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Question: Which of the following compound(s) has/have same number of atoms?...

Which of the following compound(s) has/have same number of atoms?

A

2 mole H₂SO₄

B

1 mole Fe₂(SO₄)₃

C

2 mole Na₂C₂O₄

D

44.8 L of C₂H₆ at STP

Answer

(iii) and (iv)

Explanation

Solution

To determine which compounds have the same number of atoms, we need to calculate the total number of atoms for each given option. We will use Avogadro's number (N_A) to represent the number of atoms.

(i) 2 mole H₂SO₄

  • First, count the number of atoms in one molecule of H₂SO₄:
    • Hydrogen (H): 2 atoms
    • Sulfur (S): 1 atom
    • Oxygen (O): 4 atoms
    • Total atoms per molecule = 2 + 1 + 4 = 7 atoms/molecule
  • Number of atoms in 1 mole of H₂SO₄ = 7 × N_A atoms
  • Number of atoms in 2 mole of H₂SO₄ = 2 × 7 × N_A = 14 N_A atoms

(ii) 1 mole Fe₂(SO₄)₃

  • First, count the number of atoms in one molecule of Fe₂(SO₄)₃:
    • Iron (Fe): 2 atoms
    • Sulfur (S): 3 × 1 = 3 atoms
    • Oxygen (O): 3 × 4 = 12 atoms
    • Total atoms per molecule = 2 + 3 + 12 = 17 atoms/molecule
  • Number of atoms in 1 mole of Fe₂(SO₄)₃ = 1 × 17 × N_A = 17 N_A atoms

(iii) 2 mole Na₂C₂O₄

  • First, count the number of atoms in one molecule of Na₂C₂O₄:
    • Sodium (Na): 2 atoms
    • Carbon (C): 2 atoms
    • Oxygen (O): 4 atoms
    • Total atoms per molecule = 2 + 2 + 4 = 8 atoms/molecule
  • Number of atoms in 1 mole of Na₂C₂O₄ = 8 × N_A atoms
  • Number of atoms in 2 mole of Na₂C₂O₄ = 2 × 8 × N_A = 16 N_A atoms

(iv) 44.8 L of C₂H₆ at STP

  • At Standard Temperature and Pressure (STP), 1 mole of any gas occupies 22.4 liters.
  • Number of moles of C₂H₆ = VolumeMolar volume at STP=44.8 L22.4 L/mol=2 moles\frac{\text{Volume}}{\text{Molar volume at STP}} = \frac{44.8 \text{ L}}{22.4 \text{ L/mol}} = 2 \text{ moles}
  • Now, count the number of atoms in one molecule of C₂H₆:
    • Carbon (C): 2 atoms
    • Hydrogen (H): 6 atoms
    • Total atoms per molecule = 2 + 6 = 8 atoms/molecule
  • Number of atoms in 1 mole of C₂H₆ = 8 × N_A atoms
  • Number of atoms in 2 mole of C₂H₆ = 2 × 8 × N_A = 16 N_A atoms

Comparison of total atoms:

  • (i) 14 N_A atoms
  • (ii) 17 N_A atoms
  • (iii) 16 N_A atoms
  • (iv) 16 N_A atoms

From the comparison, options (iii) and (iv) have the same number of atoms (16 N_A atoms).