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The equilibrium constant \(K_{c}\) for the synthesis of methanol, \(\mathrm{CH}_{3} \mathrm{OH}\) $$ \mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \rightleftharpoons \mathrm{CH}_{3} \mathrm{OH}(g) $$ is 4.3 at \(250^{\circ} \mathrm{C}\) and 1.8 at \(275^{\circ} \mathrm{C}\). Is this reaction endothermic or exothermic?

Short Answer

Expert verified
The reaction is exothermic.

Step by step solution

01

Understand the concept

The equilibrium constant, \( K_{c} \), changes with temperature, providing insights into the thermodynamic nature of a reaction. If \( K_{c} \) decreases with an increase in temperature, the reaction is exothermic. Conversely, if \( K_{c} \) increases with an increase in temperature, the reaction is endothermic.
02

Examine given data

We have two temperature and equilibrium constant pairs: \( K_{c} = 4.3 \) at \( 250^{\circ} \mathrm{C} \) and \( K_{c} = 1.8 \) at \( 275^{\circ} \mathrm{C} \). Observe how the equilibrium constant changes with temperature.
03

Analyze the equilibrium constant change

As temperature increases from \( 250^{\circ} \mathrm{C} \) to \( 275^{\circ} \mathrm{C} \), \( K_{c} \) decreases from 4.3 to 1.8. This indicates that the reaction tends to favor the reactants at higher temperatures.
04

Determine reaction type using equilibrium constant trend

Since \( K_{c} \) decreases with an increase in temperature, the reaction is exothermic. This is consistent with Le Chatelier's principle, which states that increasing temperature for exothermic reactions shifts the equilibrium toward the reactants.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Thermodynamics
Thermodynamics is the branch of physics that deals with the relationships and conversions between heat and other forms of energy. It helps us understand how energy changes in different reactions, including chemical processes. In chemistry, thermodynamics allows us to predict how a system behaves when conditions such as pressure, volume, or temperature change.

One of the key aspects of thermodynamics is the study of equilibrium constants. An equilibrium constant (denoted as \( K_{c} \) for concentrations) provides a mathematical way to describe the ratio of concentrations of products to reactants at equilibrium.

Knowing how to calculate and interpret \( K_{c} \) is crucial for predicting the direction and extent of chemical reactions. With changes in external conditions like temperature, thermodynamics helps us understand how \( K_{c} \) will change, thereby altering the equilibrium of a reaction.
Exothermic Reaction
An exothermic reaction is one that releases energy, usually in the form of heat, to its surroundings. This usually happens because the energy required to break the bonds in the reactants is less than the energy released when new bonds are formed in the products.

A good example of exothermic reactions includes combustion and some synthesis reactions, such as the formation of methanol from carbon monoxide and hydrogen gas.
  • Exothermic reactions result in a decrease in the enthalpy (\( \Delta H < 0 \)).
  • These reactions release heat, making their environment warmer.


When the equilibrium constant \( K_{c} \) decreases as temperature increases, it indicates that the reaction is exothermic. This is because increasing temperature shifts the equilibrium, favoring the reactants to absorb the excess heat, and reducing \( K_{c} \).
Le Chatelier's Principle
Le Chatelier's Principle is a fundamental concept in chemistry that predicts how different changes in conditions can affect the position of equilibrium in a reversible reaction. This principle states that if an external change is applied to a system at equilibrium, the system will adjust itself to partially counteract that change and establish a new equilibrium.

For exothermic reactions, increasing the temperature adds additional heat. According to Le Chatelier's Principle, if you add heat to an exothermic reaction, the equilibrium position will shift to favor the reactants.
  • Le Chatelier's Principle helps in predicting how changes in concentration, temperature, or pressure will affect the position of the equilibrium.
  • It's a tool for understanding how reaction dynamics can shift in industrial and laboratory settings.

By observing changes in \( K_{c} \) with temperature shifts, chemists can determine whether a reaction is exothermic or endothermic, utilizing Le Chatelier's Principle to predict and manipulate chemical reaction outcomes.

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Most popular questions from this chapter

When 0.0322 mol of \(\mathrm{NO}\) and \(1.52 \mathrm{~g}\) of bromine are placed in a 1.00 - \(\mathrm{L}\) reaction vessel and sealed, the mixture reacts and the following equilibrium is established: $$ 2 \mathrm{NO}(g)+\mathrm{Br}_{2}(g) \rightleftharpoons 2 \mathrm{NOBr}(g) $$ At \(25^{\circ} \mathrm{C}\) the equilibrium pressure of nitrosyl bromide is \(0.438 \mathrm{~atm} .\) What is \(K_{p} ?\)

The equilibrium-constant expression for a gas reaction is $$ K_{c}=\frac{\left[\mathrm{CO}_{2}\right]^{3}\left[\mathrm{H}_{2} \mathrm{O}\right]^{4}}{\left[\mathrm{C}_{3} \mathrm{H}_{8}\right]\left[\mathrm{O}_{2}\right]^{5}} $$ Write the balanced chemical equation corresponding to this expression.

Sulfuryl chloride is used in organic chemistry as a chlorinating agent. At moderately high temperatures it decomposes as follows: $$ \begin{array}{r} \mathrm{SO}_{2} \mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{SO}_{2}(g)+\mathrm{Cl}_{2}(g) \\ \text { with } K_{c}=0.045 \text { at } 650 \mathrm{~K} . \end{array} $$ a. A sample of \(8.25 \mathrm{~g}\) of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) is placed in a \(1.00-\mathrm{L}\) reaction vessel and heated to \(650 \mathrm{~K}\). b. What are the equilibrium concentrations of all of the species? What fraction of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) has decomposed? c. If \(5 \mathrm{~g}\) of chlorine is inserted into the reaction vessel, what qualitative effect would this have on the fraction of \(\mathrm{SO}_{2} \mathrm{Cl}_{2}\) that has decomposed?

A 2.50-L vessel contains \(1.75 \mathrm{~mol} \mathrm{~N}_{2}, 1.75 \mathrm{~mol} \mathrm{H}_{2}\), and \(0.346 \mathrm{~mol} \mathrm{NH}_{3}\). What is the direction of reaction (forward or reverse) needed to attain equilibrium at \(401^{\circ} \mathrm{C} ?\) The equilibrium constant \(K_{c}\) for the reaction $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightleftharpoons 2 \mathrm{NH}_{3}(g) $$ is 0.50 at \(401^{\circ} \mathrm{C}\)

A chemist wants to prepare phosgene, \(\mathrm{COCl}_{2}\), by the following reaction: $$ \mathrm{CO}(g)+\mathrm{Cl}_{2}(g) \rightleftharpoons \mathrm{COCl}_{2}(g) $$ He places \(4.00 \mathrm{~g}\) of chlorine, \(\mathrm{Cl}_{2}\), and an equal molar amount of carbon monoxide, \(\mathrm{CO}\), into a 10.00 - \(\mathrm{L}\) reaction vessel at \(395^{\circ} \mathrm{C}\). After the reaction comes to equilibrium, he adds another \(4.00 \mathrm{~g}\) of chlorine to the vessel in order to push the reaction to the right to get more product. What is the partial pressure of phosgene when the reaction again comes to equilibrium? \(K_{c}=1.23 \times 10^{3}\).

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