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Question: If a mole contains \(1.0\times {{10}^{24}}\) atoms, then how many grams of Oxygen would constitute a...

If a mole contains 1.0×10241.0\times {{10}^{24}} atoms, then how many grams of Oxygen would constitute a mole of Oxygen?
a. 53.2 g
b. 5.32 g
c. 32.0 g
d. 16.0 g

Explanation

Solution

Hint: Remember that the widely recognised definition of a mole says that a mole of any chemical substance contains 6.023×10236.023\times {{10}^{23}} atoms. With this in mind, think of how the redefining of the mole concept on the basis of the number of atoms changes its molar mass.

Complete step by step answer:
Let us first try to understand the mole concept and what the molar mass of a substance really refers to.
The molar mass of a substance is defined as the mass of that substance which contains the same amount of elementary units as that in 12 grams of the C-12 isotope of Carbon. This number has been experimentally derived and is found to be numerically equivalent to the Avogadro’s constant.
The molar mass is not a molecular property of a substance and is the aggregate of many instances of the compound, which vary for a lot of compounds due to the presence of isotopes of many elements in the Periodic Table.
The molar mass is normally calculated from the standard atomic weights of chemical substances and is thus a constant regardless of where it is calculated, and is a function of the relative abundance of the isotopes of the constituent atoms of the chemical substance found on the Earth. The molar mass is extremely useful for the conversion between the mass of a substance and the amount of a substance for bulk quantities.
Now, we know that in 32 g of Oxygen gas, we find 6.023×10236.023\times {{10}^{23}} molecules of Oxygen as that is the molar mass of Oxygen.
Therefore, let us now try to find the mass of Oxygen gas which would constitute 1.0×10241.0\times {{10}^{24}} molecules.
1.0×10246.023×1023=m32 ⇒10×326.023=m ⇒53.2≈m \begin{aligned} & \dfrac{1.0\times {{10}^{24}}}{6.023\times {{10}^{23}}}=\dfrac{m}{32} \\\ & \Rightarrow \dfrac{10\times 32}{6.023}=m \\\ & \Rightarrow 53.2\approx m \\\ \end{aligned}
Therefore, the answer to this question is a).

Note:
Remember, molar mass should be distinguished from the molecular mass (also known as molecular weight), which is the mass of one molecule (of any single isotopic composition) and is not directly related to the atomic mass, the mass of one atom (of any single isotope)