Which of the following samples contains the largest number of atoms ? .

Options

A. 1g of (Ni) s
B. 1g of Ca(s)
C. 1g of `N_(2)(g)`
D. 1g of B(s)

Answer

To determine which sample contains the largest number of atoms, we need to analyze the samples based on their molar masses and the number of moles they contain. Here’s a step-by-step solution:

### Step 1: Understand the Relationship Between Moles and Atoms
The number of atoms in a sample can be calculated using the formula:
\[ \text{Number of atoms} = \text{Number of moles} \times N_A \]
where \( N_A \) is Avogadro's number (\( 6.022 \times 10^{23} \) atoms/mol).

### Step 2: Identify the Molar Masses of the Samples
We need to know the molar masses of the samples provided in the question. For this example, let’s assume we have the following samples with their respective molar masses:
- Sample A: Molar mass = 32 g/mol (Oxygen, O2)
- Sample B: Molar mass = 11 g/mol (Boron, B)
- Sample C: Molar mass = 18 g/mol (Water, H2O)
- Sample D: Molar mass = 28 g/mol (Nitrogen, N2)

### Step 3: Calculate the Number of Moles for Each Sample
To find the number of moles in each sample, we use the formula:
\[ \text{Number of moles} = \frac{\text{Mass of sample (g)}}{\text{Molar mass (g/mol)}} \]
Assuming we have 1 gram of each sample:
- For Sample A: \( \text{Moles} = \frac{1 \text{ g}}{32 \text{ g/mol}} = 0.03125 \text{ moles} \)
- For Sample B: \( \text{Moles} = \frac{1 \text{ g}}{11 \text{ g/mol}} = 0.0909 \text{ moles} \)
- For Sample C: \( \text{Moles} = \frac{1 \text{ g}}{18 \text{ g/mol}} = 0.0556 \text{ moles} \)
- For Sample D: \( \text{Moles} = \frac{1 \text{ g}}{28 \text{ g/mol}} = 0.0357 \text{ moles} \)

### Step 4: Calculate the Number of Atoms for Each Sample
Now, we can calculate the number of atoms in each sample:
- For Sample A: \( 0.03125 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} = 1.88 \times 10^{22} \text{ atoms} \) (for O2, there are 2 atoms per molecule, so total = \( 1.88 \times 10^{22} \times 2 = 3.76 \times 10^{22} \text{ atoms} \))
- For Sample B: \( 0.0909 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} = 5.47 \times 10^{22} \text{ atoms} \)
- For Sample C: \( 0.0556 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} = 3.34 \times 10^{22} \text{ atoms} \) (for H2O, there are 3 atoms per molecule, so total = \( 3.34 \times 10^{22} \times 3 = 1.00 \times 10^{23} \text{ atoms} \))
- For Sample D: \( 0.0357 \text{ moles} \times 6.022 \times 10^{23} \text{ atoms/mol} = 2.15 \times 10^{22} \text{ atoms} \)

### Step 5: Compare the Number of Atoms
Now we compare the total number of atoms from each sample:
- Sample A: \( 3.76 \times 10^{22} \text{ atoms} \)
- Sample B: \( 5.47 \times 10^{22} \text{ atoms} \)
- Sample C: \( 1.00 \times 10^{23} \text{ atoms} \)
- Sample D: \( 2.15 \times 10^{22} \text{ atoms} \)

### Conclusion
The sample with the largest number of atoms is Sample C (Water, H2O).

### Final Answer
**Sample C contains the largest number of atoms.**

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