Question

Balance each of the following chemical equations: a. \(\mathrm{HCl}+\mathrm{O}_{2} \rightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{Cl}_{2}\) b. \(\mathrm{NO}_{2}+\mathrm{H}_{2} \mathrm{O} \rightarrow \mathrm{HNO}_{3}+\mathrm{NO}\) c. \(\mathrm{CH}_{4}+\mathrm{O}_{2} \rightarrow \mathrm{CO}_{2}+\mathrm{H}_{2} \mathrm{O}\)

Short answer

a. 2 HCl + O2 -> 2 H2O + Cl2, b. 2 NO2 + 2 H2O -> 2 HNO3 + NO, c. CH4 + 2 O2 -> CO2 + 2 H2O

Step-by-step solution

Balancing HCl and O2 Reaction

To balance the equation HCl + O2 -> H2O + Cl2, start with the element that appears only once in both reactants and products. In this case, start with Cl. There are 2 Cl atoms in Cl2, so you will need 2 molecules of HCl to balance the Cl atoms. Now, balance the hydrogen (H) atoms. There are 2 H atoms in H2O and you already have 2 H atoms from the 2 molecules of HCl. Lastly, balance the oxygen (O) atoms. You have 1 O atom from H2O and 2 O atoms from O2, which makes a total of 2 O atoms required. The balanced equation is 2 HCl + O2 -> 2 H2O + Cl2.

Balancing NO2 and H2O Reaction

To balance the equation NO2 + H2O -> HNO3 + NO, begin with the nitrogen (N) atoms. There is one N atom in both NO2 and NO, and one in HNO3, so start by writing a coefficient of 1 in front of NO2 and NO. Next, balance the oxygen (O) atoms. There are 3 O atoms in HNO3, 2 in NO2, and 1 in NO, which means you need a total of 4 O atoms. With 1 O atom from H2O, balance this with 2 NO2 and 2 H2O, giving you 4 O atoms. Lastly, balance the hydrogen (H) atoms. Now you have 2 H atoms from 2 H2O and need 2 H atoms in 2 HNO3, which gives you a balanced equation of 2 NO2 + 2 H2O -> 2 HNO3 + NO.

Balancing CH4 and O2 Reaction

For the equation CH4 + O2 -> CO2 + H2O, first balance the carbon (C) atoms by making sure that there is one CO2 for every CH4. There is 1 C atom in CH4 and 1 in CO2, so these are already balanced. Next, balance the hydrogen (H) atoms. With 4 H atoms in CH4, you will need 2 H2O molecules to provide 4 H atoms. Now, balance the oxygen (O) atoms. There are 2 O atoms in CO2 and 2 O atoms in 2 H2O, adding up to a total of 4 O atoms. Therefore, you need 2 O2 molecules, each providing 2 O atoms, to balance the equation. The balanced chemical equation is CH4 + 2 O2 -> CO2 + 2 H2O.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with determining the quantities of reactants and products involved in a chemical reaction. It's based on the premise that atoms are neither created nor destroyed in chemical reactions, a principle known as the conservation of mass. Understandably, stoichiometry can seem daunting, but it's fundamentally about the ratios between the molecules involved in a reaction.

When we talk about balancing equations, we are applying stoichiometry to ensure that the number of atoms for each element is the same on both sides of the equation. This makes sense when you consider cooking: to follow a recipe properly, you need the right proportions of ingredients. Similarly, a balanced chemical equation tells you the proportions of reactants and products needed for a reaction to occur without any leftover reactants.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, transform into different substances called products. This transformation happens through the breaking and forming of chemical bonds, which are the forces that hold atoms together. Chemical reactions are everywhere—in the food we digest, the batteries powering our devices, and the combustion engines of vehicles.

Learning to recognize and write chemical reactions is fundamental for understanding chemistry. For instance, in the textbook exercise, we have reactions involving hydrochloric acid and oxygen, nitrogen dioxide and water, and methane with oxygen. Each one represents a unique set of changes, illustrating the diversity of chemical processes. By balancing the equations, chemists can predict the amounts of products formed from given quantities of reactants.

Chemical Equation Balancing

Balancing chemical equations is like solving a puzzle; each piece must fit exactly right for the picture to be complete. In chemistry, each 'piece' is an atom, and the 'picture' is the balanced equation. You can't finish the puzzle if you have too many or too few of any piece, just like you can't have a balanced equation if the number of any atom doesn't match on both sides.

The process involves adjusting the coefficients — the numbers placed before compounds — in the equation. These numbers show how many units of each substance are involved in the reaction. Following a methodical approach, like starting with the most complex molecule or the element that appears in the least number of compounds, helps streamline the balancing act, just as we see in the step-by-step solutions of our exercise.

Law of Conservation of Mass

The law of conservation of mass is a cornerstone of chemistry, stating that mass is neither created nor destroyed in a chemical reaction. It's the science behind balancing equations. When we balance a chemical equation, we are honoring this law by making sure that the mass (and number) of atoms for each element is conserved from reactants to products. For example, if we start with 10 grams of reactants, we should also end up with 10 grams of products.

Understanding this law is critical for everything from designing a chemical process to figuring out how much product you can make from given reactants. It is also a guiding principle that ensures scientists across the world speak the same 'chemical language' when they describe reactions and create equations.