Calculate the number of hydrogen atoms present in `25.6 g` of sucrose `(C_12 H_22 O_11)` which has a molar mass of `342.3g`?

Options

A. `22xx10^(23)`
B. `9.91 xx 10 ^(23)`
C. `11xx10^(23)`
D. `44xx10^(23)`

Answer

To calculate the number of hydrogen atoms present in 25.6 g of sucrose (C₁₂H₂₂O₁₁), we can follow these steps:

### Step 1: Calculate the number of moles of sucrose.
The formula to calculate the number of moles is:

\[ \text{Number of moles} = \frac{\text{Given mass}}{\text{Molar mass}} \]

Given:
- Mass of sucrose = 25.6 g
- Molar mass of sucrose = 342.3 g/mol

Substituting the values:

\[ \text{Number of moles} = \frac{25.6 \, \text{g}}{342.3 \, \text{g/mol}} \approx 0.0747 \, \text{moles} \]

### Step 2: Calculate the number of sucrose molecules.
Using Avogadro's number (6.022 × 10²³ molecules/mol), we can find the number of molecules in the calculated moles:

\[ \text{Number of molecules} = \text{Number of moles} \times \text{Avogadro's number} \]

Substituting the values:

\[ \text{Number of molecules} = 0.0747 \, \text{moles} \times 6.022 \times 10^{23} \, \text{molecules/mol} \approx 4.49 \times 10^{22} \, \text{molecules} \]

### Step 3: Calculate the number of hydrogen atoms.
In one molecule of sucrose (C₁₂H₂₂O₁₁), there are 22 hydrogen atoms. Therefore, to find the total number of hydrogen atoms in the calculated number of sucrose molecules:

\[ \text{Number of hydrogen atoms} = \text{Number of molecules} \times \text{Number of hydrogen atoms per molecule} \]

Substituting the values:

\[ \text{Number of hydrogen atoms} = 4.49 \times 10^{22} \, \text{molecules} \times 22 \, \text{H atoms/molecule} \approx 9.87 \times 10^{23} \, \text{H atoms} \]

### Final Answer:
The total number of hydrogen atoms present in 25.6 g of sucrose is approximately \( 9.87 \times 10^{23} \, \text{H atoms} \).

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