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## Homework Statement

Nitrous oxide reacts with ozone to form dinitrogen pentoxide. There are four moles of each reactant and the volume of the container in which this reaction takes place is 2 L. T is constant. The equilibrium constant for this reaction is 1. How many moles of product are present when the reaction achieves equilibrium?

## Homework Equations

Balanced equation: [itex]3N_{2}[/itex][itex]O[/itex] + [itex]4O_{3}[/itex] <--> [itex]3N_{2}[/itex][itex]O_{5}[/itex]## The Attempt at a Solution

**Wrong method:**

[itex]K_{c}[/itex][itex]=[/itex][itex]\frac{[N2O5]^{3}}{[N2O]^{3}[O3]^{4}}[/itex]

All the components are gaseous, so they can go into the equation. First, however, we have to convert moles to concentrations. So we divide moles by volume (2 L). Also the equilibrium constant is equal to 1. Then we can plug in everything to the equation:

[itex]1[/itex][itex]=[/itex][itex]\frac{[N2O5]^{3}}{[2]^{3}[2]^{4}}[/itex]

From here we can solve for the concentration of dinitrogen pentoxide. [itex]1[/itex] [itex]=[/itex][itex]\frac{[N2O5]^{3}}{128}[/itex]

We get the concentration of dinitrogen pentoxide as the third root of 128, and we must multiply this value by 2 liters to get the number of moles of dinitrogen pentoxide since by dimensional analysis the liters cancel out (moles/liter * liter = moles).

**New and hopefully correct method!**

Let's surmise that x moles of product (dinitrogen pentoxide) were made.

From the balanced equation we can see that the production of x moles of product consumes x moles of nitrous oxide and (4/3)x moles of ozone.

Now, we have the equilibrium, rather than the initial, number of moles.

Equilibrium number of moles:

Nitrous oxide: 4 - x moles

Ozone: 4 - (4/3)x moles

Dinitrogen pentoxide: x moles (as I surmised).

From here we can plug stuff into our equilibrium constant equation! Volume is constant so we'll just plug in the number of moles.

[itex]\frac{x^{3}}{(4-x)^{3}(4-4x/3)^{4}}[/itex] [itex]=1[/itex] Questions:

1) I first thought nitrous oxide referred to nitrogen monoxide (NO). I was wrong. Is nitrous oxide the scientific name or just a common name? I'm suspecting it's just a common name because I can't think of a rule for "-ous" compounds outside acids (e.g. sulfuorous acid).

2) I'm still learning equilibrium here and I'm wondering if my work is correct. I'm pretty sure it's correct after consulting a textbook (which actually refers to N2O as dinitrogen monoxide). Is my answer correct? More importantly, is my process and logic correct?

3) Are the initial moles of reactant equal to the equilibrium moles of reactant? Is this relevant? I'm suspecting what I did above is

**because I didn't use the equilibrium moles but instead the initial moles (I just re-read the textbook).**

__wrong__
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