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Question: One atom of an element x weight \(6.643\times {{10}^{-23}}g\) number of moles of atom in \(20kg\) is...

One atom of an element x weight 6.643×10−23g6.643\times {{10}^{-23}}g number of moles of atom in 20kg20kg is​:
A.44
B.4040
C.100100
D.500500

Explanation

Solution

We know that on multiplying molar mass of substance to the number of molecules provided in the problem we get grams of substance contained in a particular mole of a substance. Atomic weight when multiplied to the number of mole results in its gram weight. Here we will use two formulas
1.molar mass = mass of NA atomsmolar\text{ }mass\text{ }=\text{ }mass\text{ }of\text{ }{{N}_{A}}\text{ }atoms
2.Grams atoms = MassMolar MassGrams\text{ a}toms~=~\dfrac{Mass}{Molar\text{ }Mass}

Complete step-by-step answer: Here mole is standard unit of measurement of amount of substance. Substances react in simple ratios of their respective mole. One mole consists of Avogadro number of atoms that is 6.022×1023atom6.022\times {{10}^{23}}atom . Thus the molar mass is the amount of gram present in one mole of substance. It's also the average atomic weight of a substance . For example , carbon has an atomic weight of 12amu12amu so a molar mass is given as 1212 gram per mole. The formula for conversion of molar mass of atom to gram is given as:
Mass of 11 atom =6.644×10−23g=6.644\times {{10}^{-23}}g
Similarly, molar mass = mass of NA atomsmolar\text{ }mass\text{ }=\text{ }mass\text{ }of\text{ }{{N}_{A}}\text{ }atoms
molar mass =(6.022×1023)×(6.644×10−23)=40.01gmolmolar\text{ }mass\text{ }=\left( 6.022\times {{10}^{23}} \right)\times \left( 6.644\times {{10}^{-23}} \right)=40.01\dfrac{g}{mol}
Thus we get molar mass is 40.01 g⋅mol−140.01\text{ }g\cdot mo{{l}^{-1}} . Now that we get molar mass and grams atoms is given by,
Grams atoms = MassMolar Mass =20×10340.01 g⋅mol−1=500 gram atomGrams\text{ a}toms~=~\dfrac{Mass}{Molar\text{ }Mass}~=\dfrac{20\times {{10}^{3}}}{40.01\text{ }g\cdot mo{{l}^{-1}}}=500\text{ }gram\text{ atom}
Therefore, Option D is the correct option i.e. one atom of an element x weight 6.643×10−23g6.643\times {{10}^{-23}}g number of moles of atom in 20kg20kg is 500 gram atom.

Note: Note that calculating mass is known as gram atomic mass. It's mass of one mole of element example; gram atomic mass of a hydrogen which is 11 gram for one mole of hydrogen. It's the same as the atomic weight of a hydrogen atom.