brown colorless $\ce{2no_{2}(g) \
ightleftharpoons n_{2}o_{4}(g)}$ a sample of pure $\ce{no_{2}(g)}$ in a sealed tube at $20^{\circ}\text{c}$ is placed in a temperature bath at $30^{\circ}\text{c}$. observations of changes in the color, pressure, and mass of the mixture are recorded as a function of time. which of the following is an observation that would best support the claim that the reaction represented above has reached equilibrium at $30^{\circ}\text{c}$? a the total mass of the system remains constant because the amounts of reactant and product do not change with time at equilibrium. b the color of the system changes from brown to completely colorless because only the product will be present at equilibrium. c the total pressure of the system decreases then reaches a constant value because the amounts of reactant and product no longer change at equilibrium. d the temperature of the system remains constant because the temperature must be constant at equilibrium.

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# Brief Explanations: To determine the correct option, we analyze each choice based on chemical equilibrium concepts: - Option A: In a sealed system, mass is conserved (Law of Conservation of Mass). At equilibrium, the rates of forward and reverse reactions are equal, so the amounts of reactant and product stop changing. This matches the definition of equilibrium. - Option B: The reaction is in equilibrium (not complete), so both reactant ($\ce{NO2}$, brown) and product ($\ce{N2O4}$, colorless) are present. A complete color change to colorless would imply the reaction went to completion, which is not true for equilibrium. Eliminate B. - Option C: For the reaction $\ce{2NO2(g) <=> N2O4(g)}$, the number of moles of gas decreases (2 moles $\ce{NO2}$ to 1 mole $\ce{N2O4}$). As the reaction proceeds towards equilibrium, pressure (related to moles of gas) decreases until equilibrium is reached (constant pressure). This observation supports equilibrium. Wait, but let's re - evaluate. Wait, the question is which observation supports equilibrium. Wait, no, let's check again. Wait, the reaction is $\ce{2NO2(g) <=> N2O4(g)}$. At equilibrium, the amounts of reactant and product are constant, so pressure (which depends on moles of gas) becomes constant. But let's check Option A again. Option A says total mass is constant (which is always true in a sealed system, not just at equilibrium) and amounts of reactant and product do not change with time (which is true at equilibrium). Wait, maybe I made a mistake. Wait, the key is that at equilibrium, the concentrations (or amounts) of reactants and products remain constant because the forward and reverse rates are equal. The total mass is always constant in a sealed system, so the first part of A is always true, but the second part (amounts of reactant and product do not change with time) is true at equilibrium. Now, Option C: The total pressure decreases then becomes constant. Since the reaction has a change in moles of gas (2 moles $\ce{NO2}$ to 1 mole $\ce{N2O4}$), as the reaction proceeds towards equilibrium (from pure $\ce{NO2}$ initially), the moles of gas decrease, so pressure decreases until equilibrium is reached (constant pressure). This also supports equilibrium. Wait, but the question is which is the best observation. Wait, no, let's re - examine the options. Wait, the reaction starts with pure $\ce{NO2}$ (brown) at 20°C, then is placed at 30°C. Let's think about the equilibrium state. At equilibrium, the macroscopic properties (like color, pressure, concentration) are constant because the rates of forward and reverse reactions are equal. - Option D: The temperature of the system is constant because the temperature of the bath is constant, not because of equilibrium. The system is in a temperature bath, so the temperature is controlled by the bath, not by the equilibrium (which involves energy changes, but the bath keeps T constant). So D is incorrect. Now, between A and C: - For Option A: The total mass is always constant in a sealed system (conservation of mass), so the fact that mass is constant doesn't prove equilibrium. The second part (amounts of reactant and product don't change with time) does prove equilibrium. - For Option C: The pressure decreases as the reaction proceeds (since moles of gas decrease) until equilibrium is reached (constant pressure). This also proves equilibrium. But wait, the reaction is $\ce{2NO2(g) <=> N2O4(g)}$. When the system reaches equilibrium, the rate of forward reaction ( $\ce{2NO2 -> N2O4}$ ) equals the rate of reverse reaction ( $\ce{N2O4 -> 2NO2}$ ). So the amounts of $\ce{NO2}$ and $\ce{N2O4}$ are constant, so the color (due to $\ce{NO2}$) is constant, the pressure (due to total moles of gas) is constant, and the mass is constant. Wait, maybe I misanalyzed Option A. The total mass of the system remains constant because it's a sealed system (Law of Conservation of Mass), regardless of equilibrium. The amounts of reactant and product not changing with time is the definition of equilibrium. So Option A's first part is always true, but the second part is true at equilibrium. Option C: The total pressure decreases (as the reaction proceeds, moles of gas decrease) then becomes constant (at equilibrium, moles of gas are constant, so pressure is constant). This is a valid observation for equilibrium. But wait, the question is which observation best supports the claim that equilibrium has been reached. Wait, let's check the options again: - Option A: "The total mass of the system remains constant because the amounts of reactant and product do not change with time at equilibrium." Wait, the mass is constant because it's sealed, not because reactant and product amounts don't change. The cause - effect here is wrong. The mass is constant due to conservation of mass, independent of equilibrium. The amounts of reactant and product not changing with time is because of equilibrium. So the wording of A is a bit off, but the key point is that at equilibrium, reactant and product amounts are constant. - Option C: "The total pressure of the system decreases then reaches a constant value because the amounts of reactant and product no longer change at equilibrium." The pressure decreases because the moles of gas are decreasing as the reaction proceeds towards equilibrium. Once equilibrium is reached, moles of gas are constant, so pressure is constant. This is a correct cause - effect and a valid observation for equilibrium. Wait, but maybe the correct answer is A? Wait, no, let's think about the reaction. The system is sealed, so mass is always constant. The fact that reactant and product amounts don't change with time is the definition of equilibrium. So A's second part is correct, and the first part is a general truth. But C's explanation is also correct. Wait, maybe I made a mistake. Let's check the reaction again. The reaction is $\ce{2NO2(g) <=> N2O4(g)}$. Initial state: pure $\ce{NO2}$ (brown). As the reaction proceeds, $\ce{NO2}$ is converted to $\ce{N2O4}$, so the color fades (less brown) and pressure decreases (less moles of gas). At equilibrium, the color and pressure stop changing. Now, let's re - evaluate each option: - Option A: Total mass is constant (always true) and amounts of reactant and product don't change with time (true at equilibrium). But the "because" in A is incorrect. The mass is constant because it's sealed, not because reactant and product amounts don't change. So the cause - effect is wrong. - Option B: Color changes to completely colorless. But at equilibrium, $\ce{NO2}$ (brown) is still present, so the system can't be completely colorless. So B is wrong. - Option C: Total pressure decreases then becomes constant because amounts of reactant and product no longer change at equilibrium. As the reaction proceeds, moles of gas decrease (since 2 moles $\ce{NO2}$ make 1 mole $\ce{N2O4}$), so pressure decreases. When equilibrium is reached, moles of gas are constant, so pressure is constant. This is a correct observation and correct cause - effect. - Option D: Temperature is constant because the bath is constant, not because of equilibrium. So D is wrong. So the correct option is C? Wait, no, wait. Wait, the reaction is $\ce{2NO2(g) <=> N2O4(g)}$. The key is that at equilibrium, the rates of forward and reverse reactions are equal, so the concentrations (amounts) of reactants and products are constant. So the pressure (which depends on the total moles of gas) becomes constant when the amounts of reactant and product are constant (at equilibrium). So Option C's observation (pressure decreases then becomes constant) and explanation (because amounts of reactant and product no longer change) is correct. Option A's explanation for mass being constant is wrong (mass is constant due to sealed system, not due to equilibrium). So the correct answer is C? Wait, but let's check again. Wait, maybe I messed up. Let's see the options again. Wait, the question is "Which of the following is an observation that would best support the claim that the reaction... has reached equilibrium at 30°C?" Let's analyze each option: - Option A: "The total mass of the system remains constant because the amounts of reactant and product do not change with time at equilibrium." The total mass remains constant because the system is sealed (conservation of mass), regardless of whether it's at equilibrium. So the "because" here is incorrect. The fact that amounts of reactant and product don't change with time is a sign of equilibrium, but the mass being constant is not caused by that. So A is incorrect. - Option B: "The color of the system changes from brown to completely colorless because only the product will be present at equilibrium." At equilibrium, both reactant ($\ce{NO2}$, brown) and product ($\ce{N2O4}$, colorless) are present. So the system can't be completely colorless. B is incorrect. - Option C: "The total pressure of the system decreases then reaches a constant value because the amounts of reactant and product no longer change at equilibrium." As the reaction $\ce{2NO2(g) <=> N2O4(g)}$ proceeds (forward reaction), the number of moles of gas decreases (2 moles of $\ce{NO2}$ produce 1 mole of $\ce{N2O4}$), so the total pressure (which is related to the number of moles of gas) decreases. When equilibrium is reached, the rates of forward and reverse reactions are equal, so the amounts of reactant and product stop changing. This means the number of moles of gas stops changing, so the total pressure becomes constant. This observation and explanation are correct. - Option D: "The temperature of the system remains constant because the temperature must be constant at equilibrium." The system is in a temperature bath, so the temperature is controlled by the bath, not by the equilibrium state. The temperature being constant is due to the bath, not because the reaction is at equilibrium. D is incorrect. # Answer: C. The total pressure of the system decreases then reaches a constant value because the amounts of reactant and product no longer change at equilibrium.

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