The number of molecules of helium gas contained in 11.5g of the gas is

1. Analyze the question

We are asked to find the total number of molecules (or atoms, in the case of a noble gas like Helium) present in a given mass of 11.5g of Helium gas.

2. Explain the concept

To solve this, we use the relationship between mass, molar mass, and Avogadro's constant:

• Molar Mass of Helium (He): 4 g/mol.
• Mole formula: $n = \frac{\text{mass}}{\text{molar mass}}$
• Avogadro’s Constant ($N_A$): $6.02 \times 10^{23}$ particles per mole.
• Number of particles: $N = n \times N_A$

3. Show the solution

Step 1: Calculate the number of moles ($n$) of Helium. Given: Mass = 11.5 g Molar Mass = 4 g/mol

Step 2: Calculate the number of atoms (molecules) using Avogadro’s constant.

Let's perform the multiplication:

So,

To express this in standard form (scientific notation):

4. Identify the answer

Comparing our result ($1.73 \times 10^{24}$) with the given options, it matches option C.

5. Tip

When dealing with "number of particles" questions in JAMB, always remember the "Mole Bridge": Mass $\rightarrow$ Moles $\rightarrow$ Particles. If you are given mass, divide by molar mass first to get to the "mole" island, then multiply by $6.02 \times 10^{23}$ to get to the "particles" island. Don't forget to check your powers of 10 carefully—a common trap in these questions is shifting the decimal point incorrectly!