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Chapter 16: Problem 137

Consider saturated solutions of the slightly soluble salts \(\mathrm{AgBr}\) and \(\mathrm{BaCO}_{3}\) (a) Is the solubility of AgBr increased, decreased, or unaffected by the addition of each of the following substances? (i) \(\mathrm{HBr}\) (ii) \(\mathrm{HNO}_{3}\) (iii) \(\mathrm{AgNO}_{3}\) (iv) \(\mathrm{NH}_{3}\) (b) Is the solubility of \(\mathrm{BaCO}_{3}\) increased, decreased, or unaffected by the addition of each of the following substances? (i) \(\mathrm{HNO}_{3}\) (ii) \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2}\) (iii) \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) (iv) \(\mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H}\)

Short Answer

Expert verified
(a) (i) Decreased, (ii) Unaffected, (iii) Decreased, (iv) Increased; (b) (i) Increased, (ii) Decreased, (iii) Decreased, (iv) Slightly increased.

Step by step solution

01

Understanding Solubility Product

Solubility is affected by the common ion effect, complex ion formation, and changes in pH. The solubility product constant ( K_{sp} ) affects the dissolution and precipitation of slightly soluble salts.
02

Solubility of AgBr: Addition of HBr

HBr adds Br⁻ ions to the solution, increasing the concentration of Br⁻. According to Le Chatelier's principle and the common ion effect, this will decrease the solubility of AgBr since the equilibrium will shift towards the precipitation of AgBr.
03

Solubility of AgBr: Addition of HNO3

HNO₃ is an acidic compound that does not add any common ions with AgBr. However, a very low pH can increase AgBr solubility by converting Br⁻ into HBr (which is theoretically negligible here). Thus, its main effect could be negligible under normal conditions.
04

Solubility of AgBr: Addition of AgNO3

Adding AgNO₃ increases the concentration of the common ion Ag⁺ in the solution. This will decrease the solubility of AgBr due to the common ion effect, shifting the equilibrium to favor AgBr precipitation.
05

Solubility of AgBr: Addition of NH3

Ammonia (NH₃) forms a complex ion with silver, Ag(NH₃)₂⁺, which reduces the concentration of Ag⁺ ions in solution. This reduces the common ion effect and increases the solubility of AgBr.
06

Solubility of BaCO3: Addition of HNO3

HNO₃ being an acid, reacts with carbonate ions (CO₃²⁻) to form CO₂ gas and water, lowering the CO₃²⁻ concentration. This increases the solubility of BaCO₃.
07

Solubility of BaCO3: Addition of Ba(NO3)2

Adding Ba(NO₃)₂ increases the concentration of the common ion Ba²⁺. The common ion effect reduces BaCO₃ solubility by shifting the equilibrium towards BaCO₃ precipitation.
08

Solubility of BaCO3: Addition of Na2CO3

The addition of Na₂CO₃ increases CO₃²⁻ ions in the solution. This will decrease the solubility of BaCO₃ due to the common ion effect, favoring precipitation.
09

Solubility of BaCO3: Addition of CH3CO2H

Acetic acid (CH₃COOH) is a weak acid that will increase solubility slightly by slowly reacting with CO₃²⁻ ions. However, its effect is less significant compared to strong acids like HNO₃.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Common Ion Effect
The common ion effect is a powerful concept in chemistry that plays a crucial role in influencing the solubility of salts. It occurs when a salt's solubility is reduced by the presence of a common ion added to the solution. This happens because adding an ion that is already part of the salt formula shifts the equilibrium of dissolving back towards the solid form.

For example, consider the addition of HBr to a saturated AgBr solution. HBr dissociates to provide Br⁻ ions, increasing their concentration in the solution. As a result, the solubility of AgBr decreases because the equilibrium shifts towards forming more solid AgBr. This phenomenon is also observed with BaCO₃ when Ba(NO₃)₂ is added. The Ba²⁺ ions from Ba(NO₃)₂ increase the concentration of Ba²⁺ in the solution, diminishing the solubility of BaCO₃.

To understand the common ion effect, remember:
  • It involves ions that are part of the salt's formula.
  • Increased common ion concentration shifts equilibrium towards precipitation.
  • It reduces the solubility of the salt.
Grasping this effect helps predict changes in solubility when solutions of ionic compounds are changed by adding other compounds.
Le Chatelier's Principle
Le Chatelier's Principle is an essential concept in understanding how systems at equilibrium respond to external changes. It states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium moves to counteract the change and re-establish equilibrium.

In the context of solubility, when you add a substance like AgNO₃ to a solution of AgBr, you increase the concentration of the Ag⁺ ions. According to Le Chatelier's Principle, the equilibrium will shift to decrease the concentration of Ag⁺ by favoring the formation of solid AgBr, leading to a reduction in solubility. Similarly, for BaCO₃, adding Ba(NO₃)₂ increases Ba²⁺ ions, causing a shift towards solid formation to counter the change.

Key aspects include:
  • This principle helps predict the direction of shift in equilibrium in response to changes.
  • It's crucial for understanding how and why solubility changes occur.
  • It applies to shifts caused by concentrations, pressure, temperature, etc.
Thus, Le Chatelier’s Principle is a guiding light in predicting the effects of adding ions or other changes on the solubility of compounds.
Solubility Product Constant (Ksp)
The solubility product constant ( K_{sp} ) is a fundamental concept when discussing the solubility of sparingly soluble salts. It is an expression of the product of the concentrations of the ions that are formed when a salt dissolves in water, each raised to the power of their stoichiometric coefficients. This constant is unique for every salt and dictates how much of the salt can dissolve in a solution before it precipitates.

Consider AgBr, a salt with a low K_{sp} value. This means only a small amount of AgBr can dissolve in water. When you add substances with common ions, the equilibrium of dissolving AgBr adjusts so that K_{sp} remains met, often leading to precipitation. For example, when AgNO₃, containing Ag⁺ ions, is added, these extra ions mean less AgBr can dissolve, as the K_{sp} must not be exceeded.

Important points about K_{sp} include:
  • It represents the saturation point for sparingly soluble salts.
  • A specific value unique to each salt, dictating its solubility under given conditions.
  • K_{sp} helps determine whether a salt will precipitate or remain dissolved when various ions are present in the solution.
Understanding K_{sp} allows for the anticipation of solubility changes in response to different conditions or chemical additions.

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Most popular questions from this chapter

Consider the titration of \(100.0 \mathrm{~mL}\) of \(0.016 \mathrm{M} \mathrm{HOCl}\left(K_{\mathrm{a}}=3.5 \times 10^{-8}\right)\) with \(0.0400 \mathrm{M} \mathrm{NaOH} .\) How many milliliters of \(0.0400 \mathrm{M} \mathrm{NaOH}\) are required to reach the equivalence point? Calculate the \(\mathrm{pH}\) : (a) After the addition of \(10.0 \mathrm{~mL}\) of \(0.0400 \mathrm{M} \mathrm{NaOH}\) (b) Halfway to the equivalence point (c) At the equivalence point (d) The following acid-base indicators change color in the indicated \(\mathrm{pH}\) ranges: bromthymol blue \((6.0-7.6)\), thymolphthalein \((9.4-10.6)\), and alizarin yellow \((10.1-12.0)\). Which indicator is best for the titration? Which indicator is unacceptable?

The equivalence point was reached in titrations of three unknown bases at \(\mathrm{pH} 5.53\) (base A), \(4.11\) (base B), and \(6.00\) (base C). (a) Which is the strongest base? (b) Which is the weakest base?

Explain why the uptake of \(\mathrm{CO}_{3}{ }^{2-}\) by calcifying marine organisms causes more \(\mathrm{CO}_{2}\) to dissolve in the ocean than in pure water.

(a) Calculate the change in \(\mathrm{pH}\) when \(0.002 \mathrm{~mol}\) of \(\mathrm{HNO}_{3}\) is added to \(0.100 \mathrm{~L}\) of a buffer solution that is \(0.050 \mathrm{M}\) in \(\mathrm{HF}\) and \(0.100 \mathrm{M}\) in \(\mathrm{NaF}\). (b) Will the pH change if the solution is diluted by a factor of \(2 ?\)

In qualitative analysis, \(\mathrm{Ca}^{2+}\) and \(\mathrm{Ba}^{2+}\) are separated from \(\mathrm{Na}^{+}, \mathrm{K}^{+}\), and \(\mathrm{Mg}^{2+}\) by adding aqueous \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\) to a solution that also contains aqueous \(\mathrm{NH}_{3}\) (Figure 16.18). Assume that the concentrations after mixing are \(0.080 \mathrm{M}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3}\) and \(0.16 \mathrm{M} \mathrm{NH}_{3}\). (a) List all the Brønsted-Lowry acids and bases present initially, and identify the principal reaction. (b) Calculate the \(\mathrm{pH}\) and the concentrations of all species present in the solution. (c) In order for the human eye to detect the appearance of a precipitate, a very large number of ions must come together to form solid particles. For this and other reasons, the ion product must often exceed \(K_{\mathrm{sp}}\) by a factor of about \(10^{3}\) before a precipitate can be detected in a typical qualitative analysis experiment. Taking this fact into account, show quantitatively that the \(\mathrm{CO}_{3}{ }^{2-}\) concentration is large enough to give observable precipitation of \(\mathrm{CaCO}_{3}\) and \(\mathrm{BaCO}_{3}\), but not \(\mathrm{MgCO}_{3}\). Assume that the metal-ion concentrations are \(0.010 \mathrm{M}\). (d) Show quantitatively which of the \(\mathrm{Mg}^{2+}, \mathrm{Ca}^{2+}\), and \(\mathrm{Ba}^{2+}\) ions, if any, should give an observable precipitate of the metal hydroxide. (e) Could the separation of \(\mathrm{Ca}^{2+}\) and \(\mathrm{Ba}^{2+}\) from \(\mathrm{Mg}^{2+}\) be accomplished using \(0.80 \mathrm{M} \mathrm{Na}_{2} \mathrm{CO}_{3}\) in place of \(0.080 \mathrm{M}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_{3} ?\) Show quantitatively why or why not.
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