What mass of carbon dioxide (`CO_(2)`) will contain `3.011 xx 10^(23)` molecules?

Options

A. 11.0 g
B. 22.0g
C. 4.4 g
D. 44.0 g

Explanation

To find the mass of carbon dioxide (CO₂) that contains \(3.011 \times 10^{23}\) molecules, we can follow these steps:

### Step 1: Determine the molecular mass of CO₂
The molecular formula of carbon dioxide is CO₂, which consists of:
- 1 carbon atom (C) with an atomic mass of approximately 12 g/mol
- 2 oxygen atoms (O) with an atomic mass of approximately 16 g/mol each

Calculating the molecular mass:
\[ \text{Molecular mass of CO₂} = (1 \times 12) + (2 \times 16) = 12 + 32 = 44 \text{ g/mol} \]

### Step 2: Use Avogadro's number
Avogadro's number (\(N_A\)) is \(6.022 \times 10^{23}\) molecules/mol. This means that 1 mole of any substance contains \(6.022 \times 10^{23}\) molecules.

### Step 3: Relate the number of molecules to moles
To find out how many moles correspond to \(3.011 \times 10^{23}\) molecules, we can use the formula:
\[ \text{Number of moles} = \frac{\text{Number of molecules}}{N_A} \]
Substituting the values:
\[ \text{Number of moles} = \frac{3.011 \times 10^{23}}{6.022 \times 10^{23}} \approx 0.5 \text{ moles} \]

### Step 4: Calculate the mass of CO₂
Now, we can find the mass of CO₂ using the number of moles and the molecular mass:
\[ \text{Mass} = \text{Number of moles} \times \text{Molecular mass} \]
Substituting the values:
\[ \text{Mass} = 0.5 \text{ moles} \times 44 \text{ g/mol} = 22 \text{ grams} \]

### Final Answer
The mass of carbon dioxide that contains \(3.011 \times 10^{23}\) molecules is **22 grams**.

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