A reaction has an equilibrium constant of 8.5⨉10³ at 298 K. At 755 K, the equilibrium constant is 0.65. Find ΔH°_rxnfor the reaction.

검증된 단계별 안내

First, we need to understand that the relationship between the equilibrium constant (K), the change in enthalpy of the reaction (ΔH°rxn), and the temperature (T) is given by the Van't Hoff equation: \(\ln\frac{K_2}{K_1} = -\frac{\Delta H°_{rxn}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)\), where R is the gas constant (8.314 J/(mol·K)).

Next, we substitute the given values into the Van't Hoff equation. Here, \(K_1 = 8.5\times10^3\), \(K_2 = 0.65\), \(T_1 = 298 K\), and \(T_2 = 755 K\).

Then, we solve the equation for ΔH°rxn. This involves isolating ΔH°rxn on one side of the equation.

After that, we calculate the value of \(\frac{1}{T_2} - \frac{1}{T_1}\) and \(\ln\frac{K_2}{K_1}\).

Finally, we substitute these calculated values back into the equation to find the value of ΔH°rxn.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. A high K value indicates that products are favored, while a low K value suggests that reactants are favored. Understanding K is essential for analyzing how temperature changes affect the position of equilibrium.

Van 't Hoff Equation

The Van 't Hoff equation relates the change in the equilibrium constant (K) of a reaction to the change in temperature and the standard enthalpy change (ΔH°rxn) of the reaction. It is expressed as ln(K2/K1) = -ΔH°rxn/R(1/T2 - 1/T1), where R is the gas constant. This equation is crucial for calculating ΔH°rxn when given equilibrium constants at different temperatures.

Standard Enthalpy Change (ΔH°rxn)

The standard enthalpy change (ΔH°rxn) is the heat change that occurs when a reaction takes place under standard conditions (1 atm pressure and a specified temperature, usually 298 K). It indicates whether a reaction is exothermic (releases heat, ΔH°rxn < 0) or endothermic (absorbs heat, ΔH°rxn > 0). This concept is vital for understanding the energy dynamics of chemical reactions.

A reaction has an equilibrium constant of 8.5⨉103 at 298 K. At 755 K, the equilibrium constant is 0.65. Find ΔH°rxn for the reaction.