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Question: An athlete takes \(\text{ 100 g }\) of glucose of energy equivalent to\(\text{ }1560\text{ kJ }\). H...

An athlete takes  100 g \text{ 100 g } of glucose of energy equivalent to 1560 kJ \text{ }1560\text{ kJ }. How much energy is taken up by  1 g \text{ 1 g } a molecule of glucose?
(A)  15.6 kJ \text{ 15}\text{.6 kJ }
(B)  2808 kJ \text{ 2808 kJ }
(C)  1560 kJ \text{ 1560 kJ }
(D)  28.08 kJ \text{ 28}\text{.08 kJ }

Explanation

Solution

Here, the energy produced by the  1 g \text{ 1 g }molecules of the glucose is determined by the amount of energy produced by the 1 mole of glucose. The mole is the ratio of the weight of the substance to the molecular weight. Use the concept of the mole to find out the amount of glucose in one gram of molecule and equate it to get the desired answer.

Complete step by step solution:
We have given that the athlete takes up  100 g \text{ 100 g } of the glucose.
The  100 g \text{ 100 g } of the glucose is equivalent to  1560 kJ \text{ }1560\text{ kJ } of the energy equivalent.
We have to find the amount of energy taken by the athlete when he consumes  1 g \text{ 1 g } of glucose.
We can write the relation as,
 100 g = 1560 kJ\text{ 100 g }=\text{ 1560 kJ}
And we have to find the ‘X’ amount of energy.
 1 g = X kJ\text{ 1 g }=\text{ X kJ}
Let's consider one gram of a glucose molecule. The 1 gram of glucose molecules would is considered as the 1 mole of glucose. We know that. 1 mole is equalled to the number of atoms present per molecule of glucose.
We know that the mass of 1 mole of glucose is equalled to the molecular weight of glucose which is 180 g \text{ 180 g }.
In other words, the 1 mole of glucose contains  180 g \text{ 180 g }of the glucose molecule.
 1 mole of glucose = 180 g of Glucose \text{ 1 mole of glucose = 180 g of Glucose }
We know that one mole is equalled to one gram of molecules. Thus, we have,
 1 g of glucose = 180 g of Glucose \text{ 1 g of glucose = 180 g of Glucose }
Now, if  100 g \text{ 100 g }of glucose gives  1560 kJ \text{ }1560\text{ kJ }energy equivalent then 1 g of glucose i.e.  180 g \text{ 180 g }Of glucose molecule would give,

\text{100 g } & = & \text{1560 kJ} \\\ 180\text{ g} & = & \text{X Energy} \\\ \end{matrix}$$ On solving further we get, $$\text{Energy = }\left( \dfrac{1560}{100} \right)\text{ }\times \text{ 180 kJ = 2808 kJ}$$ Therefore, the energy taken when an athlete consumes the 1 gram of glucose is equalled to$$\text{ 2808 kJ }$$. **Hence, (B) is the correct option.** **Note:** Note that, we have to consider the molecules of the glucose. Thus, we are considering that the 1 mole of glucose has $\text{ 180 g }$ of glucose in it. This is because 1 gram of a substance will be equal to the 1 mole of the substance only when it contains the weight which equals its molecular weight. In simpler words, the weight taken must be equal to the molecular weight. $\begin{aligned} &\text{ no}\text{.of moles = }\dfrac{\text{weight}}{\text{mol}\text{.wt}} \\\ &\text{For 1 mole , weight = molecular weight} \\\ \end{aligned}$