Problem 137 - General Chemistry

Question

Elemental bromine is the source of bromine compounds. The element is produced from certain brine solutions that occur naturally. These brines are essentially solutions of calcium bromide that, when treated with chlorine gas, yield bromine in a displacement reaction. What are the molecular equation and net ionic equation for the reaction? A solution containing \(40.0 \mathrm{~g}\) of calcium bromide requires \(14.2 \mathrm{~g}\) of chlorine to react completely with it, and \(22.2 \mathrm{~g}\) of calcium chloride is produced in addition to whatever bromine is obtained. How many grams of calcium bromide are required to produce \(10.0\) pounds of bromine?

Step-by-Step Solution

Answer

5675.15 grams of calcium bromide are required to produce 10.0 pounds of bromine.

Step 1: Write the Balanced Molecular Equation

First, identify the reactants and the products in the chemical reaction. The reaction involves calcium bromide (CaBr₂) and chlorine gas (Cl₂), producing bromine (Br₂) and calcium chloride (CaCl₂). The balanced molecular equation is:\[ \text{CaBr}_2 + \text{Cl}_2 \rightarrow \text{CaCl}_2 + \text{Br}_2 \]

Step 2: Write the Net Ionic Equation

The net ionic equation focuses on the species that are directly involved in the chemical change. Calcium ions (Ca²⁺) and chloride ions (Cl⁻) are spectator ions and do not participate in the reaction. Thus, the net ionic equation is:\[ 2 \text{Br}^- + \text{Cl}_2 \rightarrow \text{Br}_2 + 2 \text{Cl}^- \]

Step 3: Calculate Moles of Bromine to Be Produced

Start by converting the mass of bromine needed (10.0 pounds) to grams. Since 1 pound = 453.592 grams, calculate:\[ 10.0 \text{ pounds} \times 453.592 \text{ grams/pound} = 4535.92 \text{ grams of Br}_2 \]

Step 4: Determine Moles of Bromine Needed

Use the molar mass of Br₂ (159.808 g/mol) to find the moles of Br₂:\[ \frac{4535.92 \text{ grams}}{159.808 \text{ g/mol}} = 28.383 \text{ moles of Br}_2 \]

Step 5: Relate Moles of Calcium Bromide to Bromine

According to the balanced equation, 1 mole of CaBr₂ will produce 1 mole of Br₂. Therefore, 28.383 moles of CaBr₂ are needed to produce 28.383 moles of Br₂.

Step 6: Calculate Mass of Calcium Bromide Required

Use the molar mass of CaBr₂ (199.89 g/mol) to find the mass of CaBr₂ required:\[ 28.383 \text{ moles} \times 199.89 \text{ g/mol} = 5675.15 \text{ grams of CaBr}_2 \]

Key Concepts

Molecular Equation

A molecular equation represents all reactants and products in a chemical reaction as intact compounds. It is a complete depiction of the chemical reaction as it would appear in a solution. In a molecular equation:

• Each compound is shown as a complete formula.
• No ions are separated, even if they are soluble in water.
• The equation highlights the reactants and products without changing their chemical identities.

In the displacement reaction of calcium bromide with chlorine gas, the molecular equation is expressed as:\[\text{CaBr}_2 + \text{Cl}_2 \rightarrow \text{CaCl}_2 + \text{Br}_2\]This equation tells us which chemicals were present at the start (calcium bromide and chlorine gas) and what products are formed (calcium chloride and bromine). It helps in understanding the overall chemical change happening during the reaction.
Understanding molecular equations is important as they set the groundwork for deriving other equations like the net ionic equation.

Net Ionic Equation

A net ionic equation simplifies the chemical equation by removing spectator ions. Spectator ions are ions that do not participate in the chemical reaction and remain unchanged on both sides of the equation. The net ionic equation highlights the process of the reaction by focusing on the ions that undergo change.

• The net ionic equation only includes the ions and molecules directly involved in the reaction.
• Spectator ions are omitted for clarity.
• This equation is particularly useful for understanding the actual chemical change at the molecular level.

In our reaction, calcium ions \(\text{Ca}^{2+}\) and chloride ions \(\text{Cl}^-\) are spectators. Thus, the net ionic equation for the reaction is:\[2 \text{Br}^- + \text{Cl}_2 \rightarrow \text{Br}_2 + 2 \text{Cl}^-\]This equation shows that bromide ions react with chlorine gas to form bromine molecules and chloride ions.
Understanding net ionic equations helps to grasp how ions interact in a solution, offering insight into the driving forces behind chemical reactions.

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It is essential for predicting the amount of products formed or determining the quantity of reactants needed.

• Uses mole ratios from the balanced equation to convert between products and reactants.
• Helps determine the exact amount of reactants required or products formed.
• Involves converting between grams, moles, and molecules.

In the exercise, stoichiometry is applied to determine the moles and mass of calcium bromide needed to produce a certain mass of bromine. By using the mole ratio from the balanced equation \((1 \text{ mole CaBr}_2 : 1 \text{ mole Br}_2)\), we relate the moles of calcium bromide to bromine. After converting mass to moles, stoichiometry allows the transition from the theoretical concept of moles to practical quantities like grams or liters.
Through stoichiometry, chemists can scale reactions for practical applications such as manufacturing compounds or analyzing reaction yields.

Balanced Chemical Equation

A balanced chemical equation ensures that the law of conservation of mass is respected during a chemical reaction. It demonstrates that the same number of atoms of each element is present on both sides of the equation. Balancing a chemical equation involves:

• Adjusting coefficients in front of the chemical formulas.
• Ensuring each type of atom is equally represented among reactants and products.
• Maintaining the charge balance in ionic reactions.

In the given reaction, the balanced chemical equation is:\[\text{CaBr}_2 + \text{Cl}_2 \rightarrow \text{CaCl}_2 + \text{Br}_2\]Here, each atom type (Ca, Br, and Cl) appears exactly the same number of times on both sides of the equation, ensuring the mass is conserved. Balancing involves simple arithmetic to ensure that total atoms of each element are equal on both sides of the equation.
A balanced equation is fundamental for calculating quantities in stoichiometry, as it provides the mole ratios needed for converting between amounts of reactants and products.