Question

The largest number of molecules is present in
A. 34 g of ${{H}_{2}}O$
B. 28 g of $C{{O}_{2}}$
C. 46 g of $C{{H}_{3}}OH$
D. 54 g of ${{N}_{2}}{{O}_{5}}$

Answer 1

Hint: To calculate the number of molecules first we have to calculate the number of moles of the given elements. Then the number of atoms will be equal to the product of the number of moles and Avogadro’s number.

Complete step by step solution:
The mole is a measurement or it is the basic unit which helps to calculate the amount of substance present in the given sample. 1 mole of a number is equal to Avogadro’s constant${{N}_{A}}$.
For water-
mass of oxygen = 16g
mass of hydrogen= 2 g
molar mass of water = 18g
Number of mol is calculated by ratio of given mass to the molar mass.
Number of mol of sodium = $\dfrac{\text{given mass}}{\text{molar mass}}$
After putting the value we get,
Number of mol of carbon = $\dfrac{34}{18}=1.88$moles
And, number of molecules= $\left( \text{number of moles} \right)\times \left( {{N}_{A}} \right)$
= 1.88 ${{N}_{A}}$ molecules (${{N}_{A}}$=$6.022 \times {{10}^{23}}$)
For carbon dioxide-
mass of carbon = 12 g
 mass of oxygen= 16 g
molar mass of carbon dioxide = 44
Number of mol of carbon dioxide = $\dfrac{44}{28}=1.57$moles
And, number of molecules= $\left( \text{number of moles} \right)\times \left( {{N}_{A}} \right)$
= 1.57 ${{N}_{A}}$ molecules (${{N}_{A}}$=$6.022 \times{{10}^{23}}$)
For $C{{H}_{3}}OH$-
mass of carbon = 12 g
mass of oxygen= 16 g
molar mass of $C{{H}_{3}}OH$= 32
Number of mol of $C{{H}_{3}}OH$= $\dfrac{46}{32}=1.43$moles
And, number of molecule= $\left( \text{number of moles} \right)\times\left( {{N}_{A}} \right)$
= 1.43 ${{N}_{A}}$ molecule(${{N}_{A}}$=$6.022 \times {{10}^{23}}$)
For ${{N}_{2}}{{O}_{5}}$-
Molar mass of ${{N}_{2}}{{O}_{5}}$=108.5
Number of mol of ${{N}_{2}}{{O}_{5}}$ = $\dfrac{54}{108}=0.5$moles
And, number of molecules= $\left( \text{number of moles} \right)\times\left( {{N}_{A}} \right)$
= 0.5 ${{N}_{A}}$ molecule (${{N}_{A}}$=$6.022 \times {{10}^{23}}$)

Hence the correct option is (A).

Note: If the question asks you to find the exact number of atoms or molecules then put the value of ${{N}_{A}}$ and write the exact number of atoms. 1 mole=$6.022 \times {{10}^{23}}$ particle or atoms or molecules or electrons or protons etc.