An athlete takes 100 g of glucose of energy equivalent to 1560 kJ. How much amount of energy is uptaken by 1 g molecule of glucose?

Options

A. `15.6 kJ`
B. `2808 kJ`
C. `1560 kJ`
D. `28.08 kJ`

Answer

To solve the problem step by step, we will find out how much energy is uptaken by 1 gram of glucose based on the information provided.

### Step 1: Understand the given data
- The athlete takes **100 g of glucose**.
- The energy equivalent of **100 g of glucose** is **1560 kJ**.

### Step 2: Calculate the energy per gram of glucose
To find the energy per gram of glucose, we can use the unitary method. We divide the total energy by the mass of glucose taken.

\[ \text{Energy per gram of glucose} = \frac{\text{Total energy}}{\text{Mass of glucose}} = \frac{1560 \text{ kJ}}{100 \text{ g}} = 15.6 \text{ kJ/g} \]

### Step 3: Determine the molar mass of glucose
The molecular formula of glucose is \(C_6H_{12}O_6\). To find the molar mass, we calculate the sum of the atomic masses of all the atoms in one molecule of glucose:
- Carbon (C): 12 g/mol × 6 = 72 g/mol
- Hydrogen (H): 1 g/mol × 12 = 12 g/mol
- Oxygen (O): 16 g/mol × 6 = 96 g/mol

Adding these together gives:
\[ \text{Molar mass of glucose} = 72 + 12 + 96 = 180 \text{ g/mol} \]

### Step 4: Calculate the energy for 1 mole of glucose
Since we know the energy per gram, we can now calculate the energy for 1 mole of glucose (which is 180 g).

\[ \text{Energy for 180 g (1 mole)} = \text{Energy per gram} \times \text{Molar mass} = 15.6 \text{ kJ/g} \times 180 \text{ g} = 2808 \text{ kJ} \]

### Conclusion
Thus, the amount of energy uptaken by 1 mole (or 180 g) of glucose is **2808 kJ**.

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