What is the mass of carbon dioxide which contains the same number of molecules as are contained in 40 g of oxygen?

Options

A. 40g
B. 55g
C. 32g
D. 44g

Explanation

To find the mass of carbon dioxide (CO₂) that contains the same number of molecules as are present in 40 g of oxygen (O₂), we can follow these steps:

### Step 1: Calculate the number of moles of oxygen (O₂)
The molar mass of oxygen (O₂) is approximately 32 g/mol.

\[ \text{Number of moles of O}_2 = \frac{\text{mass of O}_2}{\text{molar mass of O}_2} = \frac{40 \, \text{g}}{32 \, \text{g/mol}} = 1.25 \, \text{moles} \]

### Step 2: Calculate the number of molecules in 40 g of oxygen
Using Avogadro's number, which is \(6.022 \times 10^{23}\) molecules/mol, we can find the number of molecules.

\[ \text{Number of molecules of O}_2 = \text{Number of moles} \times \text{Avogadro's number} = 1.25 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mole} \]

\[ = 7.529 \times 10^{23} \, \text{molecules} \]

### Step 3: Calculate the mass of carbon dioxide (CO₂) that contains the same number of molecules
The molar mass of carbon dioxide (CO₂) is approximately 44 g/mol.

To find the mass of CO₂ that contains \(7.529 \times 10^{23}\) molecules, we first calculate the number of moles of CO₂ that corresponds to this number of molecules.

\[ \text{Number of moles of CO}_2 = \frac{\text{Number of molecules}}{\text{Avogadro's number}} = \frac{7.529 \times 10^{23} \, \text{molecules}}{6.022 \times 10^{23} \, \text{molecules/mole}} \]

\[ = 1.25 \, \text{moles} \]

Now, we can calculate the mass of CO₂:

\[ \text{Mass of CO}_2 = \text{Number of moles} \times \text{molar mass of CO}_2 = 1.25 \, \text{moles} \times 44 \, \text{g/mol} \]

\[ = 55 \, \text{g} \]

### Final Answer
The mass of carbon dioxide that contains the same number of molecules as are contained in 40 g of oxygen is **55 g**.

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