Question

The number of molecules contained in the gas of mass M is ($M_o$ - molar mass, $N_A$ - Avogadro's number)

• A. $(\frac{M}{M_{o}})\frac{1}{N_{A}}$
• B. $(\frac{M_{o}}{M})N_{A}$
• C. $(MM_{\circ})N_{A}$
• D. $(MM_{\circ})\frac{1}{N_{A}}$
• E. $(\frac{M}{M_{o}})N_{A}$

Hint:

Moles = $\frac{\text{Mass}}{\text{Molar Mass}}$; Molecules = $\text{Moles} \times N_A$.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This question asks for the formula to calculate the total number of molecules in a given mass of a gas. This involves the concepts of moles, molar mass, and Avogadro's number.
Step 2: Key Formula or Approach:
1. Number of moles (n): The number of moles is the given mass (M) divided by the molar mass (\( M_o \)). \[ n = \frac{M}{M_o} \] 2. Avogadro's Number (\( N_A \)): This is the number of molecules (or atoms, particles) in one mole of a substance. \( N_A \approx 6.022 \times 10^{23} \text{ mol}^{-1} \). 3. Total number of molecules (N): The total number of molecules is the number of moles multiplied by Avogadro's number. \[ N = n \times N_A \] Step 3: Detailed Explanation:
We can combine the two formulas from Step 2 to get a direct relationship between mass and the number of molecules. Start with the formula for the total number of molecules: \[ N = n \times N_A \] Substitute the expression for the number of moles, \( n = \frac{M}{M_o} \): \[ N = \left(\frac{M}{M_o}\right) \times N_A \] This formula gives the total number of molecules (N) in a sample of mass M with molar mass \( M_o \).
Step 4: Final Answer:
The number of molecules contained in the gas of mass M is \( (\frac{M}{M_o})N_A \).