What mass of NaCl would contain the same total number of ions as 245 g of `MgCl_(2)` ?

Answer

To find the mass of NaCl that would contain the same total number of ions as 245 g of MgCl₂, we can follow these steps:

### Step 1: Calculate the number of moles of MgCl₂
To find the number of moles, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
The molar mass of MgCl₂ can be calculated as follows:
- Molar mass of Mg = 24 g/mol
- Molar mass of Cl = 35.5 g/mol (and there are 2 Cl atoms in MgCl₂)

Thus, the molar mass of MgCl₂ is:
\[ \text{Molar mass of MgCl₂} = 24 + (2 \times 35.5) = 24 + 71 = 95 \text{ g/mol} \]

Now, we can calculate the number of moles of MgCl₂ in 245 g:
\[ \text{Number of moles of MgCl₂} = \frac{245 \text{ g}}{95 \text{ g/mol}} \approx 2.58 \text{ moles} \]

### Step 2: Calculate the total number of ions from MgCl₂
Each formula unit of MgCl₂ produces 3 ions (1 Mg²⁺ and 2 Cl⁻). Therefore, the total number of ions from 2.58 moles of MgCl₂ is:
\[ \text{Total ions} = 2.58 \text{ moles} \times 3 \text{ ions/mole} = 7.74 \text{ moles of ions} \]

### Step 3: Determine the number of moles of NaCl needed to match the total number of ions
Each formula unit of NaCl produces 2 ions (1 Na⁺ and 1 Cl⁻). To find the number of moles of NaCl needed to provide the same number of ions, we use the following calculation:
\[ \text{Moles of NaCl} = \frac{\text{Total moles of ions}}{2} = \frac{7.74}{2} = 3.87 \text{ moles of NaCl} \]

### Step 4: Calculate the mass of NaCl needed
Now, we calculate the mass of NaCl using its molar mass. The molar mass of NaCl is:
- Molar mass of Na = 23 g/mol
- Molar mass of Cl = 35.5 g/mol

Thus, the molar mass of NaCl is:
\[ \text{Molar mass of NaCl} = 23 + 35.5 = 58.5 \text{ g/mol} \]

Now, we can find the mass of 3.87 moles of NaCl:
\[ \text{Mass of NaCl} = \text{Number of moles} \times \text{Molar mass} = 3.87 \text{ moles} \times 58.5 \text{ g/mol} \approx 226.5 \text{ g} \]

### Final Answer
The mass of NaCl that would contain the same total number of ions as 245 g of MgCl₂ is approximately **226.5 grams**.

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