When a 10.00 L vessel containing 42.189 g of I2 is heated to 1173 K, some I2 dissociates: I2(g)

When a 10.00 L vessel containing 42.189 g of I2 is heated to...

When a 10.00 L vessel containing 42.189 g of $\mathrm{I}_{2}$ is heated to $1173 \mathrm{K},$ some $\mathrm{I}_{2}$ dissociates: $\mathrm{I}_{2}(g) \rightarrow 2 \mathrm{I}(g) .$ If the final pressure in the vessel is $1.733 \mathrm{atm},$ what are the mole fractions of the two components $\mathrm{I}_{2}(g)$ and $\mathrm{I}(g)$ after the reaction?

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Key Concepts

Reaction Stoichiometry

Reaction stoichiometry involves using the balanced chemical equation to relate the moles of reactants and products. In a dissociation reaction, this allows the determination of how many moles of a species are consumed or produced based on the stoichiometric coefficients in the equation.

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, provides a relationship among pressure, volume, temperature, and the number of moles for a gas. This law is crucial for determining the total number of moles in a gas mixture once the conditions of pressure, temperature, and volume are known.

Mole Fraction

The mole fraction is defined as the ratio of the number of moles of a given component to the total number of moles in the mixture. It is a dimensionless quantity that helps describe the composition of a gaseous mixture or solution.

Equilibrium Dynamics

In reactions where dissociation or partial conversion occurs, equilibrium dynamics describe how the reaction reaches a state where the rates of the forward and reverse reactions are equal. This concept is critical for understanding how the concentrations or moles of species change until equilibrium is established.

Transcript

00:01 This problem gives us a reaction, and it tells us that it starts out in a volume of 10 liters.

00:07 There's originally a mass of 42 .2 grams.

00:11 It's at a temperature of 1 ,173 kelvin, and the pressure is 1 .733 atm.

00:16 The problem is asking us to find the mole fraction of i2 at the end of the reaction and the mole fraction of i at the end of the reaction.

00:26 So first we need to use the ideal gas law to find the total number of moles in the reaction.

00:35 So first we do pv equals nrt, so n equals pv divided by rt.

00:46 R equals 0 .0 821 liters times atm over moles times kelvin.

00:55 And so the number of moles equals 0 .179 moles.

01:04 This is total.

01:06 That's important.

01:08 And so then the i2, so whenever i get these types of stoichiometry problems, i like to make a bca table.

01:18 So b, c, a is the after the reaction, b is before the reaction, and c is the change.

01:25 And we need to find the after for both of these because the mole fraction is equal to i2 at the n divided by total.

01:36 So it's equal to that amount and then i divided by total.

01:43 So we found the total moles from the ideal gas law, but we need to use stoichiometry to find the individual amount of number of moles.

01:51 So first, we know that this started out with 42 .2 grams...

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