Question

From 200mg of $C{{O}_{2}}$ ,${{10}^{21}}$ molecules are removed how many moles of $C{{O}_{2}}$ are left?

Answer 1

Hint:
-The number $6.022\times {{10}^{23}}$ is also known as Avogadro’s number. The concept of mole can be used to convert between mass and number of particles.
-Number of moles of any substance is the number of molecules of that substance present per avogadro’s number.

Complete step by step answer:
Here we are given the molar mass of $C{{O}_{2}}$ = \[44{ }g\]
Given mass \[=200mg=0.2g\]
Number of moles = $\dfrac{0.2}{44}=0.0045$
So, applying the formula given below:
$\Rightarrow $ Number of molecules $=$ Avogadro’s number $\times $ number of moles-------(1)
Putting the values of number of moles and Avogadro’s number in the equation (1) we get:
$\Rightarrow $ Number of molecules = ${6}{.022 \times 1}{{{0}}^{{23}}}{\times 0}{.0045}$
$\Rightarrow $ Number of molecules = ${2}{.7 \times 1}{{{0}}^{{21}}}$
As it is given in the question that ${{10}^{21}}$ molecules are removed so the number of molecules that are left are given as;
No of molecules left = ${2}{.7 \times 1}{{{0}}^{{21}}}{- 1}{{{0}}^{{21}}}{= 1}{.7 \times 1}{{{0}}^{{21}}}$
So the number of moles of carbon dioxide that are left = $\dfrac{\text{No of molecules}}{\text{Avogadro's number}}=\dfrac{1.7 \times {{10}^{21}}}{6.022 \times {{10}^{23}}}={2}{.8 \times 1}{{{0}}^{{-3}}}$
We can see that after substituting the number of molecules of carbon dioxide left which we calculated above, and the Avogadro’s number which is a Constant term and is known to us, we found out the number of moles of carbon dioxide. Hence, the number of moles of carbon dioxide left = ${2}{.8 \times 1}{{{0}}^{{-3}}}$ . So this is the required answer.

Note: The concept of mole is important because it allows chemists with subatomic worlds with macro world units and amounts. Basically it provides a bridge between the atom and the macroscopic quantities on which we work in the laboratory. Always apply the formula used above to find the number of molecules and take care of the units of mass always.