Problem 4 - Chemistry Matter and Change

Question

Challenge Balance the following equations, and determine the possible mole ratios. \begin{equation} \begin{array}{l}{\text { a. } \mathrm{ZnO}(\mathrm{s})+\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{ZnCl}_{2}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})} \\\ {\text { b. butane }\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)+\text { oxygen } \rightarrow \text { carbon dioxide }+\text { water }}\end{array} \end{equation}

Step-by-Step Solution

Answer

a: Mole ratios 1:2:1:1. b: Mole ratios 2:13:8:10.

Step 1: Examine Reaction a

Start by writing the unbalanced chemical equation: \( \text{ZnO (s)} + \text{HCl (aq)} \rightarrow \text{ZnCl}_2 \text{(aq)} + \text{H}_2\text{O} \text{(l)} \).

Step 2: Balance Reaction a

To balance the equation, ensure that the number of atoms of each element is equal on both sides. For this reaction, balance the chlorine and hydrogen by adding a coefficient of 2 in front of \( \text{HCl} \): \( \text{ZnO (s)} + 2 \text{HCl (aq)} \rightarrow \text{ZnCl}_2 \text{(aq)} + \text{H}_2\text{O} \text{(l)} \). Now the equation is balanced.

Step 3: Determine Mole Ratios for Reaction a

The balanced equation is \( \text{ZnO (s)} + 2 \text{HCl (aq)} \rightarrow \text{ZnCl}_2 \text{(aq)} + \text{H}_2\text{O} \text{(l)} \). From this, the mole ratios are 1:2:1:1.

Step 4: Examine Reaction b

Write the unbalanced chemical equation: \( \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow \text{CO}_2 + \text{H}_2\text{O} \).

Step 5: Balance Reaction b

Balance the equation based on the number of carbon, hydrogen, and oxygen atoms. Start with carbon: Place a coefficient of 4 in front of \( \text{CO}_2 \) to balance carbon: \( \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4\text{CO}_2 + \text{H}_2\text{O} \). Next, balance hydrogen by placing a 5 in front of \( \text{H}_2\text{O} \): \( \text{C}_4\text{H}_{10} + \text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O} \). Lastly, balance oxygen by adding a coefficient of 13/2 in front of \( \text{O}_2 \): \( \text{C}_4\text{H}_{10} + \frac{13}{2} \text{O}_2 \rightarrow 4\text{CO}_2 + 5\text{H}_2\text{O} \). For whole numbers, multiply all coefficients by 2: \( 2\text{C}_4\text{H}_{10} + 13\text{O}_2 \rightarrow 8\text{CO}_2 + 10\text{H}_2\text{O} \). The equation is balanced.

Step 6: Determine Mole Ratios for Reaction b

The balanced equation is \( 2\text{C}_4\text{H}_{10} + 13\text{O}_2 \rightarrow 8\text{CO}_2 + 10\text{H}_2\text{O} \). From this, the mole ratios are 2:13:8:10.

Key Concepts

Chemical Equations

When studying chemistry, one of the foundational concepts you'll encounter is the chemical equation. A chemical equation is a symbolic representation of a chemical reaction. The substances that undergo the change are called reactants, while the substances formed as a result are called products. These are written on the left and right sides of the equation, respectively, and are separated by an arrow, indicating the direction of the reaction.

Each substance in a chemical equation is represented by its chemical formula. For example, in the equation:

• \(\text{ZnO (s)} + \text{HCl (aq)} \rightarrow \text{ZnCl}_2 \text{(aq)} + \text{H}_2\text{O} \text{(l)}\)

• \(\text{ZnO (s)}\) and \(\text{HCl (aq)}\) are the reactants
• \(\text{ZnCl}_2 \text{(aq)}\) and \(\text{H}_2\text{O} \text{(l)}\) are the products

Understanding chemical equations is crucial because they provide a lot of information about the chemical change taking place, including what substances are involved and how they interact.

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry. This process involves ensuring that the number of atoms for each element is the same on both sides of the equation. Balancing is necessary because, according to the law of conservation of mass, matter cannot be created or destroyed in a chemical reaction.

For instance, consider the reaction:

• \(\text{ZnO (s)} + \text{HCl (aq)} \rightarrow \text{ZnCl}_2 \text{(aq)} + \text{H}_2\text{O} \text{(l)}\)

Initially, this equation is not balanced. By checking the number of chlorine and hydrogen atoms, you can notice an imbalance which needs correction. By adding a coefficient of 2 in front of \(\text{HCl}\), it balances the equation as:

• \(\text{ZnO (s)} + 2\text{HCl (aq)} \rightarrow \text{ZnCl}_2 \text{(aq)} + \text{H}_2\text{O} \text{(l)}\)

Every balanced equation represents a direct reflection of the chemical change, maintaining equal mass and charge through the transformation.

Mole Ratios

In the realm of stoichiometry, mole ratios are derived from balanced chemical equations and play a critical role. They provide a quantitative relationship between the reactants and products involved in a chemical reaction. Simply put, mole ratios are the coefficients in a balanced equation which tell you how many moles of each reactant and product are involved.

From the balanced equation:

• \(\text{ZnO (s)} + 2\text{HCl (aq)} \rightarrow \text{ZnCl}_2 \text{(aq)} + \text{H}_2\text{O} \text{(l)}\)

The mole ratios are 1:2:1:1 for \(\text{ZnO}\), \(\text{HCl}\), \(\text{ZnCl}_2\), and \(\text{H}_2\text{O}\), respectively. This means that one mole of \(\text{ZnO}\) reacts with two moles of \(\text{HCl}\) to produce one mole of \(\text{ZnCl}_2\) and one mole of \(\text{H}_2\text{O}\).

Understanding and using mole ratios allows chemists to predict the amounts of substances consumed and formed and plays a crucial part in quantitative chemical analysis.

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into different substances, called products. This transformation involves the making and breaking of chemical bonds, and is represented using a chemical equation.

In the reaction between zinc oxide and hydrochloric acid, a chemical change occurs where zinc oxide and hydrochloric acid are the reactants, and zinc chloride and water are the products. During this process, the bonds within the reactants are broken, and new bonds are formed to create the products.

Chemical reactions can be characterized in several ways including:

• Exothermic or endothermic – depending on whether they release or absorb energy.
• Speed of reaction – how fast reactants are transformed into products.
• Equilibrium state – whether products revert back to reactants or not.

Understanding these transformations is critical as they explain not just basic chemical processes but also much of the biochemical activity essential for life.

As you study these reactions, remember that the essence of chemistry is understanding how different elements and compounds react and change under various conditions.