Balance the following equations: (a) C6 H12 O6 ⟶C2 H6 O+CO2 (fermentation of sugar to yield ethy

Balance the following equations: (a) C6 H12 O6 ⟶C2 H6 O+CO2...

Balance the following equations: (a) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}+\mathrm{CO}_{2}$ (fermentation of sugar to yield ethyl alcohol) (b) $\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{O}_{2} \quad$ (photosynthesis reaction in green plants) (c) $\mathrm{NH}_{3}+\mathrm{Cl}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}+\mathrm{NH}_{4} \mathrm{Cl} \quad$ (synthesis of hydrazine for rocket fuel)

Balance the following equations:
(a) $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6} \longrightarrow \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}+\mathrm{CO}_{2}$ (fermentation of sugar to yield ethyl alcohol)
(b) $\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O} \longrightarrow \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}+\mathrm{O}_{2} \quad$ (photosynthesis reaction in green plants)
(c) $\mathrm{NH}_{3}+\mathrm{Cl}_{2} \longrightarrow \mathrm{N}_{2} \mathrm{H}_{4}+\mathrm{NH}_{4} \mathrm{Cl} \quad$ (synthesis of hydrazine for rocket fuel)

Key Concepts

Algebraic Method for Balancing Equations

This method involves assigning algebraic coefficients to reactants and products and then solving a system of linear equations based on the conservation of each element. It is particularly useful for balancing complex chemical reactions.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It relies on the balanced chemical equation to calculate the proportions of substances involved in a reaction.

Balancing Chemical Equations

Balancing chemical equations involves adjusting the coefficients of reactants and products so that the number of atoms for each element is the same on both sides of the equation. This technique is essential for accurately representing chemical reactions.

Law of Conservation of Mass

This principle states that matter is neither created nor destroyed during a chemical reaction. Balancing equations ensures that the number of atoms for each element is equal on the reactants and products sides, adhering to this fundamental law.

Transcript

00:01 To do this problem, i'm going to start with the hydrogens because they only appear once on each side of the equation.

00:09 So i'm going to add a one here to say that for every one of these molecules, i need two of these molecules such that the number of hydrants is the same.

00:20 So now i have for hydrogen, 12 on the left, 12 on the right.

00:27 You don't have to use these numbers here on the bottom.

00:29 I find that for some students that helps them keep track of all their elements.

00:34 Now we'll do a count of the remaining elements.

00:37 For carbons, there's six.

00:38 Oxygen, there's six on the left -hand side.

00:41 Carbons, there's four there and one there.

00:46 So i have five carbons.

00:48 And for oxygens, i have two here and another two here.

00:52 So that is four.

00:56 Now notice my carbons and my oxygens are not balanced, but the only species that i can change at this point is, carbon dioxide.

01:04 So that is what i will do.

01:06 I need one more carbon on the right hand side.

01:10 So to do that, i'm going to add a two right here.

01:14 What that does is it adds one more carbon.

01:17 So now i've gone from five to six.

01:19 And my total number of oxygens is two here and four there.

01:25 And now i have six oxygen and notice that that fixes the elements that were unbalanced so now this reaction is balanced.

01:40 Next i have this other reaction.

01:43 I'm going to start with the carbon atoms.

01:50 I could potentially start with the hydgens, but let's start with the carbons.

01:54 I would like to leave the oxygen for the end because there's a single element.

01:59 It's a standalone element and sometimes those are easiest to balance at the end.

02:04 So i'll start with the carbons first.

02:07 There are six on the right.

02:09 So if i have one of these, i presume it's the sugar molecule, then i'm going to need a six in front of carbon dioxide.

02:16 So for carbon, i have six on each side now.

02:19 That is balanced.

02:21 For oxygen, i have 12 here, 13 there.

02:31 13.

02:32 And on the right hand side, i have six and eight...

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