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Chapter 19: Problem 110

Calculate the pressure of \(\mathrm{H}_{2}\) (in atm) required to maintain equilibrium with respect to the following reaction at \(25^{\circ} \mathrm{C}\) : $$ \mathrm{Pb}(s)+2 \mathrm{H}^{+}(a q) \rightleftharpoons \mathrm{Pb}^{2+}(a q)+\mathrm{H}_{2}(g) $$ Given that \(\left[\mathrm{Pb}^{2+}\right]=0.035 \mathrm{M}\) and the solution is buffered at \(\mathrm{pH} 1.60\).

Short Answer

Expert verified
The final pressure of \(H_2\) can be found by solving for \(P\) from the equilibrium constant expression, and the value will depend on the magnitude of \( \Delta G^{\circ} \) for the reaction at the given temperature.

Step by step solution

01

Understanding the Reaction

The first step is to understand the given chemical reaction: \( \mathrm{Pb}(s)+2 \mathrm{H}^{+}(a q) \leftrightarrow \mathrm{Pb}^{2+}(a q)+\mathrm{H}_{2}(g)\). This is an equilibrium reaction and we can tell that the reactants are solid lead (Pb), Hydrogen ions (H+), while the products are Pb2+ ions and gaseous Hydrogen (H2).
02

Use of Pressure Information in Equilibrium Constant Expression

We are given that at equilibrium, the concentration of \(\mathrm{Pb}^{2+}\) is 0.035M. Since the pH is 1.60, the \(\mathrm{[H+]}\) or concentration of Hydrogen ions will be \( 10^{-pH} = 10^{-1.60} = 0.025M \). Now, we let the partial pressure of the Hydrogen gas be P. The equilibrium constant expression for the reaction will hence be:\[K = \frac{[\mathrm{Pb^{2+}}][\mathrm{H_{2}}]}{[\mathrm{H^{+}}]^2} = \frac{0.035*P}{(0.025)^2} \]
03

Solving for Pressure Using Equilibrium Constant Value

Now we need to find the equilibrium constant value \( K \) at \(25^{\circ} \mathrm{C}\). For this, we can look up the standard free energy change \( \Delta G^{\circ} \) value for the reaction from a reference. Then, using the equation \[K = e^{(-\Delta G^{\circ}/RT)} \] where R = 8.314 J/K*mol and T = 298.15 K (or \(25^{\circ}\)C), we solve for K. After obtaining the value of K, we substitute it in the equilibrium constant expression obtained in the previous step, and solve for P, the partial pressure of the Hydrogen gas.

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Most popular questions from this chapter

Gold will not dissolve in either concentrated nitric acid or concentrated hydrochloric acid. However, the metal does dissolve in a mixture of the acids (one part \(\mathrm{HNO}_{3}\) and three parts \(\mathrm{HCl}\) by volume ), called aqua regia. (a) Write a balanced equation for this reaction. (Hint: Among the products are \(\mathrm{HAuCl}_{4}\) and \(\mathrm{NO}_{2} .\) ) (b) What is the function of \(\mathrm{HCl} ?\)

For each of the following redox reactions, (i) write the half-reactions; (ii) write a balanced equation for the whole reaction, (iii) determine in which direction the reaction will proceed spontaneously under standard-state conditions: (a) \(\mathrm{H}_{2}(g)+\mathrm{Ni}^{2+}(a q) \longrightarrow \mathrm{H}^{+}(a q)+\mathrm{Ni}(s)\) (b) \(\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Cl}^{-}(a q) \longrightarrow\) \(\mathrm{Mn}^{2+}(a q)+\mathrm{Cl}_{2}(g)\) (in acid solution) (c) \(\mathrm{Cr}(s)+\mathrm{Zn}^{2+}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{Zn}(s)\)

Discuss the advantages and disadvantages of fuel cells over conventional power plants in producing electricity.

What is a cell diagram? Write the cell diagram for a galvanic cell consisting of an Al electrode placed in a \(1 \mathrm{MAl}\left(\mathrm{NO}_{3}\right)_{3}\) solution and a Ag electrode placed in a \(1 M \mathrm{AgNO}_{3}\) solution.

Use the standard reduction potentials to find the equilibrium constant for each of the following reactions at \(25^{\circ} \mathrm{C}\): (a) \(\operatorname{Br}_{2}(l)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Br}^{-}(a q)+\mathrm{I}_{2}(s)\) (b) \(2 \mathrm{Ce}^{4+}(a q)+2 \mathrm{Cl}^{-}(a q) \rightleftharpoons$$\mathrm{Cl}_{2}(g)+2 \mathrm{Ce}^{3+}(a q)\) (c) \(5 \mathrm{Fe}^{2+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+8 \mathrm{H}^{+}(a q) \rightleftharpoons\) \(\mathrm{Mn}^{2+}(a q)+4 \mathrm{H}_{2} \mathrm{O}(l)+5 \mathrm{Fe}^{3+}(a q)\)
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