At 900 K, the following reaction has 𝐾 𝑝 = 0.345: 2 SO 2 (𝑔) + O 2 (𝑔) ⇌ 2 SO 3 (𝑔) In an equilibrium mixture the partial pressures of SO 2 and O 2 are 0.135 atm and 0.455 atm, respectively. What is the equilibrium partial pressure of SO 3 in the mixture?

Hello everyone today. We are being given the following problem and asked to solve for it. So it says the equilibrium constant K. P. For the oxidation of nitric oxide is 1152 at 1 50 degrees Celsius. Were then given the following chemical reaction In that reaction mixture at equilibrium oxygen has a partial pressure of .345 atmospheres. While the partial pressure of nitrogen dioxide is .225 atmospheres were then asked to calculate the partial pressure of nitric oxide at equilibrium. So the first thing we want to do does he want to calculate, we want to write out our K. P. For the expression below. So R. K. P. It's going to be equal to the pressures of our products over reactivates. And so putting this together, We have our pressure of our only product which is nitrogen dioxide in 02. And since there is a two coefficient we're going to make this exponent into a. two and our denominator we have to react. It's present. We have nitric oxide and so we have the pressure of N. O. Nitric oxide and that has a two coefficient as well. So we're going to give that an exponent of two. And lastly we're going to multiply the second reactant from by the first one which is just molecular oxygen. And so we have our K. P. Expression below. We also were given a partial pressure of oxygen and the partial pressure of pressure of nitrogen dioxide. And so ultimately we want to find the partial pressure of nitric oxide. So we're gonna label that X. And so Plugging our values in to this reaction that we just found we have our K. P. or equilibrium constant being 1,152. And that's going to equal Our partial pressure of our nitrogen dioxide. Which in the question Stem said that it was 0.225 atmospheres. And we're going to square that and then we're going to divide that by our partial pressure of nitric oxide, which we don't know. So we're just gonna say X. And we're gonna square that as well. And then our partial pressure for molecular oxygen or 02 is 0.345 atmospheres, solving for X. We get an X. is equal to 0.0113 atmospheres. In other words, this is our partial pressure of nitric oxide. I hope this helped. And until next time.

Ch.15 - Chemical Equilibrium

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Brown 14th Edition

Ch.15 - Chemical Equilibrium

Problem 46

Chapter 15, Problem 46

At 900 K, the following reaction has 𝐾_𝑝 = 0.345: 2 SO₂(𝑔) + O₂(𝑔) ⇌ 2 SO₃(𝑔) In an equilibrium mixture the partial pressures of SO₂ and O₂ are 0.135 atm and 0.455 atm, respectively. What is the equilibrium partial pressure of SO₃ in the mixture?

Verified step by step guidance

Write the expression for the equilibrium constant, Kp, for the reaction. For the reaction 2 SO2(g) + O2(g) ⇌ 2 SO3(g), the expression is Kp = (P_SO3)^2 / ((P_SO2)^2 * P_O2).

Substitute the given values of the partial pressures of SO2 and O2 into the Kp expression. Here, P_SO2 = 0.135 atm and P_O2 = 0.455 atm.

Rearrange the Kp expression to solve for P_SO3. This involves isolating P_SO3 on one side of the equation.

Take the square root of both sides of the equation to solve for P_SO3, since P_SO3 is squared in the Kp expression.

Ensure that the units are consistent and that the calculation is dimensionally correct to find the equilibrium partial pressure of SO3.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constant (Kp)

The equilibrium constant, Kp, is a dimensionless number that expresses the ratio of the partial pressures of products to reactants at equilibrium for a given reaction at a specific temperature. For the reaction 2 SO2(g) + O2(g) ⇌ 2 SO3(g), Kp is calculated using the formula Kp = (P_SO3^2) / (P_SO2^2 * P_O2), where P represents the partial pressures of the gases involved. A Kp value less than 1 indicates that at equilibrium, the reactants are favored over the products.

Partial Pressure

Partial pressure is the pressure exerted by a single component of a gas mixture. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of each individual gas. In this context, knowing the partial pressures of SO2 and O2 allows us to calculate the partial pressure of SO3 at equilibrium using the equilibrium constant.

Le Chatelier's Principle

Le Chatelier's Principle states that if a dynamic equilibrium is disturbed by changing the conditions, the system will adjust itself to counteract the change and restore a new equilibrium. This principle helps predict how changes in concentration, pressure, or temperature will affect the position of equilibrium. In this case, understanding how the equilibrium shifts can provide insights into the relationship between the partial pressures of the reactants and products.