Which of the following set contains same number of molecules? A. 1 gram O 2, 2 grams SO 2 B. 1 gram CO 2, 1 gram N 2O C. 1 gram O 2, 1 gram O 3
A and B
Understanding the Concept of Molecules and Molar Mass
The number of molecules in a given sample of a substance is directly related to the number of moles of that substance. One mole of any substance contains Avogadro's number (approximately $\text{6.022} \times \text{10}^{23}$) of molecules.
To find the number of moles from a given mass, we use the formula:
$\text{Moles} = \frac{\text{Mass (in grams)}}{\text{Molar Mass (in grams per mole)}}$
Therefore, to find which sets contain the same number of molecules, we need to calculate the number of moles for each substance in each set and compare them. If the number of moles is the same, the number of molecules will also be the same.
Calculating Molar Mass of Substances
Let's determine the molar mass for each substance mentioned in the question:
- Oxygen gas ($\text{O}_2$): Atomic mass of Oxygen ($\text{O}$) is approximately 16 g/mol. Molar mass of $\text{O}_2$ is $2 \times 16 = 32$ g/mol.
- Sulfur dioxide ($\text{SO}_2$): Atomic mass of Sulfur ($\text{S}$) is approximately 32 g/mol. Molar mass of $\text{SO}_2$ is $32 + 2 \times 16 = 32 + 32 = 64$ g/mol.
- Carbon dioxide ($\text{CO}_2$): Atomic mass of Carbon ($\text{C}$) is approximately 12 g/mol. Molar mass of $\text{CO}_2$ is $12 + 2 \times 16 = 12 + 32 = 44$ g/mol.
- Nitrous oxide ($\text{N}_2\text{O}$): Atomic mass of Nitrogen ($\text{N}$) is approximately 14 g/mol. Molar mass of $\text{N}_2\text{O}$ is $2 \times 14 + 16 = 28 + 16 = 44$ g/mol.
- Ozone ($\text{O}_3$): Atomic mass of Oxygen ($\text{O}$) is approximately 16 g/mol. Molar mass of $\text{O}_3$ is $3 \times 16 = 48$ g/mol.
Analyzing Each Set
Now, let's calculate the number of moles (and thus compare the number of molecules) for each set:
| Set | Substance | Mass | Molar Mass | Moles ($\frac{\text{Mass}}{\text{Molar Mass}}$) | Number of Molecules (proportional to moles) |
|---|---|---|---|---|---|
| A | $\text{O}_2$ | 1 gram | 32 g/mol | $\frac{1}{32}$ mol | $\frac{1}{32} \times N_A$ |
| A | $\text{SO}_2$ | 2 grams | 64 g/mol | $\frac{2}{64} = \frac{1}{32}$ mol | $\frac{1}{32} \times N_A$ |
| B | $\text{CO}_2$ | 1 gram | 44 g/mol | $\frac{1}{44}$ mol | $\frac{1}{44} \times N_A$ |
| B | $\text{N}_2\text{O}$ | 1 gram | 44 g/mol | $\frac{1}{44}$ mol | $\frac{1}{44} \times N_A$ |
| C | $\text{O}_2$ | 1 gram | 32 g/mol | $\frac{1}{32}$ mol | $\frac{1}{32} \times N_A$ |
| C | $\text{O}_3$ | 1 gram | 48 g/mol | $\frac{1}{48}$ mol | $\frac{1}{48} \times N_A$ |
Let's look at the results:
- Set A: 1 gram of $\text{O}_2$ and 2 grams of $\text{SO}_2$ both contain $\frac{1}{32}$ moles. This means they contain the same number of molecules.
- Set B: 1 gram of $\text{CO}_2$ and 1 gram of $\text{N}_2\text{O}$ both contain $\frac{1}{44}$ moles. This means they contain the same number of molecules.
- Set C: 1 gram of $\text{O}_2$ contains $\frac{1}{32}$ moles, while 1 gram of $\text{O}_3$ contains $\frac{1}{48}$ moles. These are different values, so they contain a different number of molecules.
Conclusion
Based on the calculations, sets A and B contain the same number of molecules, while set C does not. Therefore, the set containing the same number of molecules are A and B.
Important Questions from Basic Concepts of Chemistry
Which of the following pair is correct?
I. Isotopes – different mass numbers
II. Isobars – different atomic numbers
Which of the following is a zone of a flame?
I. Dark
II. Luminous
III. Non-Luminous
Sphalerite is an ore of:
If formula of sodium salt of an anion X is \(Na_2X\) , then the formula of its aluminium salt would be
Which of the following cannot be cut by a knife ?
