Question

Balance this chemical equation by inspection: \(\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Short answer

The balanced chemical equation is: \[\mathrm{C}_{2} \mathrm{H}_{4}+3\,\mathrm{O}_{2} \rightarrow 2\,\mathrm{CO}_{2}+2\,\mathrm{H}_{2} \mathrm{O}\]

Step-by-step solution

Identify the elements and their initial counts

On the left side of the equation, there are 2 carbon atoms, 4 hydrogen atoms, and 2 oxygen atoms. On the right side, there is 1 carbon atom, 2 hydrogen atoms, and 3 oxygen atoms.

Balance the carbon atoms

To balance the carbon atoms, we need an equal number of carbon atoms on both sides. Since there are 2 carbon atoms on the left side and only 1 on the right, we need to multiply the carbon dioxide (CO2) term by 2. This will give us the balanced equation: \[\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{O}_{2} \rightarrow 2\,\mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\]

Balance the hydrogen atoms

Now, let's balance the hydrogen atoms. There are 4 hydrogen atoms on the left side and 2 on the right. We need to multiply the water (H2O) term by 2 to get the same number of hydrogen atoms on both sides. This gives us the balanced equation: \[\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{O}_{2} \rightarrow 2\,\mathrm{CO}_{2}+2\,\mathrm{H}_{2} \mathrm{O}\]

Balance the oxygen atoms

Lastly, we have to balance the oxygen atoms. After the previous steps, there are 2 oxygen atoms on the left side (in O2) and 6 oxygen atoms on the right side (4 in the two CO2 and 2 in the two H2O). To balance the oxygens, we need to multiply the oxygen gas (O2) term by 3. This gives us the final balanced equation: \[\mathrm{C}_{2} \mathrm{H}_{4}+3\,\mathrm{O}_{2} \rightarrow 2\,\mathrm{CO}_{2}+2\,\mathrm{H}_{2} \mathrm{O}\] The chemical equation is now balanced with 2 carbon atoms, 4 hydrogen atoms, and 6 oxygen atoms on both sides.

Key concepts

Chemical Reactions

In chemistry, a reaction involves the transformation of one or more substances into new products. These substances are known as reactants, while the resulting substances are termed products. In the given exercise, ethylene (\(\mathrm{C}_2\mathrm{H}_4\)) reacts with oxygen (\(\mathrm{O}_2\)), resulting in carbon dioxide (\(\mathrm{CO}_2\)) and water (\(\mathrm{H}_2\mathrm{O}\)).
Balancing chemical equations ensures that the same number of atoms of each element is present on both sides of the equation.
This reflects an important principle about how reactions occur while respecting certain natural laws.
Understanding chemical reactions involves seeing how atoms are rearranged during the process of forming new compounds.To achieve this, one needs to know the chemical formulas of these substances and understand what goes in and what comes out during the reaction. Mastery of balancing helps in predicting the actual results of the reaction based on theoretical calculations.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction.
The term is derived from two Greek words meaning 'element' and 'measure', which is exactly what stoichiometry is about.
It helps chemists determine how much of a substance is needed to react with another to form a product.
For example, in the equation provided, we need to balance the number of atoms for each element.
\[\mathrm{C}_{2} \mathrm{H}_{4} + 3 \mathrm{O}_{2} \rightarrow 2\,\mathrm{CO}_{2} + 2\,\mathrm{H}_{2} \mathrm{O}\] This chemical equation tells us several things:

• For every 1 molecule of \(\mathrm{C}_{2} \mathrm{H}_{4}\), 3 molecules of \(\mathrm{O}_2\) are required.
• This reaction will produce 2 molecules of \(\mathrm{CO}_2\) and 2 molecules of \(\mathrm{H}_2\mathrm{O}\).

This not only helps balance the equation but also calculates the expected quantity of products when a certain amount of reactants is known.
By understanding stoichiometry, one gains insight into how mass and moles are conserved, which is crucial for practical experiments.

Law of Conservation of Mass

The Law of Conservation of Mass is a fundamental concept in chemistry which states that mass is neither created nor destroyed in a chemical reaction.
This is foundational because it guides the balancing of chemical equations.When balancing the equation (\(\mathrm{C}_{2} \mathrm{H}_{4} + 3 \mathrm{O}_{2} \rightarrow 2\,\mathrm{CO}_{2} + 2\,\mathrm{H}_{2} \mathrm{O}\)), ensuring equal numbers of each type of atom on both sides showcases this law.
This law means that the total mass of the reactants (the substances we start with) must be equal to the total mass of the products (the substances we end up with).

• 2 carbon atoms on each side ensures balance of carbon mass.
• 4 hydrogen atoms from the (\(\mathrm{C}_2\mathrm{H}_4\)) match with those in the water molecules on the product side.
• The total oxygen atoms on both sides of the equation also tally, with 6 in total for either side.

This confirms our equation reflects real-world interaction, upholding the conservation principle in all chemical reactions.
Understanding this concept not only aids in accurately balancing equations but also in comprehending the natural order and predictability of chemical processes.