An average personneeds about 10,000 kJ per day. How much carbohydrates ( in mass) will he haveto consume, assuming that all his energy needs are met only by carbohydrates in the form glucose ? Given that the heat of combustion of glucose is 2900 kJ `mol^(-1)`

Explanation

To solve the problem of how much glucose an average person needs to consume to meet their daily energy requirement of 10,000 kJ, we can follow these steps:

### Step 1: Understand the energy provided by glucose
The heat of combustion of glucose is given as 2900 kJ per mole. This means that when one mole of glucose is burned, it releases 2900 kJ of energy.

### Step 2: Calculate the number of moles of glucose needed
To find out how many moles of glucose are needed to meet the daily energy requirement of 10,000 kJ, we can use the formula:
\[ \text{Number of moles} = \frac{\text{Total energy required}}{\text{Energy per mole of glucose}} \]
Substituting the values:
\[ \text{Number of moles} = \frac{10,000 \text{ kJ}}{2900 \text{ kJ/mol}} \approx 3.448 \text{ moles} \]

### Step 3: Calculate the mass of glucose required
Next, we need to convert the number of moles of glucose into mass. The molar mass of glucose (C6H12O6) is approximately 180 g/mol. We can use the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} \]
Substituting the values:
\[ \text{Mass} = 3.448 \text{ moles} \times 180 \text{ g/mol} \approx 620.64 \text{ g} \]

### Step 4: Conclusion
Therefore, the average person needs to consume approximately **620.64 grams** of glucose to meet their daily energy requirement of 10,000 kJ.

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