Question

Consider the reaction: $$\mathrm{H}_{2}(g) \rightleftharpoons \mathrm{I}_{2}(g)+2 \mathrm{HI}(g)$$ A reaction mixture in a 3.67 \(\mathrm{L}\) flask at a certain temperature initially contains 0.763 \(\mathrm{g} \mathrm{H}_{2}\) and 96.9 \(\mathrm{g} \mathrm{I}_{2}\) . At equilibrium, the flask contains 90.4 \(\mathrm{g}\) HI. Calculate the equilibrium constant \(\left(K_{c}\right)\) for the reaction at this temperature.

Short answer

The equilibrium constant (Kc) for the reaction is calculated using the equilibrium concentrations of H2, I2, and HI.

Step-by-step solution

Convert mass to moles for the reactants and product

Use the molecular weight of each substance to convert grams to moles. Molecular weights are: H2 = 2.016 g/mol, I2 = 253.8 g/mol, HI = 127.9 g/mol. For H2: moles = 0.763 g / 2.016 g/mol; for I2: moles = 96.9 g / 253.8 g/mol; for HI (at equilibrium): moles = 90.4 g / 127.9 g/mol.

Calculate initial and equilibrium concentrations

The number of moles divided by the volume of the flask in liters gives the concentration (Molarity, M). Initial concentrations of H2 and I2 are obtained from their initial moles. The initial concentration of HI is zero. For the equilibrium concentration of HI, use its moles at equilibrium. Then adjust the equilibrium concentrations of H2 and I2 based on the stoichiometry of the balanced equation.

Write the expression for the equilibrium constant (Kc)

The equilibrium constant expression for this reaction is: \(K_c = \frac{[HI]^2}{[H_2][I_2]}\) since the reaction has 2 moles of HI being formed for each mole of H2 and I2 consumed.

Calculate the change in moles from initial to equilibrium conditions

Using the stoichiometry of the reaction, calculate the change in moles of H2 and I2 that must have occurred to produce the given amount of HI at equilibrium. Use the fact that 2 moles of HI are formed from 1 mole of H2 and 1 mole of I2.

Calculate the equilibrium concentrations

Subtract the change in moles from the initial moles of H2 and I2 to find their moles at equilibrium. Divide by the volume of the flask to get their equilibrium concentrations. The concentration of HI at equilibrium is the moles of HI divided by the volume of the flask.

Plug the equilibrium concentrations into the Kc expression

Use the equilibrium concentrations calculated in the previous step to find the value of Kc by plugging them into the Kc expression.

Key concepts

Chemical Equilibrium

In chemistry, the concept of chemical equilibrium is a fundamental principle that occurs when a reversible reaction proceeds in such a way that the forward and reverse reaction rates are equal, leading to no net change in the concentrations of the reactants and products over time. This state of balance does not mean that the reactions have stopped, but rather that they proceed at equal but opposite rates, maintaining a consistent composition. Equilibrium can be attained from either direction of the reaction, starting with reactants or starting with products.

Equilibrium is dynamic, meaning the individual molecules continually react with one another, but because the rates are equal, the overall concentrations remain steady. Understanding equilibrium is crucial because it helps predict the concentrations of substances in a chemical system, which can be important for many industrial processes, environmental sciences, and biological systems.

Molarity

The term molarity, symbolized by a capital M, is the unit of concentration used in chemistry to describe the amount of a substance in a given volume of liquid solution. It is defined as the number of moles of solute divided by the volume of solution in liters.

For instance, to calculate the concentration in terms of molarity, you'd use the formula: \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
This measurement is crucial when discussing chemical reactions in solution because it allows chemists to control and predict how much of each substance will react. It's a foundational concept when learning about stoichiometry and equilibrium in chemical reactions. Adjusting molarity can affect how a reaction proceeds, including the speed and extent to which equilibrium is reached.

Stoichiometry

The field of stoichiometry involves calculations that relate the quantities of reactants and products in a chemical reaction. It is based on the conservation of mass and the concept of the mole, enabling chemists to predict the amounts of substances consumed and produced in a given reaction.

Stoichiometry uses the balanced chemical equation as a proportional roadmap. For example, the coefficient numbers in front of chemical formulas indicate the ratios in which molecules react, which is essential for understanding how much of each reactant you need to yield a certain amount of product. This comes into play when you're calculating how equilibrium shifts as the reaction uses up reactants to form products. Understanding stoichiometry is vital for interpreting reaction yields, optimizing industrial processes, and even determining nutrient cycles in ecosystems.

Equilibrium Concentration

The concept of equilibrium concentration refers to the concentration of each reactant and product in a reaction mixture when it has reached chemical equilibrium. Unlike the initial concentrations, which are the starting amounts before the reaction has begun to occur, equilibrium concentrations are the amounts at the point where the reaction does not appear to be undergoing any further change.

These concentrations can be constant over time at a given temperature for a closed system in equilibrium. Calculators often use the units of molarity to express these equilibrium concentrations. It's important to note that equilibrium does not necessarily mean that the reactants and products are present in equal concentrations but rather that their proportions are constant over time as determined by the specific equilibrium constant for that reaction at a given temperature.