Write the balanced equation for the combustion of this compound.

Question

While working for a food science company, you need to analyze the energy content of a sugar substitute with the molecular formula C5H12O5. As part of this process, you conduct a series of bomb calorimetry experiments. In each experiment, you place a sample of the sweetener in the calorimeter, and then measure the temperature change when the sweetener undergoes combustion. The heat capacity of the calorimeter is 4.371 kJ/ ∘C.

Write the balanced equation for the combustion of this compound.

Answer 1

Whenever we work with combustion of a carbohydrate compound, we know that we take that carbohydrate plus oxygen gas as reactants and we produce carbon dioxide and water as products. With that information, we can build an unbalanced equation for the reaction first:

C₅H₁₂O₅ + a O₂ -> b CO₂ + c H₂O

Now all that's left is determine what a, b, and c are to balance the equation. We can do that by first looking at how much C is on the left side to determine how much C is on the right side. Since there are 5 C's on the left side, there needs to be 5 C's on the right side, and to get that we can let b = 5. So now our unbalanced equation looks like this:

C₅H₁₂O₅ + a O₂ -> 5 CO₂ + c H₂O

On the right side though, we now have 10 O's after we replace b with 5, since 5 * 2 = 10. We can balance this on the left side by also having a = 5, since there are 2 O's in O₂ and 5 * 2 = 10. Our unbalanced equation will now look like:

C₅H₁₂O₅ + 5 O₂ -> 5 CO₂ + c H₂O

Now just like we looked at how much C is on the left side to balance it on the right, we can look at how much H is on the left side to determine how much H needs to be on the right side. Since there's 12 H's on the left side, we will need 12 H's on the right side, and to get that we can let c = 6 since there are 2 H's in water and 6 * 2 = 12. So now our unbalanced equation looks like:

C₅H₁₂O₅ + 5 O₂ -> 5 CO₂ + 6 H₂O

But our equation is still unbalanced, because while our C's and H's are balanced on both sides, we have a total of 15 O's on the left side but 16 O's on the right side. To fix this, we can just add an additional 1/2 O₂ on the left side, so now our balanced equation is:

C₅H₁₂O₅ + 5.5 O₂ -> 5 CO₂ + 6 H₂O

But reaction equations need to have integer coefficients, we can't have decimals. We can fix this by just multiplying all the coefficients by 2, giving us our final balanced equation:

2C₅H₁₂O₅ + 11 O₂ -> 10 CO₂ + 12 H₂O

Hopefully this explanation makes sense, and if you are interested in more like this for any other course work you have, feel free to reach out to me to book a session!