Question

One mole of any substance contains $6.023\times {{10}^{23}}$ particles. If $3.0115\times {{10}^{23}}$ particles of $C{{O}_{2}}$ are present in a container. Find the number of moles of $C{{O}_{2}}$.
A. 1.5 mol
B. 1 mol
C. 0.25 mol
D. 0.5 mol

Answer 1

Hint: Think about how many molecules of any substance can be present in one mole of a substance. Consider how the molecular mass and mass of one mole of a substance are related for further insight.

Complete step by step solution:
Avogadro’s law states that in one mole of any substance, a total number of $6.023\times {{10}^{23}}$ molecules are present. These molecules will always occupy a volume of 22.4L at standard temperature and pressure. The mass of one mole of any substance is numerically equal to the molecular mass of the molecule. This further reinforces the fact that one mole of any substance contains the same number of molecules.
Now, we will calculate the number of moles of $C{{O}_{2}}$ present if the number of molecules is $3.0115\times {{10}^{23}}$. We will calculate this value using cross multiplication.
If 1 mole of $C{{O}_{2}}$ is present if the number of molecules is $6.023\times {{10}^{23}}$.
Then, how many moles of $C{{O}_{2}}$ are present if the number of molecules present is $3.0115\times {{10}^{23}}$. Let $x$ be the unknown number of moles.
\[\begin{align}
  & \dfrac{1}{6.023\times {{10}^{23}}}=\dfrac{x}{3.0115\times {{10}^{23}}} \\
 & x=\dfrac{3.0115\times {{10}^{23}}}{6.023\times {{10}^{23}}} \\
 & x=0.5mol \\
\end{align}\]
So, we can see that the number of moles of carbon dioxide present is 0.5 moles.

Hence, the answer to this question is ‘D. 0.5 mol’

Note: Do not get confused due to the fact that the given substance is specified as carbon dioxide. The fact that the given substance is $C{{O}_{2}}$ will not affect the number of moles present. If the number of molecules given is $3.0115\times {{10}^{23}}$ then the number of moles present will be 0.5 moles irrespective of what substance is present.