Question

What will be the mass of 100 atoms of hydrogen?
A. 100 g
B. $1.66\times {{10}^{-22}}g$
C. $6.023\times {{10}^{23}}g$
D. $100\times 6.023\times {{10}^{23}}g$

Answer 1

Hint: To determine the mass of one atom or 100 atoms of an element, you must determine its molar mass, and you need to know the relationship between moles and the number of atoms.

Complete Step by step solution:
1 mol of atoms = $6.023\times {{10}^{23}}atoms$
The molar mass of hydrogen is 1.00784 grams per mol.
\[Mass\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }one\text{ }\!\!~\!\!\text{ }atom\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }hydrogen=\dfrac{Molar\text{ }\!\!~\!\!\text{ }mass\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }hydrogen}{6.023\times {{10}^{23}}}\]
\[\begin{array}{*{35}{l}}
   Mass\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }one\text{ }\!\!~\!\!\text{ }atom\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }hydrogen=\dfrac{1.00784}{6.023\times {{10}^{23}}} \\
   Mass\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }one\text{ }\!\!~\!\!\text{ }atom\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }hydrogen=1.66\times {{10}^{-24}}g \\
\end{array}\]
But we have to calculate mass of 100 hydrogen atoms,
\[100\times \left( Mass\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }one\text{ }\!\!~\!\!\text{ }atom\text{ }\!\!~\!\!\text{ }of\text{ }\!\!~\!\!\text{ }hydrogen \right)\]
\[100\times 1.66\times {{10}^{-24}}=1.66\times {{10}^{-22}}g\]

According to above calculations we can conclude that the correct answer is option (B) $1.66\times {{10}^{-22}}g$.

Additional Information:
Detailed information for calculations of mass of one atom of an element:
In order to determine the mass of one atom of an element, you must determine its molar mass.
Molar mass is its atomic weight on the periodic table in grams per mol.
Atomic mass is a very important concept in chemistry because it is the connection between mass, which we can measure in the laboratory, and moles, which are numbers of atoms. Most of what we study in chemistry is determined by ratios of atoms.
It is necessary to know that relationship between moles and the number of atoms.
1 mol of atoms = $6.023\times {{10}^{23}}$atoms.
Then divide the molar mass by $6.023\times {{10}^{23}}$ for calculation of mass of one atom of a particular element.

Note: Avogadro's number is one of the most important constants used in chemistry. It is the number of particles in a single mole of a material, based on the number of atoms in exactly 12 grams of the isotope carbon-12. Although this number is a constant, it's experimentally determined, so we use an approximate value $6.023\times {{10}^{23}}$.