A mixture of N2, H2, and NH3 is at equilibrium [according to the equation N2(g)+3 H2(g) ⇌2 NH3(g

A mixture of N2, H2, and NH3 is at equilibrium [according to...

A mixture of $\mathrm{N}_{2}, \mathrm{H}_{2},$ and $\mathrm{NH}_{3}$ is at equilibrium [according to the equation $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) ]$ as depicted below: The volume is suddenly decreased (by increasing the external pressure) and a new equilibrium is established as depicted below: a. If the volume of the final equilibrium mixture is $1.00 \mathrm{L},$ determine the value of the equilibrium constant, $K,$ for the reaction. Assume temperature is constant. b. Determine the volume of the initial equilibrium mixture assuming a final equilibrium volume of 1.00 $\mathrm{L}$ and assuming a constant temperature.

A mixture of $\mathrm{N}_{2}, \mathrm{H}_{2},$ and $\mathrm{NH}_{3}$ is at equilibrium [according to the equation $\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) ]$ as depicted below:
The volume is suddenly decreased (by increasing the external pressure) and a new equilibrium is established as depicted below:
a. If the volume of the final equilibrium mixture is $1.00 \mathrm{L},$ determine the value of the equilibrium constant, $K,$ for the reaction. Assume temperature is constant.
b. Determine the volume of the initial equilibrium mixture assuming a final equilibrium volume of 1.00 $\mathrm{L}$ and assuming a constant temperature.

Key Concepts

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products in a chemical reaction. The stoichiometric coefficients determine how changes in volume or pressure affect the number of moles of gaseous species, influencing how the equilibrium position shifts according to Le Chatelier's Principle.

Effect of Volume Change on Gaseous Equilibria

In gaseous equilibria, a change in volume (and therefore pressure) impacts the equilibrium position. A decrease in volume increases the overall pressure, and the system responds by shifting the equilibrium towards the side with fewer moles of gas, which can alter the concentration of reactants and products but the equilibrium constant remains unchanged.

Chemical Equilibrium

Chemical equilibrium refers to the state in which the forward and reverse reactions occur at equal rates, so that the concentrations of reactants and products remain constant over time. It is a dynamic balance, meaning that reactions continue to occur, but no net change in concentration is observed.

Equilibrium Constant

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations or partial pressures of products to reactants at equilibrium, each raised to the power of their stoichiometric coefficients. K remains constant for a given reaction at a specified temperature, regardless of initial conditions.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium experiences a change in concentration, pressure, or temperature, the system will adjust to partially counteract the imposed change and re-establish equilibrium. This principle helps predict the qualitative response of the system to external disturbances.

Transcript

00:01 This question is an extension of some of the concepts that you have learned in this chapter, namely how the equilibrium will shift based upon a volume change.

00:14 We also need to use avogadro's number and a couple other things.

00:19 We have two containers, well, one container under two separate set of conditions.

00:26 Temperature is the same, but when we have a large container, we have eight, molecules of nitrogen, or sorry, hydrogen, four molecules of nitrogen, and just two molecules of ammonia.

00:41 Then we decrease the volume, and the reaction shifts such that we have six moles of ammonia, two moles of nitrogen, and two moles of hydrogen in one liter.

00:54 The reaction being, one mole nitrogen, reacts to a three moles hydrogen to produce two moles of ammonia.

01:01 So the equilibrium constant will be equal to the concentration of ammonia divided by squared, divided by the concentration of nitrogen, divided by the concentration of hydrogen cubed because of the three right here.

01:21 So if we want to calculate the k value, we need to know these concentrations in moles per liter.

01:27 We know molecules per liter, so we need to carry out a conversion.

01:33 If we have six molecules in a liter, then we can convert the molecules to moles by dividing by avagadro's number.

01:41 We will then have moles per one liter, which is the ammonia concentration, which we need to square.

01:50 Then we'll divide by the nitrogen concentration.

01:53 We have two molecules of nitrogen, where one mole is 6 .022 times 10 to the 23rd molecules.

02:01 So this gives us the moles of nitrogen, which we divide by one to get a concentration.

02:10 Raise it to the first power.

02:12 Then we have two molecules of hydrogen, one, two, which we can then convert to moles by dividing by avagadro's number.

02:24 Then with moles, we divide by the volume 1 liter to get concentration, and then we cube it...

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