A man needs `6.84g` of sugar `C_(12)H_(2)O_(11)` to sweeten his tea. What will be the number of carbon atoms present in the tea due to sugar `:`

Options

A. `3.6xx10^(22)`
B. `3.6xx10^(23)`
C. `1.45xx10^(22)`
D. `1.45xx10^(23)`

Explanation

To find the number of carbon atoms present in the tea due to the sugar \( C_{12}H_{22}O_{11} \), we can follow these steps:

### Step 1: Calculate the number of moles of sugar
First, we need to determine the number of moles of sugar in \( 6.84 \, g \).

The molar mass of sugar \( C_{12}H_{22}O_{11} \) is calculated as follows:
- Carbon (C): \( 12 \times 12.01 \, g/mol = 144.12 \, g/mol \)
- Hydrogen (H): \( 22 \times 1.008 \, g/mol = 22.176 \, g/mol \)
- Oxygen (O): \( 11 \times 16.00 \, g/mol = 176.00 \, g/mol \)

Adding these together:
\[ \text{Molar mass of } C_{12}H_{22}O_{11} = 144.12 + 22.176 + 176.00 = 342.296 \, g/mol \approx 342 \, g/mol \]

Now, we can calculate the number of moles of sugar:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{6.84 \, g}{342 \, g/mol} \approx 0.0200 \, moles \]

### Step 2: Calculate the number of molecules of sugar
Using Avogadro's number (\( N_A = 6.022 \times 10^{23} \, molecules/mol \)), we can find the number of molecules of sugar:
\[ \text{Number of molecules} = \text{Number of moles} \times N_A = 0.0200 \, moles \times 6.022 \times 10^{23} \, molecules/mol \approx 1.2044 \times 10^{22} \, molecules \]

### Step 3: Calculate the number of carbon atoms
Each molecule of sugar \( C_{12}H_{22}O_{11} \) contains 12 carbon atoms. Thus, the total number of carbon atoms is:
\[ \text{Number of carbon atoms} = \text{Number of molecules} \times 12 = 1.2044 \times 10^{22} \, molecules \times 12 \approx 1.4453 \times 10^{23} \, carbon \, atoms \]

### Final Answer
The number of carbon atoms present in the tea due to the sugar is approximately \( 1.45 \times 10^{23} \).

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