Question

The metabolism of carbohydrates such as glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) produces the same products as combustion in excess oxygen. Write a chemical equation representing the metabolism (combustion) of glucose.

Short answer

\[\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 + 6\mathrm{O}_2 \rightarrow 6\mathrm{CO}_2 + 6\mathrm{H}_2\mathrm{O}\]

Step-by-step solution

Identify reactants and products

For the metabolism (combustion) of glucose, the reactant is glucose, \(\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6\), and the products are carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)), as in any carbohydrate combustion reaction.

Write the unbalanced chemical equation

Put together the reactants and products into an unbalanced chemical equation: \[\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 + \mathrm{O}_2 \rightarrow \mathrm{CO}_2 + \mathrm{H}_2\mathrm{O}\]

Balance the chemical equation

Balance the equation starting by balancing the carbon atoms: \[\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 + \mathrm{O}_2 \rightarrow 6\mathrm{CO}_2 + \mathrm{H}_2\mathrm{O}\] Next, balance the hydrogen atoms: \[\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 + \mathrm{O}_2 \rightarrow 6\mathrm{CO}_2 + 6\mathrm{H}_2\mathrm{O}\] Finally, balance the oxygen atoms. There are a total of 18 oxygen atoms on the product side (12 from carbon dioxide and 6 from water), so you need 6 oxygen atoms from glucose and 12 from oxygen gas. That makes for a total of 18 oxygen atoms on the reactant side as well. The balanced equation is: \[\mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 + 6\mathrm{O}_2 \rightarrow 6\mathrm{CO}_2 + 6\mathrm{H}_2\mathrm{O}\]

Review the balanced equation

Check to ensure the number of atoms for each element is the same on both sides of the equation. If they are, the equation is balanced.

Key concepts

Chemical Equation

A chemical equation is a symbolic representation of a chemical reaction, where the reactants (substances that undergo the reaction) are shown on the left side, and the products (new substances formed) are shown on the right side. The chemical formula of glucose, \( \mathrm{C}_6\mathrm{H}_{12}\mathrm{O}_6 \), represents a molecule made up of 6 carbon (C), 12 hydrogen (H), and 6 oxygen (O) atoms.

In the equation for the combustion of glucose, this carbohydrate combines with oxygen (\( \mathrm{O}_2 \) — the reactant) to produce carbon dioxide (\( \mathrm{CO}_2 \) — a product) and water (\( \mathrm{H}_2\mathrm{O} \) — also a product). The equation is a straightforward representation allowing us to visualize the substances involved in this particular chemical reaction.

Balancing Chemical Equations

Balancing a chemical equation is akin to ensuring that you have the same number of chairs as guests at a dinner party; it's all about equating the number of atoms for each element on both sides. It's fundamental because it reflects the conservation of mass—matter is neither created nor destroyed in a chemical reaction.

The process starts by carefully arranging the coefficients (the numbers in front of molecules) to ensure that the number of atoms for each element is the same on both sides. This is a crucial step in chemistry as it ensures that the reaction adheres to the law of conservation of mass. Balancing the combustion of glucose starts with carbon and hydrogen before finally aligning the oxygen atoms.

Reactants and Products

Understanding reactants and products is central to grasping any chemical reaction. In our glucose combustion example, glucose and oxygen are the reactants—the substances we start with. The products of the reaction, carbon dioxide and water, are what we end up with post-reaction.

The ability to identify these components is the first step in writing and balancing a chemical equation. Reactants are the 'inputs' that, when combined or broken apart, generate new 'outputs' called products. It is imperative in chemistry to be able to distinguish between these to follow how atoms rearrange during reactions.

Carbohydrate Metabolism

Carbohydrate metabolism refers to the biochemical process by which the body extracts energy from carbohydrates like glucose. This metabolism is essentially an internal combustion, mirroring the burning of glucose in a fire — with the key products being energy, water, and carbon dioxide. This complex process consists of numerous steps and pathways, such as glycolysis, the Krebs cycle, and the electron transport chain.

In the context of our chemical equation, the combustion of glucose represents an oversimplified version of metabolism. It doesn't show the intricate pathways or the actual energy (in the form of ATP) produced but provides a clear picture of the initial and final substances involved in this vital biological process.