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Question: How would you balance: \[{C_{12}}{H_{22}}{O_{11}}\, + \,{H_2}O \to \,{C_2}{H_5}OH\, + \,C{O_2}\] ?...

How would you balance: C12H22O11 + H2O→ C2H5OH + CO2{C_{12}}{H_{22}}{O_{11}}\, + \,{H_2}O \to \,{C_2}{H_5}OH\, + \,C{O_2} ?

Explanation

Solution

If we want to balance a chemical equation we have to keep in mind that the number of atoms on each side should be equal. We can multiply the stoichiometric coefficient of each reactant and product and make each type of atom the same. Here, we have an organic compound which is sucrose and its hydrolysis is taking place after which we get carbon dioxide and ethanol.

Complete step-by-step answer: We have sucrose here which is a biomolecule it is a disaccharide, it means after its hydrolysis it gives glucose and fructose. So as here the product is different it means total hydrolysis is not taking place. We are making alcohol “ethyl alcohol” thus for balancing the above equation let’s start with the counting of each type of atom from both sides.
C12H22O11 + H2O→ C2H5OH + CO2−−−−−−(1){C_{12}}{H_{22}}{O_{11}}\, + \,{H_2}O \to \,{C_2}{H_5}OH\, + \,C{O_2} - - - - - - (1)
The main equation is (1)(1) so here we have (12Carbon,  24Hydrogen  and 12 Oxygen) atoms(12Carbon,\,\,24Hydrogen\,\,and\,12\,Oxygen)\,atoms on left hand side of equation while the number is different on right hand side. There are (3Carbon,  6Hydrogen  and 3 Oxygen) atoms(3Carbon,\,\,6Hydrogen\,\,and\,3\,Oxygen)\,atoms . As we are seeing that the number of atoms are less on the right hand side thus to make them equal and to balance the chemical equation we just have to start multiplying the stoichiometry of the product side. We can multiply the ethanol with a number of 44 after that the number of atoms becomes different and comes close to equal to that of the left hand side.
C12H22O11 + H2O→ 4C2H5OH + CO2−−−−−−(2){C_{12}}{H_{22}}{O_{11}}\, + \,{H_2}O \to \,4{C_2}{H_5}OH\, + \,C{O_2} - - - - - - (2)
Thus there are atoms as such we have (12Carbon,  24Hydrogen  and 12 Oxygen) atoms(12Carbon,\,\,24Hydrogen\,\,and\,12\,Oxygen)\,atoms on left hand side but on right hand side we have, (9Carbon,  21Hydrogen  and 6 Oxygen) atoms(9Carbon,\,\,21Hydrogen\,\,and\,6\,Oxygen)\,atoms . The equality can be achieved if we multiply the molecule of carbon dioxide by a number 44 thus after that the equation form is as,
C12H22O11 + H2O→ 4C2H5OH + 4CO2−−−−−−(3){C_{12}}{H_{22}}{O_{11}}\, + \,{H_2}O \to \,4{C_2}{H_5}OH\, + \,4C{O_2} - - - - - - (3)
Here, we have same number of atoms of each type on both sides (12Carbon,  24Hydrogen  and 12 Oxygen) atoms(12Carbon,\,\,24Hydrogen\,\,and\,12\,Oxygen)\,atoms on both side hence the balanced chemical equation is: C12H22O11 + H2O→ 4C2H5OH + 4CO2−−−(Balanced chemical equation){C_{12}}{H_{22}}{O_{11}}\, + \,{H_2}O \to \,4{C_2}{H_5}OH\, + \,4C{O_2} - - - (Balanced\,chemical\,equation)

Note: The number of atoms on both sides becomes equal. Sucrose is a hydrocarbon so thus the same mechanism takes place when we have to balance the other hydrocarbons. We have two categories of hydrocarbons, saturated and unsaturated. In unsaturated one we have double or triple bonds while in saturated hydrocarbons only a single bond is present. Mainly we have to balance the carbons, hydrogens and oxygens in these types of reactions.