Question

Which of the following contains the least number of molecules?
A.\[4.4\] gm of \[C{{O}_{2}}\]
B.\[3.4\] gm of \[N{{H}_{3}}\]
C.\[1.6\] gm of \[C{{H}_{4}}\]
D.\[3.2\] gm of \[S{{O}_{2}}\]

Answer 1

Hint: We know that by calculating the molar mass of each given compound and then equating it with the above relation we would get the compound which has the lowest number of molecules.
Formula Used:
The number or constant is called the Avogadro’s constant and is helpful in calculations. Mathematically, the number of moles can be determined by:
$Number~~of~~moles=\dfrac{given~~mass}{molar~~mass}.$

Complete answer:
To answer our question, we need to learn about moles and mole concepts. 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 is $6.023\times {{10}^{23}}$ atoms or substances inside it. However, molar mass is different for different elements.
Let’s consider \[C{{O}_{2}}\] for \[C{{O}_{2}}\] the molar mass is $C+\left( O\times 2 \right)$ as we know molar mass of carbon is $12$ and molar mass of oxygen is $16.$
The molar mass of \[C{{O}_{2}}=12+\left( 16\times 2 \right)=44g\] now by using the formula for number mole we get; $Number~~of~~moles=\dfrac{given~~mass}{molar~~mass}=\dfrac{4.4}{44}=\dfrac{1}{10}=0.1mol$
Now for \[N{{H}_{3}}\] for \[N{{H}_{3}}\] the molar mass is $N+\left( H\times 3 \right)$ as we know molar mass of nitrogen is $14$ and molar mass of hydrogen is $1.$
The molar mass of \[N{{H}_{3}}=14+\left( 1\times 3 \right)=17\] now by using the formula for number mole we get; $Number~~of~~moles=\dfrac{given~~mass}{molar~~mass}=\dfrac{3.4}{17}=\dfrac{1}{5}=0.2mol$
Let’s consider \[C{{H}_{4}}\] for \[C{{H}_{4}}\] the molar mass is $C+\left( H\times 4 \right)$ as we know molar mass of carbon is $12$ and molar mass of hydrogen is $1.$
The molar mass of \[C{{H}_{4}}=12+\left( 1\times 4 \right)=16g\] now by using the formula for number mole we get; $Number~~of~~moles=\dfrac{given~~mass}{molar~~mass}=\dfrac{1.6}{16}=\dfrac{1}{10}=0.1mol$
Let’s consider \[S{{O}_{2}}\] for \[S{{O}_{2}}\] the molar mass is $S+\left( O\times 2 \right)$ as we know molar mass of sulphur is $32$ and molar mass of oxygen is $16.$
The molar mass of \[S{{O}_{2}}=32+\left( 16\times 2 \right)=64g\] now by using the formula for number mole we get; $Number~~of~~moles=\dfrac{given~~mass}{molar~~mass}=\dfrac{3.2}{64}=\dfrac{1}{20}=0.05mol$

Therefore, the correct answer is option D i.e. \[3.2\] gm of \[S{{O}_{2}}\] contains the least number of molecules.

Note:
Remember that while dealing with stoichiometric problems, it is necessary to balance the chemical equation. If the equations are not balanced properly, then it may lead to mistakes in the calculations and the answer would differ greatly.