/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 73 \(\mathrm{NiO}\) is to be reduce... [FREE SOLUTION] | 91影视

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Chapter 15: Problem 73

\(\mathrm{NiO}\) is to be reduced to nickel metal in an industrial process by use of the reaction $$ \mathrm{NiO}(s)+\mathrm{CO}(g) \rightleftharpoons \mathrm{Ni}(s)+\mathrm{CO}_{2}(g) $$ At \(1600 \mathrm{~K}\) the equilibrium constant for the reaction is \(K_{p}=6.0 \times 10^{2}\). If a CO pressure of 150 torr is to be employed in the furnace and total pressure never exceeds 760 torr, will reduction occur?

Short Answer

Expert verified
The reduction of NiO to Ni is unlikely to occur under the given conditions, as the calculated equilibrium pressure of CO鈧� is \(9.0 \times 10^4\,\text{torr}\), which is much higher than the maximum allowed total pressure of 760 torr in the furnace.

Step by step solution

01

Write the expression for the equilibrium constant

We need to write the equilibrium constant expression for the reaction. In this case, the equilibrium constant is given in terms of pressure (Kp), so the expression will include the partial pressures of the gases involved. As the reaction is in equilibrium: \[K_p = \frac{P_{Ni} \cdot P_{CO_2}}{P_{NiO} \cdot P_{CO}}\]
02

Identify the given information

We have: - \(K_p = 6.0 \times 10^2\) - Pressure of CO: \(P_{CO} = 150 \,\text{torr}\) - Since Ni and NiO are solids, their partial pressures do not affect the equilibrium constant. So, \(P_{NiO} = P_{Ni} = 1\)
03

Calculate the equilibrium pressure of carbon dioxide

Now, let's plug in the given values into the equilibrium constant expression: \[K_p = \frac{P_{CO_2}}{P_{CO}}\] Rearrange for \(P_{CO_2}\): \[6.0 \times 10^2 = \frac{P_{CO_2}}{150}\] Now, simply solve for \(P_{CO_2}\): \[P_{CO_2} = 6.0 \times 10^2 \times 150\] \[P_{CO_2} = 9.0 \times 10^4 \,\text{torr}\]
04

Analyze the pressure values

In order for the reaction to occur, the total pressure in the furnace should not exceed 760 torr. The calculated \(P_{CO_2}\) is much higher than this limit, and adding the given pressure of CO (150 torr) would further increase the total pressure. Therefore, the reduction of NiO to Ni is unlikely to occur under these given conditions.

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Most popular questions from this chapter

At \(1000 \mathrm{~K}, K_{p}=1.85\) for the reaction $$ \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{SO}_{3}(g) $$ (a) What is the value of \(K_{p}\) for the reaction \(\mathrm{SO}_{3}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\frac{1}{2} \mathrm{O}_{2}(g) ?\) (b) What is the value of \(K_{p}\) for the reaction \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\) ? (c) What is the value of \(K_{c}\) for the reaction in part (b)?

Consider the following equilibrium, for which \(\Delta H<0\) $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g) $$ How will each of the following changes affect an equilibrium mixture of the three gases? (a) \(\mathrm{O}_{2}(g)\) is added to the system; (b) the reaction mixture is heated; (c) the volume of the reaction vessel is doubled; (d) a catalyst is. added to the mixture; \((e)\) the total pressure of the system is increased by adding a noble gas; (f) \(\mathrm{SO}_{3}(g)\) is removed from the system.

A mixture of \(0.2000 \mathrm{~mol}\) of \(\mathrm{CO}_{2}, 0.1000 \mathrm{~mol}\) of \(\mathrm{H}_{2}\), and \(0.1600 \mathrm{~mol}\) of \(\mathrm{H}_{2} \mathrm{O}\) is placed in a 2.000-L vessel. The following equilibrium is established at \(500 \mathrm{~K}\) : $$ \mathrm{CO}_{2}(\mathrm{~g})+\mathrm{H}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ (a) Calculate the initial partial pressures of \(\mathrm{CO}_{2}, \mathrm{H}_{2}\) and \(\mathrm{H}_{2} \mathrm{O} .\) (b) At equilibrium \(P_{\mathrm{H}_{2} \mathrm{O}}=3.51 \mathrm{~atm}\). Calculate the equilibrium partial pressures of \(\mathrm{CO}_{2}, \mathrm{H}_{2}\), and \(\mathrm{CO}\). (c) Calculate \(K_{n}\) for the reaction.

The reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)\) has \(K_{p}=0.0870\) at \(300^{\circ} \mathrm{C}\). A flask is charged with \(0.50\) atm \(\mathrm{PCl}_{3}, 0.50 \mathrm{~atm} \mathrm{Cl}_{2}\), and \(0.20 \mathrm{~atm} \mathrm{PCl}_{5}\) at this tempera- ture. (a) Use the reaction quotient to determine the direction the reaction must proceed to reach equilibrium. (b) Calculate the equilibrium partial pressures of the gases. (c) What effect will increasing the volume of the system have on the mole fraction of \(\mathrm{C}_{2}\) in the equilibrium mixture? (d) The reaction is exothermic. What effect will increasing the temperature of the system have on the mole fraction of \(\mathrm{Cl}_{2}\) in the equilibrium mixture?

Write the equilibrium-constant expression for the equilibrium $$ \mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g) $$ The table included below shows the relative mole percentages of \(\mathrm{CO}_{2}(\mathrm{~g})\) and \(\mathrm{CO}(\mathrm{g})\) at a total pressure of \(1 \mathrm{~atm}\) for several temperatures. Calculate the value of \(K_{p}\) at each temperature. Is the reaction exothermic or endothermic? Explain. $$ \begin{array}{lll} \hline \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) & \mathrm{CO}_{2}(\text { mol } \%) & \text { CO (mol \%) } \\ \hline 850 & 6.23 & 93.77 \\ 950 & 1.32 & 98.68 \\ 1050 & 0.37 & 99.63 \\ 1200 & 0.06 & 99.94 \\ \hline \end{array} $$
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