The key step in the manufacture of sulfuric acid is the...

The key step in the manufacture of sulfuric acid is the oxidation of sulfur dioxide in the presence of a catalyst, such as $\mathrm{V}_{2} \mathrm{O}_{5}$ . At $727^{\circ} \mathrm{C}, 0.010 \mathrm{mol}$ of $\mathrm{SO}_{2}$ is injected into an empty $2.00-\mathrm{L}$ container $\left(K_{\mathrm{p}}=3.18\right) .$ (a) What is the equilibrium pressure of $\mathrm{O}_{2}$ that is needed to maintain a 1$/ 1$ mole ratio of $\mathrm{SO}_{3}$ to $\mathrm{SO}_{2} ?$ (b) What is the equilibrium pressure of $\mathrm{O}_{2}$ needed to maintain a 95$/ 5$ mole ratio of $\mathrm{SO}_{3}$ to $\mathrm{SO}_{2} ?$

The key step in the manufacture of sulfuric acid is the oxidation of sulfur dioxide in the presence of a catalyst, such as $\mathrm{V}_{2} \mathrm{O}_{5}$ . At $727^{\circ} \mathrm{C}, 0.010 \mathrm{mol}$ of $\mathrm{SO}_{2}$ is injected into an empty $2.00-\mathrm{L}$ container $\left(K_{\mathrm{p}}=3.18\right) .$
(a) What is the equilibrium pressure of $\mathrm{O}_{2}$ that is needed to maintain a 1$/ 1$ mole ratio of $\mathrm{SO}_{3}$ to $\mathrm{SO}_{2} ?$
(b) What is the equilibrium pressure of $\mathrm{O}_{2}$ needed to maintain a 95$/ 5$ mole ratio of $\mathrm{SO}_{3}$ to $\mathrm{SO}_{2} ?$

Key Concepts

Chemical Equilibrium

Chemical equilibrium refers to the state in a reversible reaction where the rates of the forward and reverse reactions are equal, resulting in constant concentrations or partial pressures of all reactants and products. It is foundational for understanding how reactions can adjust to changes and how the composition of a reacting system stabilizes over time.

Equilibrium Constant (Kp)

The equilibrium constant expressed in terms of partial pressures, Kp, quantifies the ratio of the products' partial pressures to those of the reactants, each raised to the power of their stoichiometric coefficients. It provides a measure of the position of equilibrium and allows calculations of unknown pressures when the system is at equilibrium.

Partial Pressures

Partial pressures refer to the pressures that individual gases in a mixture exert as if they alone occupied the entire volume. This concept is critical in gas-phase equilibrium calculations, where each component's contribution to the overall pressure is used to determine the reaction conditions at equilibrium.

Reaction Stoichiometry

Reaction stoichiometry involves the quantitative relationships between reactants and products as dictated by a balanced chemical equation. It is used to relate the changes in the number of moles of each substance to their respective partial pressures in gas-phase reactions, enabling the derivation of equilibrium conditions.

Catalysis

Catalysis involves the use of a catalyst to accelerate the rate at which equilibrium is reached without altering the position of the equilibrium itself. In industrial processes, catalysts are essential for enhancing reaction rates and improving process efficiency, even though they do not affect the equilibrium constant.

Transcript

00:01 So this question is dealing with the oxidation of so2.

00:05 And so the oxidation of so2, it goes from so2 plus oxygen and gives so3.

00:14 And this is a common oxidation step that's used in the production of sulfuric acid.

00:21 So this is a reaction you should know and recognize.

00:23 Balancing this gives us two in front of both the sulfur -containing species.

00:29 And so this problem actually gives us quite a bit of extra information that isn't necessary.

00:34 And so to see that, we're going to just start out using writing the kp out, which we're given is 3 .1a, and we should write out what the mass action expression is.

00:46 And so it's products overreactant.

00:49 So we have the pressure of so3, whole thing squared, because of the two in front of it.

00:57 And in the bottom we have pressure of o2 times the pressure of s .o2 squared.

01:10 This is what the kp expression is saying.

01:13 Now, the first part of the question just asks what happens, what level of, what pressure of oxygen is needed to have the amount of moles of s .o3 and s .o2 be equal.

01:25 Now, something you need to know from gas theory is that if the same number of moles of s .o3 and s .o .2, assuming they're all behaving like ideal gases exist, then the pressure will be the same.

01:38 And so this pressure of s .o3 is going to be equal to the pressure of s .o2, and you can just cancel these out.

01:46 These are the same thing.

01:47 And so then what we have is we have that the pressure of o2 that's required is 1 over 3 .18.

01:57 And that gives us 0 .3144 atmospheres.

02:06 The second part of the question requires the same idea, but just a little bit more finesse to get an equation for the pressure of o2...

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