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At $25^{\circ} \mathrm{C},$ a mixture of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ gases are in equilibrium in a cylinder fitted with a movable piston. The concentrations are $\left[\mathrm{NO}_{2}\right]=0.0475 M$ and $\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=0.487 \mathrm{M} .$ The volume of the gas mixture is halved by pushing down on the piston at constant temperature. Calculate the concentrations of the gases when equilibrium is reestablished. Will the color become darker or lighter after the change? [Hint: $K_{\mathrm{c}}$ for the dissociation of $\mathrm{N}_{2} \mathrm{O}_{4}$ to $\mathrm{NO}_{2}$ is $4.63 \times 10^{-3} . \mathrm{N}_{2} \mathrm{O}_{4}(g)$ is colorless and $\mathrm{NO}_{2}(g)$ has a brown color.]

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$\left[\mathrm{N}_{2} \mathrm{O}_{4}\right]=0.988 \mathrm{M}$$\left[\mathrm{NO}_{2}\right]=0.0676 \mathrm{M}$The color becomes darker.

Chemistry 102

Chapter 14

Chemical Equilibrium

University of Central Florida

University of Maryland - University College

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.

03:38

At $25^{\circ} \mathrm{C}$…

10:14

At $25^{\circ} \mathrm{C},…

04:24

At $503 \mathrm{~K}$ the e…

03:45

The equilibrium reaction $…

05:23

The reaction $\mathrm{NO}_…

05:45

A sample of $\mathrm{N}_{2…

for this problem. Let's rewrite the chemical reaction where we have into a four. Going to to, you know, to the problem states that we have an initial concentration of into 04 at 0.97 four Moeller and an initial concentration of ANO, too at 0.95 Moeller, Where did we get these concentrations? Well, the concentration of into 04 waas 0.487 Moeller And then we cut the volume in half, which means we doubled that concentration of 0.4872 point 974 and then this concentration concentration of ano, too. WAAS 0.475 And then when we cut the concentration in half, we doubled its concentration 2.95 Now we I recognize that the's concentrations are no longer equilibrium concentrations, but we need to determine our direction of shift to determine the direction of shift. We recognize that there is one mole of gas here and two moles of gas here. And when we decrease the volume, we always shift to the side with fewer balls of gas. So we're going to shift to the left if we shift to the left than the N 02 Concentration is going to decrease by two x and the end to a four. Concentration is going to increase by X, so we determine the direction of shift by recognizing decrease in the volume shifts the reaction towards the fewer moles of gas. Now we have our new equilibrium concentrations expressed in terms of X. The new equilibrium concentration of N 204 will be 2040.974 plus X and N 02 will be 20.95 minus two X. Then we plug everything into our equilibrium. Constant expression where K C was given to us at 4.63 times 10 to the negative three. That then will equal the No. Two concentration 20.95 minus two x squared, divided by the end 204 concentration which it equilibrium is now 0.974 plus X. Then we could use a couple sheets of paper or you could review your algebra or just use a program like Mathematica or Excel or your calculator and solve for X X then becomes 0.14 so we can now solve for the final equilibrium concentrations of both of them, knowing that the end 204 equilibrium concentration will be 2040.974 plus X or 0.0 988 Moeller and the new equilibrium concentration of N 02 will be 20.95 minus two x or 0.68 now to determine whether or not it has gotten darker or lighter. Well, we know that, you know, to has a brown color and the, you know, to color after we, um, decreased the volume toe 1/2. Then this ended up shifting to the left. So in comparison to the 0.95 because the concentration has decreased from 0.95 we would say that the color is now lighter in comparison to what it waas right after. We, um, decrease the volume toe 1/2. But if we're comparing it to the 0.475 concentration, which we had before we decrease the volume toe 1/2 we would say that this 0.68 Moeller concentration would actually be darker. So depending on our reference, we could answer this as lighter or darker

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