Problem 1 - Introductory Chemistry Atoms First

Question

\(\quad \mathrm{CH}_{4}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\) Answer: Because oxygen appears as a pure elemental substance, we save it for last. Starting with carbon (an arbitrary choice), we note that there is one carbon on each side of the equation, meaning \(\mathrm{C}\) is balanced. There are four hydrogen atoms on the left and only two on the right. To fix this, we put a balancing coefficient \(2 \mathrm{in}\) front of the \(\mathrm{H}_{2} \mathrm{O}\) : \(\mathrm{CH}_{4}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\) This balances the hydrogen. Now it's time to balance the oxygen. There are two oxygen atoms on the left and four on the right (two from the \(\mathrm{CO}_{2}\) molecule and two from the two \(\mathrm{H}_{2} \mathrm{O}\) molecules). To balance the equation, we put a \(2 \mathrm{in}\) front of the \(\mathrm{O}_{2}\). \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\)

Step-by-Step Solution

Answer

Answer: To balance the given chemical equation, first balance the carbon and hydrogen. The balanced equation is: \(\mathrm{CH}_{4}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\). Then, balance the oxygen by adding a coefficient of 2 in front of the O2: \(\mathrm{CH}_{4}+2 \mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+2 \mathrm{H}_{2} \mathrm{O}\). Now, all elements are balanced in the chemical equation.

Step 1: Balancing Carbon

As there is one carbon atom in both methane (CH4) and carbon dioxide (CO2), carbon is already balanced in the given equation. So, no changes are needed for carbon atoms.

Step 2: Balancing Hydrogen

There are four hydrogen atoms in methane (CH4) and two hydrogen atoms in water (H2O). To balance the hydrogen, we need to place a coefficient of 2 in front of the H2O, resulting in the following equation: CH4 + O2 → CO2 + 2 H2O Now, there are four hydrogen atoms on both sides of the equation, so the hydrogen is balanced.

Step 3: Balancing Oxygen

We now have two oxygen atoms in O2 and four oxygen atoms on the right side (two from CO2 and two more from 2 H2O). To balance the oxygen atoms, we need to place a coefficient of 2 in front of the O2, resulting in this balanced equation: CH4 + 2 O2 → CO2 + 2 H2O Now, there are four oxygen atoms on both sides of the equation, so all elements are balanced in the chemical equation.

Key Concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves the calculation of reactants and products in chemical reactions. It is like a recipe, ensuring that the proportions of ingredients are just right to achieve a desired outcome. Using stoichiometry helps us understand how much of each substance is required or produced in a reaction.

Imagine making a cake: if the recipe calls for 2 cups of flour and 1 cup of sugar, then doubling the recipe means doubling every ingredient. Similarly, stoichiometry involves balancing chemical equations by adjusting molecular coefficients, just like altering ingredient amounts to maintain balance.

In the exercise given:

• We began with balancing carbon, which was already balanced across methane and carbon dioxide.
• Next, hydrogen was balanced by adjusting the coefficient of water.
• Finally, the coefficient for oxygen was adjusted to achieve a balanced equation.

These adjustments are like fine-tuning a recipe to ensure everything is perfectly aligned.

Combustion Reaction

Combustion reactions are a type of chemical reaction where a substance combines with oxygen to release energy. This reaction is very common and often observed in everyday phenomena like burning wood or gasoline.

In a combustion reaction, a hydrocarbon, like methane (CH₄), reacts with oxygen (O₂) to produce carbon dioxide (CO₂) and water (H₂O). The primary goal is to achieve a complete burn, where all carbon turns into CO₂ and all hydrogen into H₂O.

The balanced chemical equation for the combustion of methane is:

• CH₄ + 2 O₂ → CO₂ + 2 H₂O

This equation shows that methane and oxygen react in a 1:2 ratio, yielding carbon dioxide and water. Combustion reactions are exothermic, meaning they release energy, which is why they are used for heating and in engines.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. These changes involve breaking and forming of bonds between atoms and are crucial for a myriad of functions in our world, from digestion in our bodies to energy production.

Every reaction obeys the Law of Conservation of Mass, meaning mass is neither created nor destroyed. This law is a cornerstone in balancing chemical equations. For instance, every atom of carbon, hydrogen, and oxygen in the reactants must be accounted for in the products.

In the provided exercise:

• Reactants were CH₄ and O₂, and the products were CO₂ and H₂O.
• The process of balancing ensured that the number of each type of atom was the same on both sides of the equation.

These reactions are essential in fields such as chemistry, biology, and environmental science, showing how elements interact and transform.

Molecular Coefficients

Molecular coefficients are numerical values placed in front of the chemical formulas in an equation. They are crucial for indicating the number of molecules or moles involved in a reaction. Adjusting these coefficients correctly is what balances a chemical equation and ensures that the stoichiometry is accurate.

For example, in the equation

• CH₄ + 2 O₂ → CO₂ + 2 H₂O,

we placed a '2' as the coefficient in front of O₂ and H₂O to balance the number of hydrogen and oxygen atoms. Without these coefficients being precisely adjusted, the reaction would not accurately represent reality.

The role of molecular coefficients is similar to measuring teaspoons in a recipe—they ensure that all ingredients are used in the correct proportion to produce the desired dish. By grasping the concept of molecular coefficients, one gains a deeper understanding of the precise nature of chemical reactions.