Question Details

Among the following, choose the ones with equal number of atoms.


A. 212 g of Na2CO3(s) [molar mass = 106 g]
B. 248 g of Na2O(s) [molar mass = 62 g]
C. 240 g of NaOH(s) [molar mass = 40 g]
D. 12 g of H2(g) [molar mass = 2 g]
E. 220 g of CO2(g) [molar mass = 44 g]


Choose the correct answer from the options given below :

Options

A

A, B, and D only

B

B, C, and D only

C

B, D, and E only

D

A, B, and C only

Show Answer

Correct Answer :

Option A

A, B, and D only

A, B, and D only

Solution :

To find the options with an equal number of atoms, we need to calculate the total number of atoms in each given sample. The number of atoms in a sample can be calculated using the formula:

Number of atoms = \text{Number of moles of compound} \times \text{Number of atoms per molecule/formula unit} \times N_A

where NA is Avogadro's number (6.022×1023 mol-1).
Since NA is a constant, we can compare the quantity:
Total moles of atoms = \text{Moles of compound} \times \text{Atoms per formula unit}

Let's calculate this value for each option step-by-step:

A. 212 g of Na2CO3(s) [molar mass = 106 g/mol]
Moles of Na2CO3 = 212106=2 mol.
One formula unit of Na2CO3 contains 2 Na + 1 C + 3 O = 6 atoms.
Total moles of atoms = 2×6=12 moles of atoms (or 12×NA atoms).

B. 248 g of Na2O(s) [molar mass = 62 g/mol]
Moles of Na2O = 24862=4 mol.
One formula unit of Na2O contains 2 Na + 1 O = 3 atoms.
Total moles of atoms = 4×3=12 moles of atoms (or 12×NA atoms).

C. 240 g of NaOH(s) [molar mass = 40 g/mol]
Moles of NaOH = 24040=6 mol.
One formula unit of NaOH contains 1 Na + 1 O + 1 H = 3 atoms.
Total moles of atoms = 6×3=18 moles of atoms (or 18×NA atoms).

D. 12 g of H2(g) [molar mass = 2 g/mol]
Moles of H2 = 122=6 mol.
One molecule of H2 contains 2 atoms.
Total moles of atoms = 6×2=12 moles of atoms (or 12×NA atoms).

E. 220 g of CO2(g) [molar mass = 44 g/mol]
Moles of CO2 = 22044=5 mol.
One molecule of CO2 contains 1 C + 2 O = 3 atoms.
Total moles of atoms = 5×3=15 moles of atoms (or 15×NA atoms).

Comparing the total moles of atoms:
- A has 12 moles of atoms.
- B has 12 moles of atoms.
- C has 18 moles of atoms.
- D has 12 moles of atoms.
- E has 15 moles of atoms.

Thus, options A, B, and D contain an equal number of atoms.

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