Problem 85 - General Chemistry: Principles and Modern Applications

Question

A 2.50 g sample of \(\mathrm{Ag}_{2} \mathrm{SO}_{4}(\mathrm{s})\) is added to a beaker containing 0.150 L of 0.025 M BaCl\(_2\) (a) Write an equation for any reaction that occurs. (b) Describe the final contents of the beaker- -that is, the masses of any precipitates present and the concentrations of the ions in solution.

Step-by-Step Solution

Answer

The balanced chemical reaction is \(Ag_2SO_4 + BaCl_2 \rightarrow 2AgCl (\downarrow) + BaSO_4 (\downarrow)\). The precipitates formed are AgCl and BaSO4 with masses 1.074 g and 0.875 g respectively. The Ag and SO4 ions have a concentration of 0 M in the solution while Ba and Cl ions are present in the excess Ag2SO4.

Step 1: Write the Balanced Chemical Reaction

When Ag2SO4 and BaCl2 react, they undergo a double replacement reaction. In this reaction, the silver (Ag) ions react with the chloride (Cl) ions, and the barium (Ba) ions react with the sulfate (SO4) ions. This reaction can be written as follows: \[ Ag_2SO_4 + BaCl_2 \rightarrow 2AgCl (\downarrow) + BaSO_4 (\downarrow) \] (^) The down arrow indicates that the product is a precipitate. The equation is already balanced, so it's not necessary to add any coefficients.

Step 2: Identify the Limiting Reagent

This step involves finding the limiting reagent which will determine how much precipitate (product) can be formed. The number of moles of each reactant can be calculated using the given quantities. The number of moles of Ag2SO4 is \(\frac{2.50 g}{331.8 g/mol} = 0.0075 mol\). Since the BaCl2 solution is 0.025 M and has a volume of 0.150 L, the moles of BaCl2 can be calculated as \((0.025 mol/L) \times 0.150 L = 0.00375 mol\). As the reaction ratio of Ag2SO4 to BaCl2 is 1:1, it's clear that BaCl2 is the limiting reagent because there are fewer moles of it.

Step 3: Compute the Mass and Concentration of the Precipitates

Using the molar ratios from the chemical equation, the amount of precipitates formed can be computed. For every mole of BaCl2, 2 moles of AgCl and 1 mole of BaSO4 are produced. Therefore, given that there are 0.00375 moles of BaCl2, there will be 0.00375 moles of BaSO4 and 0.0075 moles of AgCl produced. The masses of these substances can be computed by multiplying by the respective molar mass: For BaSO4, 0.00375 moles * (233.4 g/mol) = 0.875 g; and for AgCl, 0.0075 moles * (143.3 g/mol) = 1.074 g. The concentration of the ions in solution should be 0 for Ag and SO4 ions as all have reacted to form precipitates. Ba and Cl ions only remain in the excess reagent Ag2SO4, with concentration equal to (initial concentration - consumed concentration).

Step 4: Describe the Solution and Final Contents of the Beaker

From the computed data, the final content of the beaker is as follow: the precipitates are AgCl and BaSO4 with masses 1.074 g and 0.875 g respectively, the concentrations of the Ag and SO4 ions in the solution are 0 M, and the concentrations of the Ba and Cl ions are present in the excess Ag2SO4.

Key Concepts

Chemical Equation Balancing

Balancing a chemical equation is essential to understand and predict the outcome of a chemical reaction. For a double replacement reaction like the one between silver sulfate \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) and barium chloride \(\mathrm{BaCl}_{2}\), we swap the ions to form new compounds. This specific reaction creates two new products: silver chloride \(\mathrm{AgCl}\) and barium sulfate \(\mathrm{BaSO}_{4}\).
The balanced equation is:\[\mathrm{Ag}_{2} \mathrm{SO}_{4} + \mathrm{BaCl}_{2} \rightarrow 2\mathrm{AgCl} \downarrow + \mathrm{BaSO}_{4} \downarrow\]The equation shows all reactants and products with a 1:1 ratio, meaning one mole of \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) reacts with one mole of \(\mathrm{BaCl}_{2}\). This is fundamental because it helps us determine how much of each substance is involved in the reaction, ensuring matter is neither created nor destroyed as per the Law of Conservation of Mass. Symbols like the downward arrow indicate the formation of a solid precipitate, which aids in visualizing the reaction's result.

Limiting Reagent

The concept of a limiting reagent is crucial in chemistry as it determines the maximum amount of product that can be formed in a reaction. When \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) and \(\mathrm{BaCl}_{2}\) react, we need to identify which reactant runs out first.

Given:

• Moles of \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\): \(0.0075\) mol
• Moles of \(\mathrm{BaCl}_{2}\): \(0.00375\) mol

Since they react in a 1:1 ratio, clearly, \(\mathrm{BaCl}_{2}\) is the limiting reagent with fewer moles available. This means it will be completely consumed before \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) is used up, dictating the amount of precipitate formed. Understanding which reactant is the limiting one helps us calculate how much product is formed and identify the leftover substances.

Precipitate Formation

In many reactions, especially double replacement reactions, precipitates are formed. A precipitate is a solid that emerges from a liquid solution during a chemical reaction. When mixing \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) and \(\mathrm{BaCl}_{2}\), silver ions bond with chloride ions to form silver chloride, \(\mathrm{AgCl}\), and barium ions bond with sulfate ions to form barium sulfate, \(\mathrm{BaSO}_{4}\).

Both \(\mathrm{AgCl}\) and \(\mathrm{BaSO}_{4}\) are insoluble in water and appear as solids, which is shown by the down arrow in the equation.

• Mass of \(\mathrm{BaSO}_{4}\): \(0.875\, g\)
• Mass of \(\mathrm{AgCl}\): \(1.074\, g\)

These precipitates are evidence of a chemical reaction occurring. Identifying them helps to confirm whether the expected reaction takes place and provides insight into the reaction's progress and completeness.

Ion Concentration

Ion concentration in a solution provides information about how much of each ion remains after a reaction has taken place. Initially, solutions contain dissolved ions, but after the double replacement reaction between \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) and \(\mathrm{BaCl}_{2}\), most ions form solid precipitates and are thus removed from the solution.

After the reaction:

• Concentration of \(\mathrm{Ag}^{+}\) and \(\mathrm{SO}_{4}^{2-}\) ions is \(0 \, M\) as they form insoluble precipitates.
• Any unreacted ions from excess \(\mathrm{Ag}_{2} \mathrm{SO}_{4}\) would retain original concentrations minus those used to form precipitates.

Understanding ion concentration is vital for predicting not only the course of reactions but also for processes such as titrations and balancing chemical reactions in aqueous conditions. Monitoring changes in ion concentration allows us to control the reaction environment effectively.