Consider the system A(g)+2 B(g)+C(s) ⇌2 D(g) at 25^∘ C. At zero time, only A, B, and C are pres

step 1 Okay, so we have a balanced equation. We have some reactants, which are A and B and C, and our p

Consider the system A(g)+2 B(g)+C(s) ⇌2 D(g) at 25^∘ C. At...

Consider the system $$ \mathrm{A}(g)+2 \mathrm{~B}(g)+\mathrm{C}(s) \rightleftharpoons 2 \mathrm{D}(g) $$ at $25^{\circ} \mathrm{C}$. At zero time, only $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ are present. The reaction reaches equilibrium 10 min after the reaction is initiated. Partial pressures of $A, B,$ and $D$ are written as $P_{\mathrm{A}}, P_{\mathrm{B}},$ and $P_{\mathrm{D}}$ Answer the questions below, using LT (for is less than), GT (for is greater than), $\mathrm{EQ}$ (for is equal to), or MI (for more information required). (a) $P_{\mathrm{D}}$ at $11 \mathrm{~min} \longrightarrow P_{\mathrm{D}}$ at $12 \mathrm{~min}$. (b) $P_{\mathrm{A}}$ at $5 \mathrm{~min}_{\mathrm{A}}$ at $7 \mathrm{~min}$. (c) $K$ for the forward reaction $\quad K$ for the reverse reaction. (d) At equilibrium, $K_{\longrightarrow} Q$. (e) After the system is at equilibrium, more of gas $\mathrm{B}$ is added. After the system returns to equilibrium, $K$ before the addition of $\mathrm{B}$ $K$ after the addition of $\mathrm{B}$. (f) The same reaction is initiated, this time with a catalyst. $K$ for the system without a catalyst $\quad K$ for the system with a catalyst. (g) $K$ for the formation of one mole of $\mathrm{D}$ $K$ for the formation of two moles of $\mathrm{D}$. (h) The temperature of the system is increased to $35^{\circ} \mathrm{C} . P_{\mathrm{B}}$ at equilibrium at $25^{\circ} \mathrm{C}_{ } \quad P_{\mathrm{B}}$ at equilibrium at $35^{\circ} \mathrm{C}$. (i) Ten more grams of $\mathrm{C}$ are added to the system. $P_{\mathrm{B}}$ before the addition of $C$ $P_{\mathrm{B}}$ after the addition of $\mathrm{C}$

Consider the system
$$
\mathrm{A}(g)+2 \mathrm{~B}(g)+\mathrm{C}(s) \rightleftharpoons 2 \mathrm{D}(g)
$$
at $25^{\circ} \mathrm{C}$. At zero time, only $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ are present. The reaction reaches equilibrium 10 min after the reaction is initiated. Partial pressures of $A, B,$ and $D$ are written as $P_{\mathrm{A}}, P_{\mathrm{B}},$ and $P_{\mathrm{D}}$
Answer the questions below, using LT (for is less than), GT (for is greater than), $\mathrm{EQ}$ (for is equal to), or MI (for more information required). (a) $P_{\mathrm{D}}$ at $11 \mathrm{~min} \longrightarrow P_{\mathrm{D}}$ at $12 \mathrm{~min}$.
(b) $P_{\mathrm{A}}$ at $5 \mathrm{~min}_{\mathrm{A}}$ at $7 \mathrm{~min}$.
(c) $K$ for the forward reaction $\quad K$ for the reverse reaction.
(d) At equilibrium, $K_{\longrightarrow} Q$.
(e) After the system is at equilibrium, more of gas $\mathrm{B}$ is added. After the system returns to equilibrium, $K$ before the addition of $\mathrm{B}$
$K$ after the addition of $\mathrm{B}$.
(f) The same reaction is initiated, this time with a catalyst. $K$ for the system without a catalyst $\quad K$ for the system with a catalyst.
(g) $K$ for the formation of one mole of $\mathrm{D}$ $K$ for the formation
of two moles of $\mathrm{D}$.
(h) The temperature of the system is increased to $35^{\circ} \mathrm{C} . P_{\mathrm{B}}$ at equilibrium at $25^{\circ} \mathrm{C}_{ } \quad P_{\mathrm{B}}$ at equilibrium at $35^{\circ} \mathrm{C}$.
(i) Ten more grams of $\mathrm{C}$ are added to the system. $P_{\mathrm{B}}$ before the addition of $C$ $P_{\mathrm{B}}$ after the addition of $\mathrm{C}$

Key Concepts

Effect of Temperature on Equilibrium

Temperature changes can affect the equilibrium position and the value of the equilibrium constant. For exothermic reactions, increasing the temperature generally decreases K, while for endothermic reactions, K typically increases with temperature. This is because temperature directly influences the energetic favorability of the forward or reverse reaction.

Partial Pressure and Equilibrium

In reactions involving gases, partial pressures are used in place of concentrations in the equilibrium constant expression. The measurement and comparison of partial pressures allow predictions of how the system responds to changes such as pressure adjustments or the addition of more gaseous reactants or products.

Reaction Stoichiometry and Equilibrium Expression

Stoichiometry in a chemical reaction provides the proportional relationships between reactants and products and is essential in writing the equilibrium constant expression. The stoichiometric coefficients are used as exponents in these expressions, and altering these coefficients (e.g., expressing the equilibrium formation on a per mole basis) will change the mathematical form of the equilibrium constant but not its underlying thermodynamic meaning.

Role of Catalyst in Equilibrium

A catalyst speeds up both the forward and reverse reaction rates without altering the equilibrium constant or the equilibrium position. It helps the reaction reach equilibrium faster, but it does not change the concentrations of reactants and products at equilibrium.

Effect of Concentration Changes

Changing the concentration or partial pressures of reactants or products can shift the equilibrium position. According to Le Chatelier’s Principle, an increase in the concentration of a reactant will shift the equilibrium toward the products, while an increase in a product’s concentration will shift it back toward the reactants.

Le Chatelier’s Principle

Le Chatelier’s Principle states that if a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, the system will adjust to partially counteract the disturbance and re-establish equilibrium. This principle is used to predict how changes such as the addition of more reactant or product will affect the system's equilibrium state.

Reaction Quotient (Q) and its Relation to K

The reaction quotient, Q, is calculated using the same expression as the equilibrium constant but for any arbitrary state of the reaction. Comparing Q to K allows prediction of the direction in which the reaction will shift to reach equilibrium: if Q is less than K, the forward reaction is favored, and if Q is greater than K, the reverse reaction is favored.

Equilibrium Constant (K)

The equilibrium constant, K, is a ratio that expresses the relationship between product and reactant activities (or partial pressures/concentrations for homogeneous systems) at equilibrium. Importantly, K is only affected by changes in temperature and is independent of initial conditions or the addition of inert substances or catalysts.

Reaction Rate and Dynamic Equilibrium

The rate at which the forward reaction produces products is exactly matched by the rate at which the reverse reaction regenerates reactants at equilibrium. This dynamic balance means that while the system appears to be static macroscopically, molecular activity continues at the same rate in both directions.

Chemical Equilibrium

Chemical equilibrium occurs when a reversible reaction reaches a state in which the forward and reverse reaction rates are equal. At this point, the concentrations or partial pressures of the reactants and products remain constant over time, even though the individual molecular events continue to occur.

Transcript

00:01 Okay, so we have a balanced equation.

00:03 We have some reactants, which are a and b and c, and our product is d.

00:08 We know that our equilibrium is reached at 10 minutes.

00:13 Okay.

00:14 So we know that we're at equilibrium at 10 minutes.

00:20 So the partial pressure of our product, d, at 11 minutes.

00:26 Okay, so now we're at equilibrium is going to equal the partial pressure of d at 12 minutes.

00:34 Once you've reached equilibrium, the partial pressures won't change.

00:42 So in this example, the second one, we have not reached equilibrium yet, okay? so we've not yet reached equilibrium.

00:50 So that means the partial pressures are still changing.

00:53 The partial pressures of our reactants are decreasing, and the partial pressures of our products are increasing.

00:59 So the partial pressure of a at five minutes is going to be greater than the partial pressure of a, at seven minutes.

01:10 So using the key that they want.

01:13 So we'll say eq for equals on this one and we'll say greater than gt for this one.

01:21 So on this next piece, we know that k for the forward reaction is 1 over k for the reverse reaction, but we don't know the value for k.

01:33 Okay, so we don't know k.

01:36 So we can't answer this question.

01:41 We don't know which.

01:42 One is bigger or smaller.

01:44 If k were less than one, that number would, the inverse would make it quite large, but if it's greater than one, it makes it quite small.

01:51 So we can't answer that question without an actual value for k.

01:57 So the next one, we're trying to, we're at equilibrium.

02:03 Okay...

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