10000kJ energy is needed per day and heat of combustion 2700kj/mol, then find the grams of glucose needed?

Answer

To find the grams of glucose needed to produce 10,000 kJ of energy, we can follow these steps:

### Step 1: Understand the Heat of Combustion
The heat of combustion for glucose is given as 2700 kJ/mol. This means that when 1 mole of glucose is completely burned, it releases 2700 kJ of energy.

### Step 2: Calculate the Molecular Mass of Glucose
The molecular formula for glucose is C₆H₁₂O₆. We can calculate its molecular mass as follows:
- 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:
\[ \text{Molecular mass of glucose} = 72 + 12 + 96 = 180 \text{ g/mol} \]

### Step 3: Set Up the Proportion
We know that 1 mole of glucose (180 g) produces 2700 kJ of energy. We need to find out how many grams of glucose are required to produce 10,000 kJ of energy.

### Step 4: Use the Proportion to Find the Required Grams
We can set up a proportion based on the energy provided by glucose:
\[ \frac{180 \text{ g}}{2700 \text{ kJ}} = \frac{x \text{ g}}{10000 \text{ kJ}} \]

### Step 5: Solve for x
Cross-multiply to solve for x:
\[ x \cdot 2700 = 180 \cdot 10000 \]
\[ x = \frac{180 \cdot 10000}{2700} \]

### Step 6: Calculate x
Now, perform the calculation:
\[ x = \frac{1800000}{2700} \approx 666.67 \text{ g} \]

### Conclusion
Thus, the amount of glucose needed to produce 10,000 kJ of energy is approximately **666.67 grams**.

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