Equilibrium Constants at Different Temperatures

Oct 13, 2025 by leolavanderia.com.br 138 views

Introduction

Chemical equilibrium is a fundamental concept in chemistry that describes the balance between the forward and reverse reactions of a chemical process. The equilibrium constant, denoted by Kc, is a measure of the ratio of the concentrations of the products to the reactants at equilibrium. In this article, we will discuss the equilibrium constants of a reaction at two different temperatures.

The Reaction

The reaction we will be discussing is the equilibrium between hydrogen gas (H2) and iodine gas (I2) to form hydrogen iodide gas (HI):

H2(g) + I2(g) ⇌ 2 HI(g)

This reaction has an equilibrium constant (Kc) of 67 at a temperature of 850°C.

Equilibrium Constants at Different Temperatures

The equilibrium constant of a reaction is temperature-dependent. This means that the value of Kc changes with temperature. In the case of the reaction between H2 and I2, we have two equilibrium constants at two different temperatures:

Kc = 67 at 850°C
Kc = ? at another temperature

To determine the equilibrium constant at another temperature, we can use the van 't Hoff equation:

ln(K2/K1) = -ΔH/R (1/T2 - 1/T1)

where K1 and K2 are the equilibrium constants at temperatures T1 and T2, respectively, ΔH is the enthalpy change of the reaction, R is the gas constant, and T is the temperature in Kelvin.

Calculating the Equilibrium Constant at Another Temperature

Let's assume we want to find the equilibrium constant at 500°C. We can use the van 't Hoff equation to calculate Kc at this temperature.

First, we need to convert the temperatures from Celsius to Kelvin:

T1 = 850°C + 273 = 1123 K T2 = 500°C + 273 = 773 K

Next, we need to find the enthalpy change (ΔH) of the reaction. We can do this by using the standard enthalpy of formation of the reactants and products.

ΔH = ΔHf(HI) - ΔHf(H2) - ΔHf(I2)

Using the standard enthalpy of formation values, we get:

ΔH = -35.6 kJ/mol - 0 kJ/mol - 62.4 kJ/mol = -98 kJ/mol

Now, we can plug in the values into the van 't Hoff equation:

ln(K2/K1) = -ΔH/R (1/T2 - 1/T1) ln(K2/67) = -(-98 kJ/mol)/(8.314 J/mol*K) (1/773 K - 1/1123 K)

Simplifying the equation, we get:

ln(K2/67) = 0.0125 K2/67 = e^0.0125 K2 = 67 * e^0.0125 K2 ≈ 70.3

Therefore, the equilibrium constant at 500°C is approximately 70.3.

Conclusion

In conclusion, the equilibrium constant of a reaction is temperature-dependent. We can use the van 't Hoff equation to calculate the equilibrium constant at a different temperature. In this article, we discussed the equilibrium constants of a reaction at two different temperatures and calculated the equilibrium constant at 500°C using the van 't Hoff equation.

References

Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
Chang, R. (2010). Physical chemistry for the life sciences. W.H. Freeman and Company.
Levine, I. N. (2014). Physical chemistry. McGraw-Hill Education.

Discussion

What are some real-world applications of the van 't Hoff equation?

How does the equilibrium constant change with temperature?

What are some common mistakes to avoid when using the van 't Hoff equation?

Additional Resources

Khan Academy: Equilibrium constants
MIT OpenCourseWare: Physical Chemistry
University of California, Berkeley: Physical Chemistry
Q&A: Equilibrium Constants at Different Temperatures =====================================================

Introduction

In our previous article, we discussed the equilibrium constants of a reaction at two different temperatures. We also calculated the equilibrium constant at 500°C using the van 't Hoff equation. In this article, we will answer some frequently asked questions about equilibrium constants at different temperatures.

Q: What is the van 't Hoff equation?

A: The van 't Hoff equation is a mathematical equation that relates the equilibrium constant of a reaction to the temperature. It is given by:

ln(K2/K1) = -ΔH/R (1/T2 - 1/T1)

where K1 and K2 are the equilibrium constants at temperatures T1 and T2, respectively, ΔH is the enthalpy change of the reaction, R is the gas constant, and T is the temperature in Kelvin.

Q: What is the significance of the van 't Hoff equation?

A: The van 't Hoff equation is significant because it allows us to calculate the equilibrium constant at a different temperature, given the equilibrium constant at a known temperature and the enthalpy change of the reaction.

Q: How do I calculate the equilibrium constant at a different temperature?

A: To calculate the equilibrium constant at a different temperature, you need to follow these steps:

Convert the temperatures from Celsius to Kelvin.
Find the enthalpy change (ΔH) of the reaction.
Plug in the values into the van 't Hoff equation.
Simplify the equation to get the equilibrium constant at the new temperature.

Q: What are some common mistakes to avoid when using the van 't Hoff equation?

A: Some common mistakes to avoid when using the van 't Hoff equation include:

Not converting the temperatures from Celsius to Kelvin.
Not finding the enthalpy change (ΔH) of the reaction.
Not plugging in the correct values into the van 't Hoff equation.
Not simplifying the equation correctly.

Q: What are some real-world applications of the van 't Hoff equation?

A: Some real-world applications of the van 't Hoff equation include:

Calculating the equilibrium constant of a reaction at a different temperature.
Predicting the effect of temperature on the equilibrium constant of a reaction.
Designing experiments to study the effect of temperature on the equilibrium constant of a reaction.

Q: How does the equilibrium constant change with temperature?

A: The equilibrium constant changes with temperature in a predictable way. As the temperature increases, the equilibrium constant also increases. This is because the reaction is endothermic, meaning it absorbs heat energy.

Q: What are some common reactions that involve equilibrium constants at different temperatures?

A: Some common reactions that involve equilibrium constants at different temperatures include:

The reaction between hydrogen gas (H2) and iodine gas (I2) to form hydrogen iodide gas (HI).
The reaction between nitrogen gas (N2) and oxygen gas (O2) to form nitrogen oxide gas (NO).
The reaction between carbon dioxide gas (CO2) and water vapor (H2O) to form carbonic acid (H2CO3).

Conclusion

In conclusion, the van 't Hoff equation is a powerful tool for calculating the equilibrium constant at a different temperature. By following the steps outlined in this article, you can use the van 't Hoff equation to predict the effect of temperature on the equilibrium constant of a reaction. Remember to avoid common mistakes and to use the equation correctly.

References

Atkins, P. W., & de Paula, J. (2010). Physical chemistry. Oxford University Press.
Chang, R. (2010). Physical chemistry for the life sciences. W.H. Freeman and Company.
Levine, I. N. (2014). Physical chemistry. McGraw-Hill Education.

Discussion

What are some other real-world applications of the van 't Hoff equation?

How does the equilibrium constant change with pressure?

What are some common mistakes to avoid when using the van 't Hoff equation in a laboratory setting?

Additional Resources

Khan Academy: Equilibrium constants
MIT OpenCourseWare: Physical Chemistry
University of California, Berkeley: Physical Chemistry