Question

Atoms of three different elements are represented by \(\mathrm{O}, \square\), and \(\Delta\). Which compound is left over when three molecules of \(\mathrm{O} \Delta\) and three molecules of \(\square \square \Delta\) react to form \(\mathrm{O} \square \Delta\) and \(\mathrm{O} \Delta \Delta ?\)

Short answer

The leftover compound after the reaction is \(\mathrm{O}\Delta\).

Step-by-step solution

Write down the unbalanced equation

Write down the given reactants and products without worrying about balancing them: $$\text{3}\mathrm{O} \Delta + \text{3}\square \square \Delta \rightarrow \mathrm{O}\square \Delta + \mathrm{O} \Delta \Delta$$

Count the number of atoms of each element on both sides

Count the numbers of \(\mathrm{O}\), \(\square\), and \(\Delta\) atoms on both sides of the equation: Left side (Reactants): - \(\mathrm{O} \Delta\) contains 3 \(\mathrm{O}\) atoms and 3 \(\Delta\) atoms - \(\square \square \Delta\) contains 6 \(\square\) atoms and 3 \(\Delta\) atoms - Total: 3 \(\mathrm{O}\) atoms, 6 \(\square\) atoms, and 6 \(\Delta\) atoms Right side (Products): - \(\mathrm{O}\square \Delta\) contains 1 \(\mathrm{O}\) atom, 1 \(\square\) atom, and 1 \(\Delta\) atom - \(\mathrm{O} \Delta \Delta\) contains 1 \(\mathrm{O}\) atom, and 2 \(\Delta\) atoms - Total: 2 \(\mathrm{O}\) atoms, 1 \(\square\) atom, and 3 \(\Delta\) atoms

Balance the equation

Since the equation is not balanced, let's balance it by adding coefficients to the products: $$\text{3}\mathrm{O} \Delta+\text{3}\square \square \Delta\rightarrow\text{2}\mathrm{O}\square \Delta +\text{2}\mathrm{O} \Delta \Delta$$ Now, let's again count the atoms on both sides: Left side (Reactants): 3 \(\mathrm{O}\) atoms, 6 \(\square\) atoms, 6 \(\Delta\) atoms Right side (Products): 4 \(\mathrm{O}\) atoms, 2 \(\square\) atoms, 6 \(\Delta\) atoms The equation is still not balanced. We have an excess of \(\mathrm{O}\) atoms on the right and an excess of \(\square\) atoms on the left. To balance the \(\mathrm{O}\) atoms, we can add a molecule of \(\mathrm{O}\Delta\) on the right side: $$\text{3}\mathrm{O} \Delta+\text{3}\square \square \Delta\rightarrow \text{2}\mathrm{O}\square \Delta+\text{2}\mathrm{O} \Delta \Delta+\mathrm{O}\Delta$$ Now, the number of atoms for each element is: Left side (Reactants): 3 \(\mathrm{O}\) atoms, 6 \(\square\) atoms, 6 \(\Delta\) atoms Right side (Products): 6 \(\mathrm{O}\) atoms, 2 \(\square\) atoms, 8 \(\Delta\) atoms In order to balance the \(\square\) atoms, we can add two molecules of \(\square\square\Delta\) on the right side: $$\text{3}\mathrm{O} \Delta+\text{3}\square \square \Delta\rightarrow \text{2}\mathrm{O}\square \Delta+\text{2}\mathrm{O} \Delta \Delta+\mathrm{O}\Delta+\text{2}\square\square\Delta$$ Finally, we have 8 \(\Delta\) atoms on both sides, and the balanced equation is: $$\text{3}\mathrm{O} \Delta+\text{3}\square \square \Delta\rightarrow \text{2}\mathrm{O}\square \Delta+\text{2}\mathrm{O} \Delta \Delta+\mathrm{O}\Delta+\text{2}\square\square\Delta$$ Now, the number of atoms for each element is: Left side (Reactants): 3 \(\mathrm{O}\) atoms, 6 \(\square\) atoms, 6 \(\Delta\) atoms Right side (Products): 6 \(\mathrm{O}\) atoms, 6 \(\square\) atoms, 6 \(\Delta\) atoms

Identify the leftover compound

From the balanced equation, we can see that the compound that is left over after the reaction is: $$\boxed{\mathrm{O}\Delta}$$

Key concepts

Chemical Equation

The chemical equation is essentially a recipe for a chemical reaction. It shows which substances react (reactants) and which substances are produced (products). Similar to how a cooking recipe specifies the amounts of each ingredient and the final dish, a chemical equation lists the molecules involved and predicts the outcome of their interactions.

Writing down an unbalanced chemical equation is the first step in understanding a reaction. For example, if we have molecules of \(\mathrm{O} \Delta\) and \(\square \square \Delta\) as reactants and \(\mathrm{O}\square \Delta\) and \(\mathrm{O} \Delta \Delta\) as products, we write the equation as \(3\mathrm{O} \Delta + 3\square \square \Delta \rightarrow \mathrm{O}\square \Delta + \mathrm{O} \Delta \Delta\) even though it is unbalanced. The next task is to balance this equation to comply with the conservation of mass—the number of atoms of each element needs to be equal on both sides of the equation.

Stoichiometry

Stoichiometry is the method used to determine what amount of substances are consumed and produced in a given reaction. It deals with the calculation of the quantities of reactants and products, often utilizing the mole concept for these calculations. In our chemical reaction, stoichiometry will guide us to balance the equation according to the quantities of each reactant needed and each product formed.

Following the initial steps to balance our example equation requires adjusting coefficients—the numbers placed before molecules to indicate how many units of each are involved. These coefficients are the key to stoichiometry in chemical equations. They must be integers, and while balancing the equation, we adjust these coefficients so that the numbers of each type of atom on both sides of the reaction are the same.

Conservation of Mass

The conservation of mass is a fundamental principle in chemistry stating that mass is neither created nor destroyed in a chemical reaction. Therefore, the mass of the reactants must equal the mass of the products. In terms of a chemical equation, this means that the number of atoms for each element must be the same on both sides of the equation.

In our chemical reaction, we balance the equation to respect the conservation of mass. Initially, we have 3 \(\mathrm{O}\) atoms on the left but only 2 on the right, along with imbalances in \(\square\) and \(\Delta\) atoms. We adjust the coefficients until the mass is conserved, leading to an equal number of atoms on both sides.

Mole Concept

The mole concept is a bridge between the microscopic world of atoms and the macroscopic world we live in. It allows chemists to count atoms by weighing, which makes laboratory work feasible. One mole is Avogadro's number (approximately \(6.022 \times 10^{23}\)) of particles, whether they're atoms, ions, or molecules.

For our sample reaction, after achieving a balanced chemical equation, we can use the mole concept to determine the amount of each substance needed. For instance, if we need to know how many grams of \(\mathrm{O}\Delta\) are needed to completely react with \(\square \square \Delta\), we would convert the moles of \(\mathrm{O}\Delta\) indicated by the balanced equation into grams using its molar mass.