if `50` atoms of carbon reacts with` 200` molecules of oxygen, find out the correct statement(s)

Options

A. `O_2` is the limiting reagent
B. `50` molecules of` CO_2` are formed
C. `100` molecules of` CO_2` are formed
D. Both (1) & (2)

Answer

To solve the problem of how many molecules of carbon dioxide (CO2) are formed when 50 atoms of carbon react with 200 molecules of oxygen (O2), we can follow these steps:

### Step 1: Understand the Reaction
When carbon reacts with oxygen, it forms carbon dioxide (CO2). The balanced chemical equation for this reaction is:
\[ C + O_2 \rightarrow CO_2 \]

### Step 2: Determine the Number of Atoms
- We have **50 atoms of carbon (C)**.
- Each molecule of oxygen (O2) contains **2 oxygen atoms**. Therefore, **200 molecules of O2** will contain:
\[ 200 \text{ molecules} \times 2 \text{ atoms/molecule} = 400 \text{ atoms of oxygen (O)} \]

### Step 3: Identify the Limiting Reagent
To determine the limiting reagent, we need to compare the number of moles of reactants available:
- From the reaction, 1 atom of carbon reacts with 1 molecule of O2 to produce 1 molecule of CO2.
- Therefore, 50 atoms of carbon will require 50 molecules of O2 to completely react.

Since we have 200 molecules of O2 available, which is more than enough to react with 50 atoms of carbon, **carbon (C)** is the limiting reagent.

### Step 4: Calculate the Amount of Product Formed
Since carbon is the limiting reagent, the number of CO2 molecules formed will be equal to the number of carbon atoms that reacted:
\[ \text{Number of CO2 molecules formed} = \text{Number of carbon atoms} = 50 \]

### Conclusion
The correct statement is that **50 molecules of CO2 are formed** from the reaction of 50 atoms of carbon with 200 molecules of oxygen.