From 200 mg of `CO_(2)` when x molecules are removed, `2.89 xx 10^(-3)` moles of `CO_(2)` are left. x will be

Options

A. `10^(20)` molecules
B. `10^(10)` molecules
C. 21 molecules
D. `10^(21)` molecules

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

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

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

### Step 2: Calculate the number of moles of CO₂ in 0.2 g.
The molecular weight of CO₂ can be calculated as follows:
- Carbon (C) = 12 g/mol
- Oxygen (O) = 16 g/mol

Molecular weight of CO₂ = 12 + (2 × 16) = 12 + 32 = 44 g/mol

Now, we can calculate the number of moles using the formula:
\[ \text{Number of moles} = \frac{\text{Weight (g)}}{\text{Molecular weight (g/mol)}} \]
\[ \text{Number of moles of CO₂} = \frac{0.2 \text{ g}}{44 \text{ g/mol}} \approx 0.004545 \text{ moles} \approx 4.54 \times 10^{-3} \text{ moles} \]

### Step 3: Determine the number of moles of CO₂ left after removing x molecules.
We are given that after removing x molecules, there are \(2.89 \times 10^{-3}\) moles of CO₂ left.

### Step 4: Calculate the number of moles of CO₂ removed.
The number of moles removed can be calculated as:
\[ \text{Moles removed} = \text{Initial moles} - \text{Remaining moles} \]
\[ \text{Moles removed} = 4.54 \times 10^{-3} - 2.89 \times 10^{-3} = 1.65 \times 10^{-3} \text{ moles} \]

### Step 5: Convert the moles removed to the number of molecules.
Using Avogadro's number (\(6.022 \times 10^{23}\) molecules/mol), we can find the number of molecules removed:
\[ \text{Number of molecules removed} = \text{Moles removed} \times \text{Avogadro's number} \]
\[ \text{Number of molecules removed} = 1.65 \times 10^{-3} \text{ moles} \times 6.022 \times 10^{23} \text{ molecules/mol} \]
Calculating this gives:
\[ \text{Number of molecules removed} \approx 9.93 \times 10^{20} \text{ molecules} \approx 10 \times 10^{20} \text{ molecules} = 10^{21} \text{ molecules} \]

### Conclusion
Thus, the value of \(x\) (the number of molecules removed) is \(10^{21}\).

### Final Answer
\[ x = 10^{21} \text{ molecules} \]