Problem 5 - Introductory Chemistry Atoms First

Question

Write the equilibrium constant expression for the reaction \(\mathrm{H}_{2}(g)+\mathrm{I}_{2}(g) \rightleftarrows 2 \mathrm{HI}(g)\)

Step-by-Step Solution

Answer

The equilibrium constant expression for the reaction \(\mathrm{H}_2(g) + \mathrm{I}_2(g) \rightleftarrows 2 \mathrm{HI}(g)\) is \(K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\).

Step 1: Identify the reactants and products

In this reaction, the reactants are hydrogen gas, \(\mathrm{H}_2(g)\), and iodine gas, \(\mathrm{I}_2(g)\). The product is hydrogen iodide gas, \(\mathrm{HI}(g)\).

Step 2: Write the general equilibrium expression

When writing the general equilibrium expression, we need to raise the concentrations of the products to the power of their stoichiometric coefficients, divided by the concentrations of the reactants raised to the power of their stoichiometric coefficients. For this reaction: \(K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\)

Step 3: Final Equilibrium Constant Expression

The final equilibrium constant expression for this reaction is: \(K_c = \frac{[\mathrm{HI}]^2}{[\mathrm{H}_2][\mathrm{I}_2]}\)

Key Concepts

Chemical Equilibrium

Chemical equilibrium is a fascinating state in chemical reactions where the rate of the forward reaction, where reactants are converted into products, is equal to the rate of the reverse reaction, where products break down into reactants. It's like a peaceful tug-of-war where both teams are equally strong, and the rope stays in the middle. For our given reaction \( H_2(g) + I_2(g) \rightleftarrows 2 HI(g) \) chemical equilibrium would occur when the rate at which \( H_2 \) and \( I_2 \) combine to form \( HI \) is the same as the rate at which \( HI \) decomposes back into \( H_2 \) and \( I_2 \). But remember, being at equilibrium doesn't mean the amounts of reactants and products are equal; it just means their concentrations stop changing over time.

Stoichiometry

When we bake, we carefully measure ingredients to get the perfect cake. Stoichiometry is the 'cooking recipe' of chemistry, which tells us how much of each reactant we need to produce a certain amount of product. It's all about balancing the equation—like making sure you have just the right amount of eggs for the amount of flour in your recipe. In our equation \( H_2(g) + I_2(g) \rightleftarrows 2 HI(g) \), for each molecule of \( H_2 \) and \( I_2 \) you get two molecules of \( HI \). That '2' in front of \( HI \) is huge–it means \( HI \) is produced twice as much.

Reaction Quotient

Ever check the scoreboard during a game to see which team is leading? That's similar to what the reaction quotient, \( Q \), does for chemical reactions. It's a way to know 'where' a reaction is at any given moment. The reaction quotient looks just like the equilibrium constant expression but uses current, not equilibrium, concentrations. For our reaction, we'd write \( Q = \frac{[HI]^2}{[H_2][I_2]} \). If \( Q = K_c \), the system is at equilibrium. If \( Q < K_c \), the reaction will move forward to make more \( HI \), and if \( Q > K_c \), the reaction will go in reverse to make more \( H_2 \) and \( I_2 \).

Gas Phase Reactions

Bubbles in soda, the smell of perfume, and even our breathing—all of these involve gases reacting. Gas phase reactions are a bit special because gases behave differently than solids or liquids; they have lots of energy and move freely, spreading out to fill their containers. When gases react, the space they occupy, or volume, and the temperature can significantly affect the reaction. Pressure also comes into play, especially for reactions involving a change in the number of gas molecules. Our discussed reaction involves only gases, \( H_2 \) and \( I_2 \) react to form \( HI \) gas, showing these fascinating characteristics of gas phase reactions.