Problem 49 - Chemistry and Chemical Reactivity

Question

When solutions of \(\mathrm{BaCl}_{2}\) and \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) are mixed, the mixture becomes cloudy. After a few days, a white solid is observed on the bottom of the beaker with a clear liquid above it. (a) Write a balanced equation for the reaction that occurs. (b) Why is the solution cloudy at first? (c) What happens during the few days of waiting?

Step-by-Step Solution

Answer

(a) \( \mathrm{BaCl}_{2} + \mathrm{Na}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{BaSO}_{4} + 2\mathrm{NaCl} \). (b) Cloudiness is due to insoluble \( \mathrm{BaSO}_{4} \) precipitate. (c) \( \mathrm{BaSO}_{4} \) settles, leaving clear liquid above.

Step 1: Identify the Reactants and Products

The solutions of \( \mathrm{BaCl}_{2} \) and \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) react. One of the products is \( \mathrm{BaSO}_{4} \), a solid, while the other is \( \mathrm{NaCl} \), remaining in solution. The chemical reaction is a double displacement reaction.

Step 2: Write the Unbalanced Reaction Equation

From the reactants and products, we establish: \( \mathrm{BaCl}_{2} + \mathrm{Na}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{BaSO}_{4} + \mathrm{NaCl} \)

Step 3: Balance the Chemical Equation

To balance the equation, ensure equal numbers of each type of atom on both sides:\[ \mathrm{BaCl}_{2} + \mathrm{Na}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{BaSO}_{4} + 2\mathrm{NaCl} \] This shows that you need two moles of NaCl for every mole of \( \mathrm{BaCl}_{2} \) and \( \mathrm{Na}_{2} \mathrm{SO}_{4} \).

Step 4: Explain Initial Cloudiness

The cloudiness occurs because \( \mathrm{BaSO}_{4} \) is a precipitate, which means it forms as an insoluble solid in the liquid mixture, causing the cloudy appearance.

Step 5: Describe the Change Over Time

Over a few days, the white solid \( \mathrm{BaSO}_{4} \) settles at the bottom because it's denser than the solution. This leaves a clear liquid above the precipitate.

Key Concepts

Chemical Equation Balancing

Balancing a chemical equation is crucial because it represents the conservation of mass in a chemical reaction. It ensures that the same number of each type of atom is present on both sides of the equation, aligning with the law of conservation of matter. To balance the equation for the reaction between barium chloride (\( \mathrm{BaCl}_{2} \)) and sodium sulfate (\( \mathrm{Na}_{2} \mathrm{SO}_{4} \)), start by writing the reactants and products.- The reactants are \( \mathrm{BaCl}_{2} \) and \( \mathrm{Na}_{2} \mathrm{SO}_{4} \).- The products are \( \mathrm{BaSO}_{4} \) and \( \mathrm{NaCl} \).The unbalanced chemical equation is:\[ \mathrm{BaCl}_{2} + \mathrm{Na}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{BaSO}_{4} + \mathrm{NaCl} \]To balance it, notice that the chlorine atoms and sodium atoms are unequal:

• You have 2 sodium atoms in the reactants (\( \mathrm{Na}_{2} \)), so you need 2 sodium atoms in the products (\( 2\mathrm{NaCl} \)).
• Adjust for the chlorine atoms accordingly, resulting in the balanced equation:\[ \mathrm{BaCl}_{2} + \mathrm{Na}_{2} \mathrm{SO}_{4} \rightarrow \mathrm{BaSO}_{4} + 2\mathrm{NaCl} \]

This equation is now balanced, confirming that both mass and charge are conserved in the reaction.

Double Displacement Reaction

A double displacement reaction, also known as a metathesis reaction, involves the exchange of ions between two reacting compounds to form new compounds. In these reactions, the cations and anions swap places, leading to the formation of two new products.For the reaction between \( \mathrm{BaCl}_{2} \) and \( \mathrm{Na}_{2} \mathrm{SO}_{4} \), the double displacement process unfolds as follows:- Barium (\( \mathrm{Ba}^{2+} \)) ions from \( \mathrm{BaCl}_{2} \) combine with sulfate (\( \mathrm{SO}_{4}^{2-} \)) ions from \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) to form \( \mathrm{BaSO}_{4} \), a precipitate.- At the same time, sodium (\( \mathrm{Na}^{+} \)) ions from \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) bond with chloride (\( \mathrm{Cl}^{-} \)) ions from \( \mathrm{BaCl}_{2} \) to form sodium chloride (\( 2\mathrm{NaCl} \))) in the solution.This ion exchange is characteristic of double displacement reactions, where the driving force is often the formation of a precipitate, like \( \mathrm{BaSO}_{4} \) in this case.

Precipitation Process

The precipitation process is an essential phenomenon in this reaction. A precipitate is an insoluble solid that emerges from a liquid solution. The driving force behind the formation of a precipitate can include saturation, temperature changes, or the presence of specific reactants.In the reaction we are considering, barium sulfate (\( \mathrm{BaSO}_{4} \)) serves as the precipitate. Here’s why the process occurs:- When \( \mathrm{BaCl}_{2} \) and \( \mathrm{Na}_{2} \mathrm{SO}_{4} \) solutions mix, \( \mathrm{BaSO}_{4} \) forms because it is insoluble in water. - Initially, tiny particles of \( \mathrm{BaSO}_{4} \) give the solution a cloudy appearance as they disperse.Over time, these particles aggregate and settle due to gravity, forming a layer of solid at the bottom of the beaker. This settling process is natural for many precipitates and results in the clear liquid observed above the solid after a few days. This visible separation is key to understanding the complete precipitation process.