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If molecular weight of glucose$ - 1 - $phosphate is $260$ and its density is $1.5gc{m^{ - 3}}$. What is the average volume occupied by a molecule of this compound?
A.$4.3 \times {10^{ - 23}}c{m^3}$
B.$0.67c{m^3}$
C.$0.17 \times {10^{ - 23}}c{m^3}$
D.$29 \times {10^{ - 23}}c{m^3}$

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Last updated date: 13th Jun 2024
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Answer
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Hint:We know that density is the mass per volume. As it is mass per volume so its unit is gram per centimetre cube. Avogadro number is the number of molecules in one mole of the substance i.e. $6.022 \times {10^{23}}$.

Complete step by step answer:
First of all let us discuss density and Avogadro numbers.
Density: It is defined as the mass per volume. Its unit is $gram/c{m^3}$.
Avogadro number: One mole of a substance contains $6.022 \times {10^{23}}$number of molecules. This number is known as Avogadro number. Its unit is per mole $(mo{l^{ - 1}})$. If we want to calculate the number of particles in a mole then multiply the number of moles with avogadro's number. And if we want to calculate the number of moles in a given number of particles then divide the number of particles with the Avogadro number.
Molar mass: The mass of an atom in an element, is known as molar mass. It is the sum of the number of neutrons and the number of protons present in the atom of an element.
Atomic number: It is defined as the number of protons present in the atom of an element.
Isotopes: They are those elements which have the same atomic number but different mass number i.e. they have the same number of protons but different numbers of neutrons. For example: Carbon$ - 12$ and carbon$ - 14$.
Isobars: They are those elements which have the same atomic mass but different atomic number. For example: calcium and potassium both have mass equal to $40$.
Now, coming to the question we are given with the density and the molar mass. So we can calculate the volume I.e. mass divided by density.
${\text{Volume = }}\dfrac{{{\text{mass}}}}{{{\text{density}}}} = \dfrac{{260}}{{1.5}} = 173.33gc{m^{ - 3}}$
Now, we know that one mole contains $6.022 \times {10^{23}}$molecules.
Average volume occupied is defined as volume divided by Avogadro number.
$\dfrac{{173.33}}{{6.02 \times {{10}^{23}}}} \simeq 29 \times {10^{23}}$.
So option D is the correct option.

Note: Average volume occupied and volume occupied they both are different. Volume occupied is defined as volume occupied by the whole substance and average volume occupied is defined as volume occupied per molecule of an atom.