Question

Calculate the total number of atoms in $0.1$ mole of $NH_3$.

• A. $6.022\times10^{22}$ atoms
• B. $2.4088\times10^{23}$ atoms
• C. $6.022\times10^{23}$ atoms
• D. $2.4088\times10^{22}$ atoms

Hint:

Mole Tip: Moles $\rightarrow$ Molecules (multiply by $N_A$). Molecules $\rightarrow$ Atoms (multiply by atomicity). Don't stop at the molecular count!

Answer 1

The Correct Option is B

Concept: Chemistry (Basic Concepts) - Mole Concept and Atomicity.

Step 1: Determine the number of molecules in the given moles. One mole of any substance contains Avogadro's number ($N_A = 6.022 \times 10^{23}$) of molecules. For 0.1 mole of $NH_3$: Number of molecules $= 0.1 \times 6.022 \times 10^{23} = 6.022 \times 10^{22}$ molecules.

Step 2: Identify the atomicity of the molecule. The formula for ammonia is $NH_3$. One molecule of ammonia consists of 1 Nitrogen atom and 3 Hydrogen atoms. Total atoms per molecule $= 1 + 3 = 4$ atoms.

Step 3: Set up the calculation for total atoms. Total atoms $= (\text{Number of molecules}) \times (\text{Atoms per molecule})$. Total atoms $= (6.022 \times 10^{22}) \times 4$.

Step 4: Perform the multiplication. $6.022 \times 4 = 24.088$. So, Total atoms $= 24.088 \times 10^{22}$.

Step 5: Convert to standard scientific notation. To express the result in standard scientific notation, move the decimal one place to the left: $2.4088 \times 10^{23}$ atoms. This matches option B. $$ \therefore \text{The total number of atoms is } 2.4088\times10^{23}. $$