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What is the maximum possible concentration of \(\mathrm{Ni}^{2+}\) ion in water at \(25^{\circ} \mathrm{C}\) that is saturated with \(0.10 \mathrm{M} \mathrm{H}_{2} \mathrm{S}\) and maintained at \(\mathrm{pH} 3.0\) with HCl?What is the maximum possible concentration of \(\mathrm{Ni}^{2+}\) ion in water at \(25^{\circ} \mathrm{C}\) that is saturated with \(0.10\) \(M\) \(\mathrm{H}_{2} \mathrm{S}\) and maintained at \(\mathrm{pH} 3.0\) with \(\mathrm{HCl}\)?

Short Answer

Expert verified
The maximum possible concentration of Ni虏鈦 ion in water at 25掳C that is saturated with 0.10 M H鈧係 and maintained at pH 3.0 with HCl is 3.3 x 10鈦烩伌 M.

Step by step solution

01

Finding the [H鈦篯 concentration *at equilibrium*

Given that the pH of the solution is 3.0, we can calculate the [H鈦篯 concentration using the pH formula: pH = -log10[H鈦篯 3.0 = -log10[H鈦篯 Solving for [H鈦篯: [H鈦篯 = 10鈦宦矼
02

Calculating the [HS鈦籡 concentration at equilibrium

Using the Ka1 value and the equilibrium expression for H鈧係: Ka1 = [H鈦篯[HS鈦籡 / [H鈧係] Rearranging to solve for [HS鈦籡: [HS鈦籡 = (Ka1 * [H鈧係]) / [H鈦篯 Plugging in the given values for [H鈧係] = 0.10M and [H鈦篯 = 10鈦宦矼: [HS鈦籡 = (9.1 x 10鈦烩伕 * 0.10) / 10鈦宦 [HS鈦籡 = 9.1 x 10鈦烩伓M
03

Calculating the [S虏鈦籡 concentration at equilibrium

Using the Ka2 value and the equilibrium expression for HS鈦: Ka2 = [H鈦篯[S虏鈦籡 / [HS鈦籡 Rearranging to solve for [S虏鈦籡: [S虏鈦籡 = (Ka2 * [HS鈦籡) / [H鈦篯 Plugging in the calculated [HS鈦籡 = 9.1 x 10鈦烩伓M and [H鈦篯 = 10鈦宦矼: [S虏鈦籡 = (1.0 x 10鈦宦孤 * 9.1 x 10鈦烩伓) / 10鈦宦 [S虏鈦籡 = 9.1 x 10鈦宦光伆M
04

Finding the maximum possible concentration of Ni虏鈦

Now, we use the Ksp value and the equilibrium expression for NiS: Ksp = [Ni虏鈦篯[S虏鈦籡 Rearranging to solve for [Ni虏鈦篯: [Ni虏鈦篯 = Ksp / [S虏鈦籡 Plugging in the calculated [S虏鈦籡 = 9.1 x 10鈦宦光伆M and Ksp = 3.0 x 10鈦宦孤: [Ni虏鈦篯 = (3.0 x 10鈦宦孤) / (9.1 x 10鈦宦光伆) [Ni虏鈦篯 = 3.3 x 10鈦烩伌M So, the maximum possible concentration of Ni虏鈦 ion in water at 25掳C that is saturated with 0.10 M H鈧係 and maintained at pH 3.0 with HCl is 3.3 x 10鈦烩伌 M.

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Key Concepts

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

Ni虏鈦 Ion Concentration
Ni虏鈦 ion concentration in a solution can be influenced by various factors, such as the presence of other ions and the pH level of the solution.
The exercise challenges us to find the maximum concentration of nickel ions ( Ni虏鈦 ) in a saturated environment where hydrogen sulfide ( H鈧係 ) is present.
In such scenarios, understanding the solubility equilibrium becomes crucial.
Sulfide ions ( S虏鈦 ) , which result from dissolved H鈧係 in the water, play an important role in determining the nickel ion concentration.

By calculating the concentrations of HS鈦 and S虏鈦 ions through their equilibrium expressions involving their respective dissociation constants, we get the necessary details to find the Ni虏鈦 concentration using the solubility product constant ( K_{sp} ) .
  • This involves calculating the S虏鈦 ion concentration, which is vital due to its direct relation with Ni虏鈦 in the solubility product ( Ksp ) expression of NiS compound.
  • A higher S虏鈦 concentration would imply a lower maximum Ni虏鈦 that can exist in water before precipitation occurs, as a result of the equilibrium constraints detailed by K_{sp} .
This principle of equilibria allows chemists to predict and control the ion concentrations in a solution, preventing undesirable precipitations.
pH Calculation
Calculating the pH of a solution is a fundamental skill in chemistry, reflecting the acidic or basic nature of the solution.
In this exercise, the solution is maintained at a pH of 3.0, indicating a relatively acidic solution.
The pH is calculated using the formula defined by pH = -log_{10}[ H鈦篯 .

Since pH is easily found or given, it is useful to derive the H鈦 concentration from it whenever necessary.
  • For example, a pH of 3.0 gives us H鈦 concentration as 10^{-3} M, depicting a considerable amount of acidic character.
  • It's important to understand how pH influences solubility rates and equilibria by altering ion concentrations in the solution, particularly for complex equilibria like the one in this example with nickel and sulfide.
Being able to manipulate pH provides control over chemical reactions and equilibria in a solution, an essential aspect in both academic and industrial chemistry applications.
Ksp Value
The solubility product constant, Ksp, defines the point at which a solute will precipitate from a solution, making it a critical aspect when discussing chemical equilibria.
For this problem, the Ksp value of NiS represents the equilibrium between dissolved Ni虏鈦 and S虏鈦 ions in the saturated solution.
  • Given as 3.0 脳 10^{-13}, this value shows how sparingly soluble NiS is in the environment.
  • Higher values of Ksp would indicate greater solubility and thus, higher concentrations of Ni虏鈦 in the solution are possible without triggering precipitation.
The calculation involves solving the expression Ksp = [Ni虏鈦篯[S虏鈦籡 for Ni虏鈦 by substituting known Ksp and calculated S虏鈦 values.
This allows determining the maximum permissible Ni虏鈦 in solution, providing insights into the solubility limits imposed by the system's conditions. By mastering the use of Ksp values, you can predict how compounds will behave in different solutions, a useful tool in many fields of science and engineering.

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