Question

Which of the following has the smallest number of molecules?
A. $22.4\times {{10}^{3}}mL\,C{{O}_{2}}$ gas
B. 22g of $C{{O}_{2}}$ gas
C. 11.2L of $C{{O}_{2}}$ gas
D. 0.1 mole of $C{{O}_{2}}$ gas.

Answer 1

Hint: Find out the number of moles of carbon dioxide gas in each case, the option having the least number of moles will have the least number of molecules too.

Complete answer:
In order to answer our question, we need to learn about moles and mole concept. Now, matter is made up of atoms and every single atom has a definite mass. Now, the molar mass of an element or compound is the mass which houses $6\times {{10}^{23}}$ atoms or substances inside it. However, molar mass is different for different elements. Hydrogen atom has a molar mass of 1 gram and Helium has a molar mass of 2 grams. So, they have different molar masses, but what they have in common is the number of particles, they have equal numbers of particles which is $6\times {{10}^{23}}$. This number or constant is called the Avogadro’s constant and is helpful in calculations. Mathematically, the number of moles can be found out as:
\[no.\,of\,moles=\dfrac{given\,mass}{molar\,mass}\]
It means that the number of moles is directly proportional to the number of particles. If the number of moles are more, the number of molecules will be more too, and vice versa. With the help of this logic, we will solve the question. Let us find out the number of moles in each of the four options.
According to the formula, the number of moles in option A is $\dfrac{22.4\times {{10}^{3}}}{22.4\times {{10}^{3}}}=1\,mole$. In option B, the number of moles are $\dfrac{22g}{44g}=0.5\,mole$. In option C, number of moles are $\dfrac{11.2g}{22.4g}=0.5\,mole$, whereas I option D, we have 0.1 mole of $C{{O}_{2}}$ present, which is the lowest of all. It means the number of molecules will be least in this case.

So, we obtain the correct answer as option (D) for this question.

Note:
In order to find out the molar mass of a compound, the individual molar masses of the elements are added up. In order to find the molar mass of a diatomic or triatomic molecule, the molar mass is multiplied with the atomicity.