Question

44 gms of \( CO_2 \) contains how many molecules of \( CO_2 \)?

• A. \( 6.023 \times 10^{22} \) molecules
• B. \( 6.023 \times 10^{23} \) molecules
• C. \( 6.023 \times 10^{-23} \) molecules
• D. \( 6.023 \times 10^{-22} \) molecules

Hint:

Remember these important chemistry facts:
• \( 1 \) mole of any substance contains \( 6.023 \times 10^{23} \) particles.
• If the given mass equals the molar mass, then the substance contains exactly one mole.
• For \( CO_2 \), molar mass \( = 44 \text{ g/mol} \). Using these ideas makes molecule-based numerical problems very easy to solve quickly in competitive examinations.

Answer 1

The Correct Option is B

Concept:
To determine the number of molecules present in a given mass of a substance, we use the concept of:
• Molar mass
• Avogadro's number
• Relationship between moles and molecules The important standard fact used in chemistry is: \[ 1 \text{ mole of any substance } = 6.023 \times 10^{23} \text{ molecules} \] This number is called Avogadro's Number. Also, \[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \] Once the number of moles is known, the number of molecules can be calculated by: \[ \text{Number of molecules} = \text{Number of moles} \times 6.023 \times 10^{23} \]

Step 1: Find the molar mass of \( CO_2 \).
The molecular formula of carbon dioxide is: \[ CO_2 \] This means one molecule of carbon dioxide contains:
• 1 Carbon atom
• 2 Oxygen atoms Atomic masses: \[ \text{Carbon} = 12 \] \[ \text{Oxygen} = 16 \] Therefore, molar mass of \( CO_2 \) is: \[ 12 + 2(16) \] \[ = 12 + 32 \] \[ = 44 \text{ g/mol} \] Hence, \[ \boxed{\text{Molar mass of } CO_2 = 44 \text{ g/mol}} \]

Step 2: Calculate the number of moles present in 44 g of \( CO_2 \).
Given mass of carbon dioxide: \[ 44 \text{ g} \] Using the formula: \[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \] Substituting the values: \[ = \frac{44}{44} \] \[ = 1 \text{ mole} \] Thus, \[ 44 \text{ g of } CO_2 = 1 \text{ mole of } CO_2 \]

Step 3: Use Avogadro's number to determine the number of molecules.
We know that: \[ 1 \text{ mole } = 6.023 \times 10^{23} \text{ molecules} \] Since 44 g of \( CO_2 \) is exactly 1 mole, \[ \text{Number of molecules} = 6.023 \times 10^{23} \] Therefore, \[ \boxed{6.023 \times 10^{23} \text{ molecules}} \]

Step 4: Identify the correct option.
Comparing the obtained answer with the given options: \[ \boxed{(2)\ 6.023 \times 10^{23} \text{ molecules}} \] is the correct answer.