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 solve the problem of finding the mass of carbon dioxide (CO2) that contains the same number of molecules as are contained in 40 g of oxygen (O2), we can follow these steps:

### Step 1: Calculate the number of moles of oxygen in 40 g
The molar mass of oxygen (O2) is 32 g/mol. Therefore, the number of moles of O2 in 40 g can be calculated using the formula:

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

### Step 2: Calculate the number of molecules in 40 g of oxygen
Using Avogadro's number (approximately \(6.022 \times 10^{23}\) molecules/mol), we can find the number of molecules in 1.25 moles of O2:

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

Calculating this gives:

\[ \text{Number of molecules} \approx 7.53 \times 10^{23} \text{ molecules} \]

### Step 3: Calculate the mass of carbon dioxide that contains the same number of molecules
The molar mass of carbon dioxide (CO2) is 44 g/mol. We need to find the mass of CO2 that corresponds to \(7.53 \times 10^{23}\) molecules.

First, we calculate the number of moles of CO2 that corresponds to this number of molecules:

\[ \text{Number of moles of CO2} = \frac{\text{Number of molecules}}{\text{Avogadro's number}} = \frac{7.53 \times 10^{23}}{6.022 \times 10^{23}} \approx 1.25 \text{ moles} \]

Now, we can find the mass of this amount of CO2:

\[ \text{Mass of CO2} = \text{Number of moles} \times \text{molar mass} = 1.25 \text{ moles} \times 44 \text{ g/mol} = 55 \text{ g} \]

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

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