Question

How many molecules of \[C{{O}_{2}}\] are formed when one milligram of 100% pure \[CaC{{O}_{3}}\,\] is treated with excess hydrochloric acid?
(a) \[6.023\times {{10}^{23}}\]
(b) \[6.023\times {{10}^{21}}\]
(c) \[6.023\times {{10}^{20}}\]
(d) \[6.023\times {{10}^{19}}\]
(e) \[6.023\times {{10}^{18}}\]

Answer 1

Hint:Molar mass is the relationship between moles and mass. In other words, the weight in grams of one mole of a substance. We can find the molar mass for any element under the symbol on the periodic table.

Complete step by step solution:
\[CaC{{O}_{3}}+2HCl\to CaC{{l}_{2}}+{{H}_{2}}O+C{{O}_{2}}\]
We can see from the equation that 1 mole of calcium carbonate is treated with excess hydrochloric acid to form 1 mole of carbon dioxide. We know that the mass remains conserved in a chemical reaction.
Molar mass of \[CaC{{O}_{3}}\,\] can be calculated as:
\[CaC{{O}_{3}}:(1\times 40\text{ }g/mol\text{ }Ca)+(1\times 12\text{ }g/mol\text{ }C)+(3\times 16\text{ }g/mol\text{ }O)=100\text{ }g/mol\text{ Ca}C{{O}_{3}}\]
We will now convert the given mass of \[CaC{{O}_{3}}\] to moles by dividing by its molar mass.
\[Moles\,of\,CaC{{O}_{3}}=\dfrac{1\times {{10}^{-3}}}{100}=1\times {{10}^{-5}}\,mole\,CaC{{O}_{3}}\]
Now, we will multiply \[CaC{{O}_{3}}\,\] by the mole ratio between \[C{{O}_{2}}\] and \[CaC{{O}_{3}}\,\] from the balanced equation. This will give us the mol of \[C{{O}_{2}}\] in the reaction
\[1\times {{10}^{-3}}\,g\,CaC{{O}_{3}}\,\times \,\dfrac{1\,mol\,CaC{{O}_{3}}}{100g\,CaC{{o}_{3}}}\,\times \,\dfrac{1\,mol\,C{{O}_{2}}}{1\,mol\,CaC{{O}_{3}}}=1\times {{10}^{-5}}\,mol\,C{{O}_{2}}\,\]
We know 1 mole of any substance contains Avogadro’s number of molecules or atoms.
Finally, using unitary method \[1\times {{10}^{-5}}\,mol\,C{{O}_{2}}\,\]will give:
Number of molecules of \[\begin{align}
  & C{{O}_{2}}=6.023\times {{10}^{23}}\times 1\times {{10}^{-5}}\,mol\,C{{O}_{2}}\, \\
 & \,\,\,\,\,\,\,\,\,\,=6.023\times {{10}^{18}} \\
\end{align}\]

So, the correct option is (e).

Note:Avogadro’s number is equal to \[6.023\times {{10}^{23}}\] units. It is valid for any substance, whether it is an ion, atom or molecule. It is also known as Avogadro’s constant is some literature. Generally speaking, a mole of any substance contains \[6.023\times {{10}^{23}}\] particles of that substance.