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Question: Human beings require 2500 Kcal of energy per day. \({C_{12}}{H_{22}}{O_{11}} + 12{O_2} \to 12C{O_2...

Human beings require 2500 Kcal of energy per day.
C12H22O11+12O2→12CO2+11H2O{C_{12}}{H_{22}}{O_{11}} + 12{O_2} \to 12C{O_2} + 11{H_2}O
ΔH=−5.6×106 J/mol\Delta H = - 5.6 \times {10^6}{\text{ J/mol}}
(i) Human beings require ___ kJ of energy per day.
(ii) Amount of sucrose required per day and volume of CO2C{O_2} evolved during the process (at STP)

Explanation

Solution

The above given reaction is oxidation of sucrose which is a carbohydrate. We shall convert the energy given in Kcal to kJ. For this energy, we shall calculate the moles and thus the amounts of sucrose required in one day and use the reaction equation to find the volume of carbon dioxide evolved.

Complete step by step answer:
i.The above reaction is an exothermic reaction as ΔH\Delta H is negative. This indicates that energy is released at the end of that reaction.
Kcal that is kilo calorie and kJ that is kilojoule are both the units of conversion of energy.
1 Kcal=4.184 kJ1{\text{ Kcal}} = 4.184{\text{ kJ}}
Human beings require 2500 Kcal of energy per day.
Therefore, human beings require 2500×4.1842500 \times 4.184 = 10460 kJ of energy per day.
C12H22O11+12O2→12CO2+11H2O{C_{12}}{H_{22}}{O_{11}} + 12{O_2} \to 12C{O_2} + 11{H_2}O
ΔH=−5.6×106 J\Delta H = - 5.6 \times {10^6}{\text{ J}} = −5600 kJ - 5600{\text{ kJ}}
Total molecular weight of sucrose = 12×12+22×1+11×1612 \times 12 + 22 \times 1 + 11 \times 16 = 342 g
342 g of sucrose gives 5600 kJ of energy.
X g of sucrose will give 10460 kJ of energy.
Therefore, X = 10460×3425600\dfrac{{10460 \times 342}}{{5600}} = 638 g
638 g of sucrose will give 10460 kJ of energy.

Hence, the mass of sucrose required to provide 10460 kJ of energy per day is 638 g.

ii.In the given reaction, the volume of carbon dioxide that is CO2C{O_2} evolved is 12×22.412 \times 22.4 litre.
So, 342 g of sucrose gives 12×22.412 \times 22.4 litre of carbon dioxide.
So, 638 g of sucrose will give = 12×22.4×638342\dfrac{{12 \times 22.4 \times 638}}{{342}} litre of carbon dioxide = 501 litre

Therefore, the volume of CO2C{O_2} evolved during the process is 501 litre.

Note:
In the given reaction, sucrose is oxidized and oxygen is reduced. It is a redox reaction. This reaction is initiated by H2SO4{H_2}S{O_4} which acts as a catalyst. ΔH\Delta H is the amount of energy used or released in the reaction. If it is negative, then it is an exothermic reaction. If it is positive, then it is an endothermic reaction.