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Question: The number of molecules in 16 g of methane is: a.\(3.0 \times 10^{23}\) b.\(6.02 \times 10^{23}\...

The number of molecules in 16 g of methane is:
a.3.0×10233.0 \times 10^{23}
b.6.02×10236.02 \times 10^{23}
c.166.02×1023\dfrac{16}{6.02} \times 10^{23}
d.163.0×1023\dfrac{16}{3.0} \times 10^{23}

Explanation

Solution

The mole is the International System of Units' basic unit of material quantity (SI). It is defined as a collection of precisely 6.02214076×10236.02214076\times {{10}^{23}} particles, which may be atoms, molecules, ions, or electrons. The Avogadro number (6.02214076×10236.02214076\times {{10}^{23}}) was set such that the mass of one mole of a chemical compound in gram is numerically equivalent to the average mass of one molecule of the compound in daltons for most practical applications.

Complete answer:
The molecular mass of an element is equal to the sum of its component elements' atomic masses. The atomic mass units are also used to denote this number. By multiplying the number of moles by the Avogadro constant, the total number of atoms/molecules in a sample may be determined. This formula is worded as follows:
Number of Atoms or Molecules = (Number of Moles)x(6.022 x 1023)\text{Number of Atoms or Molecules = }\left( \text{Number of Moles} \right)\text{x}\left( \text{6}\text{.022 x 1}{{\text{0}}^{\text{23}}} \right)
The mass of a sample of a chemical compound divided by the amount of material in that sample, measured in moles, is the molar mass of that compound in chemistry. In grams, it is the mass of 1 mole of the material, or 6.02214076×10236.02214076\times {{10}^{23}} particles. The molar mass of a material is a bulk characteristic, not a molecular property. The molar mass is a weighted average of several different occurrences of the chemical, which might vary in mass due to isotopes.
Molecular mass of methane is 16g
Hence one mole of methane is 16g.
Using Number of Atoms or Molecules = (Number of Moles)x(6.022 x 1023)\text{Number of Atoms or Molecules = }\left( \text{Number of Moles} \right)\text{x}\left( \text{6}\text{.022 x 1}{{\text{0}}^{\text{23}}} \right)
Number of Atoms or Molecules = 1x(6.022 x 1023)\text{Number of Atoms or Molecules = 1x}\left( \text{6}\text{.022 x 1}{{\text{0}}^{\text{23}}} \right)
Hence Number of Molecules of Methane = (6.022 x 1023)\text{Number of Molecules of Methane = }\left( \text{6}\text{.022 x 1}{{\text{0}}^{\text{23}}} \right)

Hence option b is correct.

Note:
In any reaction, billions of atoms are rearranged, resulting in chemical changes. Counting or visualising all of these atoms is impossible, but scientists require a method to refer to the whole number. They also require a method of comparing these figures and relating them to the weights of the substances, which they can measure and witness. The notion of the mole, which is crucial in quantitative chemistry, is the solution.