answer this question we should know the mole formula and Avogadro law. By using the Avogadro law first we will determine the moles of carbon dioxide removed. Then by using mole formula we will determine the mole of carbon dioxide present. Then by substituting the removed mole from the present mole we can determine the mole of carbon dioxide left.

Complete step-by-step answer:
According to Avogadro number one mole of any substance contains 6.023 × 10236.023\, \times \,{10^{23}} atoms ions or molecules.
From the Avogadro law, 6.023 × 10236.023\, \times \,{10^{23}} carbon dioxide molecules are equal to one mole of carbon dioxide gas so, 1021{10^{21}} carbon dioxide molecules will be equal to,
6.023 × 10236.023\, \times \,{10^{23}} carbon dioxide molecules = One mole of carbon dioxide gas
And we know,
One mole of carbon dioxide gas = One carbon dioxide molecule

So, 1021{10^{21}}molecule of the carbon dioxide gas = 10216.023 × 1023\dfrac{{{{10}^{21}}}}{{6.023\, \times \,{{10}^{23}}}} carbon dioxide molecules
1021{10^{21}}molecule of the carbon dioxide gas = 1.66× 10−31.66 \times \,{10^{ - 3}} carbon dioxide molecules
So, the mole of carbon dioxide removed is 1.66× 10−31.66 \times \,{10^{ - 3}}mol.
We will use the mole formula to determine the mole of CO2{\text{C}}{{\text{O}}_{\text{2}}}in 200{\text{200}} mg.

First we will convert the milligram into gram.
1000 mg  =  1 g{\text{1000}}\,{\text{mg}}\,{\text{ = }}\,{\text{1}}\,{\text{g}}
200 mg  =  0.2 g{\text{200}}\,{\text{mg}}\,{\text{ = }}\,0.2\,{\text{g}}
The mole formula is as follows:
mole  =  massmolar  mass{\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{mass}}}}{{{\text{molar}}\,\,{\text{mass}}}}
Molar mass of carbon dioxide is 4444g/mol.
On substituting 0.20.2g for mass and 4444g/mol for molar mass,
mole  =  0.244{\text{mole}}\,{\text{ = }}\,\dfrac{{{\text{0}}{\text{.2}}}}{{{\text{44}}}}
mole  =  4.54 ×10−3{\text{mole}}\,{\text{ = }}\,4.54\, \times {10^{ - 3}}
So, the mole of carbon dioxide present are 4.5 ×10−34.5\, \times {10^{ - 3}}mol.
Out of the 4.5 ×10−34.5\, \times {10^{ - 3}} mole, 1.66× 10−31.66 \times \,{10^{ - 3}}mole of carbon dioxide is removed so, the left mole of carbon dioxide is,
Left mole = 4.5 ×10−3 −1.66× 10−3 4.5\, \times {10^{ - 3}}\, - 1.66 \times \,{10^{ - 3}}\,
Left mole = 2.88 ×10−32.88\, \times {10^{ - 3}}
So, the number of moles of CO2{\text{C}}{{\text{O}}_{\text{2}}} left is 2.88 × 10−32.88\, \times \,{10^{ - 3}}.

Therefore, option (A) 2.88 × 10−32.88\, \times \,{10^{ - 3}}is correct.

Note: The number of atoms present in 12{\text{12}} gram of C12{{\text{C}}^{{\text{12}}}} is known as one mole. The number 6.023 × 10236.023\, \times \,{10^{23}} is known as Avogadro number. Molar mass is determined by adding the atomic mass of each atom of the molecule. By using the Avogadro number we can determine the number of atoms, molecules and ions. If here, we have to determine the number of atoms in place of molecules, then we will multiply the Avogadro number with three because one mole of carbon dioxide has three atoms.