Number of atoms in the following samples of substances is largest in

Options

A. 4 g of hydrogen
B. 71 g of chlorine
C. 127 g of iodine
D. 48 g of magnesium

Answer

To determine which sample of substances contains the largest number of atoms, we will use the formula to calculate the number of atoms based on the given mass and molar mass of each substance. The formula we will use is:

\[ n = \frac{w}{M} \times N_a \]

Where:
- \( n \) = number of atoms
- \( w \) = given weight of the substance
- \( M \) = molar mass of the substance
- \( N_a \) = Avogadro's number (approximately \( 6.022 \times 10^{23} \))

Now, let's calculate the number of atoms for each substance provided in the question.

### Step 1: Calculate the number of atoms in Hydrogen (H)

Given:
- Weight of Hydrogen (\( w \)) = 4 grams
- Molar mass of Hydrogen (\( M \)) = 1 g/mol

Using the formula:
\[ n_H = \frac{4 \text{ g}}{1 \text{ g/mol}} \times N_a = 4N_a \]

### Step 2: Calculate the number of atoms in Chlorine (Cl)

Given:
- Weight of Chlorine (\( w \)) = 71 grams
- Molar mass of Chlorine (\( M \)) = 35.5 g/mol

Using the formula:
\[ n_{Cl} = \frac{71 \text{ g}}{35.5 \text{ g/mol}} \times N_a \approx 2N_a \]

### Step 3: Calculate the number of atoms in Iodine (I)

Given:
- Weight of Iodine (\( w \)) = 1.27 grams
- Molar mass of Iodine (\( M \)) = 127 g/mol

Using the formula:
\[ n_I = \frac{1.27 \text{ g}}{127 \text{ g/mol}} \times N_a \approx 0.01N_a \]

### Step 4: Calculate the number of atoms in Magnesium (Mg)

Given:
- Weight of Magnesium (\( w \)) = 48 grams
- Molar mass of Magnesium (\( M \)) = 24 g/mol

Using the formula:
\[ n_{Mg} = \frac{48 \text{ g}}{24 \text{ g/mol}} \times N_a = 2N_a \]

### Summary of Results

- Number of atoms in Hydrogen: \( 4N_a \)
- Number of atoms in Chlorine: \( 2N_a \)
- Number of atoms in Iodine: \( 0.01N_a \)
- Number of atoms in Magnesium: \( 2N_a \)

### Conclusion

The substance with the largest number of atoms is Hydrogen, with \( 4N_a \) atoms.

**Final Answer: Option 1 (Hydrogen)**

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