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Chapter 14: Problem 10

Write the equation relating \(K_{\mathrm{c}}\) to \(K_{P}\), and define all the terms.

Short Answer

Expert verified
The equation relating \(K_c\) to \(K_p\) is \[ K_p = K_c(RT)^{\Delta n} \]. Here, \(K_c\) is the equilibrium constant in terms of concentration, \(K_p\) is the equilibrium constant in terms of pressure, \(R\) is the ideal gas constant (0.0821 L·atm/mol·K), \(T\) is the absolute temperature in Kelvin, and \(\Delta n\) is the change in the number of moles of gas in the reaction (calculated as moles of gaseous products – moles of gaseous reactants).

Step by step solution

01

Define the Constants

The constants \(K_c\) and \(K_p\) are chemical equilibrium constants. \(K_c\) is the equilibrium constant in terms of concentration (moles per liter), while \(K_p\) is the equilibrium constant in terms of pressure (atmospheres).
02

Relating \(K_c\) to \(K_p\)

The relationship between the two constants is given by the equation \[ K_p = K_c(RT)^{\Delta n} \] where \(R\) is the ideal gas constant (0.0821 L·atm/mol·K), \(T\) is the absolute temperature in Kelvin, and \(\Delta n\) is the change in the number of moles of gas in the reaction, calculated as the difference between the numbers of moles of gaseous products and gaseous reactants.
03

Explanation of the Terms

In the earlier formula, \(R\) represents the ideal gas constant (0.0821 L·atm/mol·K). It's a constant that appears in ideal gas law. \(T\) is the absolute temperature, which should be measured in Kelvin for this formula. \(\Delta n\) is the change in the moles of gas in the reaction. It is determined from the balanced chemical equation and is calculated as the sum of the stoichiometric coefficients of the gaseous products minus the sum of stoichiometric coefficients of gaseous reactants.

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Most popular questions from this chapter

The equilibrium constant \(\left(K_{P}\right)\) for the reaction \(\mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{PCl}_{5}(g)\) is 2.93 at \(127^{\circ} \mathrm{C}\) Initially there were 2.00 moles of \(\mathrm{PCl}_{3}\) and 1.00 mole of \(\mathrm{Cl}_{2}\) present. Calculate the partial pressures of the gases at equilibrium if the total pressure is 2.00 atm.

For the reaction $$\mathrm{H}_{2}(g)+\mathrm{CO}_{2}(g) \rightleftharpoons \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{CO}(g)$$ at \(700^{\circ} \mathrm{C}, K_{\mathrm{c}}=0.534 .\) Calculate the number of moles of \(\mathrm{H}_{2}\) that are present at equilibrium if a mixture of 0.300 mole of \(\mathrm{CO}\) and \(0.300 \mathrm{~mole}\) of \(\mathrm{H}_{2} \mathrm{O}\) is heated to \(700^{\circ} \mathrm{C}\) in a 10.0 -L container.

Does the addition of a catalyst have any effects on the position of an equilibrium?

Consider the dissociation of iodine: $$\mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g)$$ A 1.00-g sample of \(I_{2}\) is heated to \(1200^{\circ} \mathrm{C}\) in a \(500-\mathrm{mL}\) flask. At equilibrium the total pressure is 1.51 atm. Calculate \(K_{P}\) for the reaction. [Hint: Use the result in \(14.117(\mathrm{a}) .\) The degree of dissociation \(\alpha\) can be obtained by first calculating the ratio of observed pressure over calculated pressure, assuming no dissociation.]

A student placed a few ice cubes in a drinking glass with water. A few minutes later she noticed that some of the ice cubes were fused together. Explain what happened.
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