From 200 mg of `CO_2, 10^(21)` molecules are removed. How many molecules are left ?

Options

A. 2.73
B. `17.3xx10^(21)`
C. `1.73xx10^(21)`
D. None

Answer

To solve the problem of how many molecules of CO₂ are left after removing \(10^{21}\) molecules from 200 mg of CO₂, we can follow these steps:

### Step 1: Convert the mass of CO₂ from mg to grams.
Given:
- Mass of CO₂ = 200 mg

To convert mg to grams:
\[ \text{Mass in grams} = \frac{200 \text{ mg}}{1000} = 0.2 \text{ g} \]

### Step 2: Calculate the molar mass of CO₂.
The molar mass of CO₂ can be calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol (and there are 2 oxygen atoms in CO₂)

Thus, the molar mass of CO₂ is:
\[ \text{Molar mass of CO₂} = 12 + (2 \times 16) = 12 + 32 = 44 \text{ g/mol} \]

### Step 3: Calculate the number of moles of CO₂.
Using the formula for moles:
\[ \text{Number of moles} = \frac{\text{mass in grams}}{\text{molar mass}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{0.2 \text{ g}}{44 \text{ g/mol}} \approx 4.545 \times 10^{-3} \text{ moles} \]

### Step 4: Calculate the total number of molecules of CO₂.
Using Avogadro's number (\(N_A = 6.022 \times 10^{23}\) molecules/mol), we can find the total number of molecules:
\[ \text{Total number of molecules} = \text{Number of moles} \times N_A \]
Substituting the values:
\[ \text{Total number of molecules} = 4.545 \times 10^{-3} \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \approx 2.73 \times 10^{21} \text{ molecules} \]

### Step 5: Subtract the number of molecules removed.
We need to remove \(10^{21}\) molecules from the total:
\[ \text{Molecules left} = \text{Total number of molecules} - \text{Molecules removed} \]
Substituting the values:
\[ \text{Molecules left} = 2.73 \times 10^{21} - 10^{21} = 1.73 \times 10^{21} \text{ molecules} \]

### Final Answer:
The number of molecules left after removing \(10^{21}\) molecules from 200 mg of CO₂ is:
\[ \boxed{1.73 \times 10^{21} \text{ molecules}} \]