Question

How many molecules of glucose are in 0.5 moles of glucose?

Answer 1

Hint: To solve this question, we first need to understand what is a mole. Mole is the SI unit of measurement and is used to determine the amount of a substance. A mole of any substance has exactly $6.022\times {{10}^{23}}$ particles which can be ions, atoms, electrons, or molecules.

Complete answer:
Avogadro's constant is used to find the relation between the amount of substance in a sample and the number of particles (which can be ions, atoms, electrons, or molecules) constituted in a sample. Its SI unit is $mo{{l}^{-1}}$ and has value ${{N}_{A}}=6.022\times {{10}^{23}}mo{{l}^{-1}}$.
Now, the exact number of particles present in one mole of a substance can be expressed by the numerical value of Avogadro's constant without its dimension. This is called the Avogadro's number.
So, one mole of a substance contains exactly the Avogadro number $(N)$ of particles.
$N=6.022\times {{10}^{23}}$
So, the number of particles or molecules in n moles of a substance will be
\[{{N}_{S}}=n\times N\] (eq (i))
Where ${{N}_{S}}$ is the number of molecules in the substance.
It is given to us that there are 0.5 moles of glucose present.
So the number of molecules present will be
\[\begin{align}
  & {{N}_{S}}=0.5\times 6.022\times 1{{0}^{23}} \\
 & {{N}_{S}}=3.011\times {{10}^{23}} \\
\end{align}\]
Hence, there are $3.011\times {{10}^{23}}$ molecules in 0.5moles of glucose.

Additional Information:
The molar mass of a substance is the mass of one mole of the substance. Its SI base unit is kg/mol but it is usually expressed in g/mol. It is a bulk property of a substance, not a molecular property.
Now, the molecular mass of one mole of a compound is equal to the sum of atomic masses of all the elements present in the molecule.
Since the molecular formula of glucose is ${{C}_{6}}{{H}_{12}}{{O}_{6}}$, its molecular mass will be
\[\begin{align}
  & {{M}_{{{C}_{6}}{{H}_{12}}{{O}_{6}}}}=6\times {{M}_{C}}+12\times {{M}_{H}}+6\times {{M}_{O}} \\
 & {{M}_{{{C}_{6}}{{H}_{12}}{{O}_{6}}}}=6\times 12.0107+12\times 1.00794+6\times 15.999 \\
 & {{M}_{{{C}_{6}}{{H}_{12}}{{O}_{6}}}}=180.156g/mol \\
\end{align}\]

Note:
The number of particles in a mole of a given substance does not depend on the type or nature of a substance. So, the number of moles of any substance can be determined by dividing the number of particles in the sample by Avogadro's constant.