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An average person needs about 10000 kJ energy per day. The amount of glucose (molar mass = 180.0 g mol$$^{-1}$$) needed to meet this energy requirement is ___ g.
(Use : $$\Delta_C$$H (glucose) = -2700 kJ mol$$^{-1}$$)
Correct Answer: 667
The combustion of glucose provides energy according to: C₆H₁₂O₆ + 6O₂ → 6CO₂ + 6H₂O, with $$\Delta_C H = -2700 \text{ kJ mol}^{-1}$$.
The energy needed per day is 10000 kJ. The number of moles of glucose required is:
$$n = \frac{10000 \text{ kJ}}{2700 \text{ kJ mol}^{-1}} = \frac{10000}{2700} = \frac{100}{27} \approx 3.7037 \text{ mol}$$
The mass of glucose required is:
$$m = n \times M = \frac{100}{27} \times 180.0 \text{ g mol}^{-1} = \frac{18000}{27} = \frac{2000}{3} \approx 666.67 \text{ g}$$
Rounding to the nearest integer, the mass of glucose needed is approximately $$\boxed{667}$$ g.
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