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Question: If the molecular mass of \(C{O_2}\) is \({\text{44amu}}\) and Avogadro's number is \(6.022 \times {1...

If the molecular mass of CO2C{O_2} is 44amu{\text{44amu}} and Avogadro's number is 6.022×10236.022 \times {10^{23}}. Therefore, what is the mass of one molecule of CO2C{O_2}?
(A)7.31×10237.31 \times {10^{ - 23}}
(B) 3.65×10233.65 \times {10^{ - 23}}
(C) 1.01×10231.01 \times {10^{ - 23}}
(D) 2.01×10232.01 \times {10^{ - 23}}

Explanation

Solution

The mass of a given molecule is termed as molecular mass, It is expressed in units Dalton (Da)\left( {Da} \right) or uu. Different Molecules have different masses. The molecules are mass of the, generally represent the mass of one mole of that substance, it can also be calculated for a single molecule.

Complete step by step answer:
In this question, we are provided with the molecular mass of CO2C{O_2} that is 44amu{\text{44amu}}(atomic mass unit).
It implies that the mass of one mole CO2C{O_2} molecules is 44amu{\text{44amu}}.
We are also provided with the Avogadro number that is 6.022×10236.022 \times {10^{23}}
It implies the total number of particles are entities present in the mole of a substance 6.022×10236.022 \times {10^{23}}. Therefore, if we want to calculate the mass of one molecule of CO2C{O_2}, we need to divide the mass of one more CO2C{O_2} by the number of particles present in one mole, that is Avogadro's number.
Therefore,
Mass of one molecule of
CO2=molecular mass of CO2Avogadro’s numberC{O_2} = \dfrac{{{\text{molecular mass of C}}{{\text{O}}_{\text{2}}}}}{{{\text{Avogadro's number}}}}.
=446×1023= \dfrac{{44}}{{6 \times {{10}^{23}}}}
=7.31×1023= 7.31 \times {10^{ - 23}}
Hence the mass of one molecule of CO2C{O_2} is 7.31×10237.31 \times {10^{ - 23}}.

Hence the correct option is (A) 7.31×10237.31 \times {10^{ - 23}}.

Additional information:
Avogadro’s number is named so in the honour Of Amedeo Avogadro. He discovered the number of particles (atoms or molecules or ions) of substance have proportional relationship with the mass of that substance.
As one dozen means 12,12, one gross means 144144, in the same way Avogadro's number means 6.022×10236.022 \times {10^{23}} particles. Avogadro’s number is represented as NA{N_A}.
The Avogadro's number is related to many constants such as gas constant(RR ),Boltzmann constant (KB{K_B}), Faraday constant (F)(F), molar mass constant (Mu)({M_u}). etc.

Note: The mass of the molecule is calculated with the help of Avogadro’s number. In the same way if mass of one molecule is given and we are asked to calculate the molar mass of the substance. Then, In that case we would simply multiply the mass of the molecule with Avogadro number to obtain the molecular mass of the substance.
molecular mass == mass of one molecule ×\times avogadro's number