Calculate the mass of sodium which contains the same number of atoms as are present in 10 g of magnesium.

Answer

To calculate the mass of sodium that contains the same number of atoms as are present in 10 g of magnesium, we can follow these steps:

### Step 1: Calculate the number of moles of magnesium
To find the number of moles of magnesium, we use the formula:

\[ \text{Moles of Magnesium} = \frac{\text{Mass of Magnesium}}{\text{Molar Mass of Magnesium}} \]

Given:
- Mass of Magnesium = 10 g
- Molar Mass of Magnesium = 24 g/mol

Substituting the values:

\[ \text{Moles of Magnesium} = \frac{10 \, \text{g}}{24 \, \text{g/mol}} = 0.4167 \, \text{moles} \]

### Step 2: Calculate the number of atoms in magnesium
Using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) atoms/mol, we can find the number of atoms in the moles of magnesium:

\[ \text{Number of Atoms in Magnesium} = \text{Moles of Magnesium} \times \text{Avogadro's Number} \]

Substituting the values:

\[ \text{Number of Atoms in Magnesium} = 0.4167 \, \text{moles} \times 6.022 \times 10^{23} \, \text{atoms/mol} \approx 2.51 \times 10^{23} \, \text{atoms} \]

### Step 3: Set the number of atoms in sodium equal to that in magnesium
Since we need the same number of atoms in sodium, we have:

\[ \text{Number of Atoms in Sodium} = 2.51 \times 10^{23} \, \text{atoms} \]

### Step 4: Calculate the number of moles of sodium
Using Avogadro's number again, we can find the number of moles of sodium:

\[ \text{Moles of Sodium} = \frac{\text{Number of Atoms in Sodium}}{\text{Avogadro's Number}} \]

Substituting the values:

\[ \text{Moles of Sodium} = \frac{2.51 \times 10^{23} \, \text{atoms}}{6.022 \times 10^{23} \, \text{atoms/mol}} \approx 0.4167 \, \text{moles} \]

### Step 5: Calculate the mass of sodium
Now, we can find the mass of sodium using its molar mass:

\[ \text{Mass of Sodium} = \text{Moles of Sodium} \times \text{Molar Mass of Sodium} \]

Given:
- Molar Mass of Sodium = 23 g/mol

Substituting the values:

\[ \text{Mass of Sodium} = 0.4167 \, \text{moles} \times 23 \, \text{g/mol} \approx 9.6 \, \text{g} \]

### Final Answer
The mass of sodium which contains the same number of atoms as are present in 10 g of magnesium is approximately **9.6 g**.

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