Question

How many grams are there in $1.5\times {{10}^{25}}$molecules of $~C{{O}_{2}}$ ?

Answer 1

Hint :We know that the amount of One mole which is the same as the gram atomic weight of a compound, always contains Avogadro number of molecules which is $6.0223\times {{10}^{23}}$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.

Complete Step By Step Answer:
We have been given the number of molecules as $1.5\times {{10}^{25}}$ , which are present in some unknown amount of carbon dioxide, $~C{{O}_{2}}$ . We have to determine this unknown mass (in grams) of this carbon dioxide. As the molecules of $~C{{O}_{2}}$ , given are more in number than Avogadro number, which are $6.0223\times {{10}^{23}}$ molecules present in one mole of a compound. Here inferred that the amount of carbon dioxide is more than one mole.
So, number of moles of $~C{{O}_{2}}$ , in molecules of $~C{{O}_{2}}$ can be calculated by stoichiometric ratio factors as: Moles of $~C{{O}_{2}}=1.5\times {{10}^{25}}$ molecule$\times \dfrac{1moleC{{O}_{2}}}{6.022\times {{10}^{23}}molecules}$
Moles of $~C{{O}_{2}}=51.5molesC{{O}_{2}}$
Thus we know that molar mass of carbon dioxide which is predefined value is $44g/mol.$
Now by multiplying moles of carbon dioxide and Molar mass we get the required grams of mass;
$\left( 51.5moles \right)\centerdot \left( 44g/mol \right)=2266g$

Note :
It should be noted that the number of particles in a mole of a given substance does not depend on the type or nature of a substance and the mass of all the particles ($6.0223\times {{10}^{23}}$ ) in one mole of a substance is equivalent to the molar mass of that compound. The mass of one mole of a substance is known as the molar mass of that 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.