A sample of `MgCO_3` contains `3.01 xx 10^(23) Mg^(2+)` ions and `3.01 xx 10^(23) CO_(3)^(2+)` ions. The mass of the sample is:

Options

A. 42 mg
B. 84 g
C. 0.042 kg
D. 42 mol

Explanation

To solve the problem of finding the mass of the sample of \( \text{MgCO}_3 \) containing \( 3.01 \times 10^{23} \) \( \text{Mg}^{2+} \) ions and \( 3.01 \times 10^{23} \) \( \text{CO}_3^{2-} \) ions, we can follow these steps:

### Step 1: Determine the number of moles of \( \text{Mg}^{2+} \) ions
We know that 1 mole of any substance contains \( 6.022 \times 10^{23} \) particles (Avogadro's number).

\[ \text{Number of moles of } \text{Mg}^{2+} = \frac{3.01 \times 10^{23}}{6.022 \times 10^{23}} = 0.5 \text{ moles} \]

### Step 2: Calculate the mass of \( \text{Mg}^{2+} \)
The molar mass of \( \text{Mg}^{2+} \) is approximately 24 g/mol.

\[ \text{Mass of } \text{Mg}^{2+} = \text{Number of moles} \times \text{Molar mass} = 0.5 \times 24 = 12 \text{ grams} \]

### Step 3: Determine the number of moles of \( \text{CO}_3^{2-} \) ions
Since the number of \( \text{CO}_3^{2-} \) ions is the same as the \( \text{Mg}^{2+} \) ions, we also have:

\[ \text{Number of moles of } \text{CO}_3^{2-} = 0.5 \text{ moles} \]

### Step 4: Calculate the mass of \( \text{CO}_3^{2-} \)
The molar mass of \( \text{CO}_3^{2-} \) can be calculated as follows:
- Carbon (C): 12 g/mol
- Oxygen (O): 16 g/mol (and there are 3 oxygen atoms)

\[ \text{Molar mass of } \text{CO}_3^{2-} = 12 + (3 \times 16) = 12 + 48 = 60 \text{ g/mol} \]

Now, calculate the mass of \( \text{CO}_3^{2-} \):

\[ \text{Mass of } \text{CO}_3^{2-} = \text{Number of moles} \times \text{Molar mass} = 0.5 \times 60 = 30 \text{ grams} \]

### Step 5: Calculate the total mass of the sample
Now, we can find the total mass of the sample by adding the masses of \( \text{Mg}^{2+} \) and \( \text{CO}_3^{2-} \):

\[ \text{Total mass} = \text{Mass of } \text{Mg}^{2+} + \text{Mass of } \text{CO}_3^{2-} = 12 + 30 = 42 \text{ grams} \]

### Step 6: Convert grams to kilograms (if needed)
To convert grams to kilograms, we divide by 1000:

\[ \text{Total mass in kg} = \frac{42}{1000} = 0.042 \text{ kg} \]

### Final Answer
The mass of the sample is **42 grams** or **0.042 kilograms**.

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