Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

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 mole of $\mathrm{H}_{2} \mathrm{O}$ is heated to $700^{\circ} \mathrm{C}$ in a $10.0-\mathrm{L}$ container.

$$0.173$$

Chemistry 102

Chapter 14

Chemical Equilibrium

Carleton College

University of Central Florida

Rice University

Brown University

Lectures

10:03

In thermodynamics, a state of thermodynamic equilibrium is a state in which a system is in thermal equilibrium with its surroundings. A system in thermodynamic equilibrium is in thermal equilibrium, mechanical equilibrium, electrical equilibrium, and chemical equilibrium. A system is in equilibrium when it is in thermal equilibrium with its surroundings.

00:54

In chemistry, chemical equilibrium (also known as dynamic equilibrium) is a state of chemical stability in which the concentrations of the chemical substances do not change in the course of time due to their reaction with each other in a closed system. Chemical equilibrium is an example of dynamic equilibrium, a thermodynamic concept.

02:25

For the reactionH(g) C…

03:31

For the reaction $$\mathrm…

03:22

For the reaction$$…

05:38

The equilibrium constant $…

04:23

One mole of $\mathrm{H}_{2…

02:48

The reaction$\mathrm{C…

02:39

Calculate the equilibrium …

we're given the value of the equilibrium constant Casey, for this reaction at 700 degrees Celsius. And we want to determine how many moles of H two guests. Our president, once we achieve equilibrium, if we react 0.300 moles of both H 20 in CEO gas. So we initially have no reactant. And so it will be more convenient for us to first reverse this reaction so that we have initial species concentrations for the reactant and no products present. And we know that all we have to do to find the value of K C for the reverse of the given reaction is to take the inverse of the forward of that reaction. So one divided by 0.534 and that comes out to about 1.87 And now we can proceed through a reaction table. We're told we start with 0.3 moles of water and CEO, and so we have no products now based on the way that was read at this equation. Initially, the changes are minus X for both of the reactions and plus X for both of the products. So the equilibrium concentration expressions are now 0.3 minus X for both react INTs and X for both of the products now conform the equilibrium constant expression for Casey based on the overall reaction. So that is the equilibrium concentration of each to gas times the equilibrium concentration of CO two gas divided by the equilibrium concentration of H 20 gas times the equilibrium concentration of CEO gas. Now we're at a constant volume. We know that for concentrations, that's, you know, that's measured in units of polarity, which is moles her leader. Remember that were ultimately interested in determining the total number of moles of H two guests that we have at equilibrium. And so we do need to plug in concentration values into our equilibrium expression. However, since we're at a constant volume, the volume units will cancel out. So that means that we can fill in the reaction table with just the total number of moles of each species. If we plug in those equilibrium expressions for the number of moles of each species into the equilibrium concentrations for our equilibrium expression, then the ratio was still come out to the value of K. C. So we can plug in from the ice table are equilibrium expressions for the total number of moles for each species. And then we see that at equilibrium when we solve for X, that will be equal to the total number of moles of H two gas. So we plug in those expressions. So for both of the products, it's X. In either case, that would be X squared for both of the reactant 0.3 minus X. So you multiply this together to give a 0.3 minus X quantity squared. We set this equal to the adjusted value for Casey after we reversed the initial reaction that we were given. So that's equal to 1.87 Now we noticed that the numerator and denominator or both, squared so we can take the square root of both sides. And so that leaves us with X over 0.3 minus X is equal to the spirit of 1.87 which is about 1.368 Now we multiply over the denominator and distribute with that square root of K C. And then we just do some algebra to solve for X. So she get about zero point for 105 minus 1.368 X is equal to X 0.41 05 is equal to 2.368 x Now, when we divide over, we solve for X and remember that X is equal to a number of moles of H two at equilibrium, which is what we're solving for, and that comes out to a value of about 0.173 moles of hydrogen gas it equilibrium.

View More Answers From This Book

Find Another Textbook

05:36

Consider the dissolution of an ionic compound such as potassium fluoride in …

02:01

(a) From the following data calculate the bond enthalpy of the $\mathrm{F}_{…

13:49

A mixture of calcium carbonate $\left(\mathrm{CaCO}_{3}\right)$ and magnesiu…

03:37

Describe the basic features of a galvanic cell. Why are the two components o…

06:12

The carat is the unit of mass used by jewelers. One carat is exactly $200 \m…

01:52

An equimolar mixture of $\mathrm{H}_{2}$ and $\mathrm{D}_{2}$ effuses throug…

01:40

State the third law of thermodynamics and explain its usefulness in calculat…

08:07

Photosynthesis produces glucose, $\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_…

00:49

A 0.86 percent by mass solution of $\mathrm{NaCl}$ is called "physiolog…

19:12

Calculate the percent ionization of hydrofluoric acid at the following conce…