What is the maximum number of moles of `CO_(2)` that could be obtained from the carbon in 4 moles of `Ru_(2)(CO_(3))_(3)` ?

Answer

To determine the maximum number of moles of \( CO_2 \) that could be obtained from the carbon in 4 moles of \( Ru_2(CO_3)_3 \), we can follow these steps:

### Step 1: Identify the number of carbon atoms in one mole of \( Ru_2(CO_3)_3 \)

In the chemical formula \( Ru_2(CO_3)_3 \), each \( CO_3 \) unit contains 1 carbon atom. Since there are 3 \( CO_3 \) units in one mole of \( Ru_2(CO_3)_3 \), we can calculate the total number of carbon atoms in one mole:

\[ \text{Number of moles of carbon in 1 mole of } Ru_2(CO_3)_3 = 3 \text{ moles of carbon} \]

### Step 2: Calculate the total number of moles of carbon in 4 moles of \( Ru_2(CO_3)_3 \)

Now, if we have 4 moles of \( Ru_2(CO_3)_3 \), we can find the total moles of carbon:

\[ \text{Total moles of carbon} = 3 \text{ moles of carbon} \times 4 \text{ moles of } Ru_2(CO_3)_3 = 12 \text{ moles of carbon} \]

### Step 3: Determine the maximum number of moles of \( CO_2 \) produced from the carbon

When carbon reacts with oxygen to form carbon dioxide (\( CO_2 \)), the reaction can be represented as:

\[ C + O_2 \rightarrow CO_2 \]

From this reaction, we see that 1 mole of carbon produces 1 mole of \( CO_2 \). Therefore, the total number of moles of \( CO_2 \) produced from the 12 moles of carbon is:

\[ \text{Total moles of } CO_2 = 12 \text{ moles of carbon} \times 1 = 12 \text{ moles of } CO_2 \]

### Final Answer

Thus, the maximum number of moles of \( CO_2 \) that could be obtained from the carbon in 4 moles of \( Ru_2(CO_3)_3 \) is **12 moles**.

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