Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 15: Problem 10

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

Short Answer

Expert verified
The equation relating \(K_{P}\) and \(K_{\mathrm{c}}\) is \(K_{P} = K_{\mathrm{c}} (RT)^{\Delta n}\), where \(R\) is the ideal gas constant, \(T\) is the temperature (in Kelvin), and \(\Delta n\) is the difference in moles of gaseous products and gaseous reactants in the balanced chemical reaction.

Step by step solution

01

Understand and Define the Terms

The equilibrium constant, \(K\), for a chemical reaction is the ratio of the concentrations (if \(K_{\mathrm{c}}\)) or the partial pressures (if \(K_{P}\)) of the products to the reactants, each raised to a power equal to the stoichiometric coefficient in the balanced chemical reaction.
02

Write the general equation of \(K_{\mathrm{c}}\)

In the equilibrium constant \(K_{\mathrm{c}}\), the concentrations of products and reactants are used. \(K_{\mathrm{c}}\) is usually given in the form: \[ K_{\mathrm{c}} = \frac{[\text{{Products}}]}{[\text{{Reactants}}]} \]
03

Write the general equation of \(K_{P}\)

In the equilibrium constant \(K_{P}\), the partial pressures of products and reactants are used. \(K_{P}\) is usually given in the form: \[ K_{P} = \frac{(\text{{Pressure of Products}})}{(\text{{Pressure of Reactants}})} \]
04

Relate \(K_{P}\) and \(K_{\mathrm{c}}\)

The relationship between \(K_{\mathrm{c}}\) and \(K_{P}\) is given by the equation: \[ K_{P} = K_{\mathrm{c}} (RT)^{\Delta n} \] where \(R\) is the ideal gas constant, \(T\) is the temperature (in Kelvin), and \(\Delta n\) is the difference in moles of gaseous products and gaseous reactants in the balanced chemical reaction.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A sample of pure \(\mathrm{NO}_{2}\) gas heated to \(1000 \mathrm{~K}\) decomposes: $$ 2 \mathrm{NO}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) $$ The equilibrium constant \(K_{P}\) is \(158 .\) Analysis shows that the partial pressure of \(\mathrm{O}_{2}\) is 0.25 atm at equilibrium. Calculate the pressure of \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\) in the mixture.

The equilibrium constant \(K_{\mathrm{c}}\) for the reaction $$ \mathrm{I}_{2}(g) \rightleftharpoons 2 \mathrm{I}(g) $$ is \(3.8 \times 10^{-5}\) at \(727^{\circ} \mathrm{C}\). Calculate \(K_{\mathrm{c}}\) and \(K_{P}\) for the equilibrium $$ 2 \mathrm{I}(g) \rightleftharpoons \mathrm{I}_{2}(g) $$ at the same temperature.

A quantity of 0.20 mole of carbon dioxide was heated at a certain temperature with an excess of graphite in a closed container until the following equilibrium was reached: $$ \mathrm{C}(s)+\mathrm{CO}_{2}(g) \rightleftharpoons 2 \mathrm{CO}(g) $$ Under this condition, the average molar mass of the gases was found to be \(35 \mathrm{~g} / \mathrm{mol}\). (a) Calculate the mole fractions of \(\mathrm{CO}\) and \(\mathrm{CO}_{2}\). (b) What is the \(K_{P}\) for the equilibrium if the total pressure was 11 atm? (Hint: The average molar mass is the sum of the products of the mole fraction of each gas and its molar mass.)

A mixture of 0.47 mole of \(H_{2}\) and 3.59 moles of \(H C l\) is heated to \(2800^{\circ} \mathrm{C}\). Calculate the equilibrium partial pressures of \(\mathrm{H}_{2}, \mathrm{Cl}_{2}\), and \(\mathrm{HCl}\) if the total pressure is 2.00 atm. The \(K_{P}\) for the reaction \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons 2 \mathrm{HCl}(g)\) is 193 at \(2800^{\circ} \mathrm{C}.\)

At \(25^{\circ} \mathrm{C}\), the equilibrium partial pressures of \(\mathrm{NO}_{2}\) and \(\mathrm{N}_{2} \mathrm{O}_{4}\) are \(0.15 \mathrm{~atm}\) and \(0.20 \mathrm{~atm}\), respectively. If the volume is doubled at constant temperature, calculate the partial pressures of the gases when a new equilibrium is established.
See all solutions

Recommended explanations on Chemistry Textbooks

Nuclear Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemistry Branches

Read Explanation

Inorganic Chemistry

Read Explanation

Organic Chemistry

Read Explanation

Physical Chemistry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free