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When phosphorus pentachloride, \(\mathrm{PCl}_{5}(g),\) is placed in a sealed container, it breaks apart reversibly. h e concentrations of the starting substance and products are monitored. Use the data in the table to create a graph showing the concentrations of the starting substance and products over time. $$\mathrm{PCl}_{5}(g) \leftrightharpoons \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g)$$ \(\begin{array}{|c|c|c|c|}\hline \text{ Time (s)} & \text{ \)\left[\mathbf{P} \mathrm{I}_{\mathrm{5}}\right](\mathrm{mol} / \mathrm{L})\(} & \text{ \)\left[\mathbf{P} \mathrm{I}_{\mathrm{3}}\right](\mathrm{mol} / \mathrm{L})\(} & \text{ \)\left[\mathrm{Cl}_{2}\right](\mathrm{mol} / \mathrm{L})\(} \\ \hline 0 & {0.00} & {1.00} & {1.00} \\ \hline 20 & {0.10} & {0.90} & {0.90} \\ 40 & {0.20} & {0.80} & {0.80} \\ \hline 60 & {0.25} & {0.75} & {0.75} \\ \hline 80 & {0.29} & {0.71} & {0.71} \\ \hline 100 & {0.29} & {0.71} & {0.71} \\\ \hline 120 & {0.29} & {0.71} & {0.71} \\ \hline\end{array}\) a. What are the equilibrium concentrations of the starting substance and the products? b. At what time did the mixture reach equilibrium? How do you know? c. At 20 seconds, which process is faster, the forward or the reverse process? At 100 seconds? d. Why is the amount of starting substance, \(\mathrm{PCl}_{5},\) not equal to the amounts of each of the products, \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2},\) at equilibrium? Support your answer with evidence. e. Why are the amounts of \(\mathrm{PCl}_{3}\) and \(\mathrm{Cl}_{2}\) always equal to one another?

Step by step solution

01

Understanding the Reaction

The chemical equilibrium reaction given is \(PCl_5(g) \leftrightharpoons PCl_3(g) + Cl_2(g)\). This reversibility means the reaction is dynamic, where the forward reaction forms products and the reverse reaction reforms the reactant.

02

Gathering and Analyzing Data

We have the concentrations of \(PCl_5, PCl_3,\) and \(Cl_2\) at different times. As the reaction proceeds, we observe changes in these concentrations until equilibrium is reached.

03

Plotting the Graph

Create a graph with the time on the x-axis and concentrations on the y-axis. Plot the data points for \([PCl_5]\), \([PCl_3]\), and \([Cl_2]\) using the table values. The graph will show lines that represent how these concentrations change over time.

04

Determining Equilibrium Concentrations

From the given data, equilibrium is reached when concentrations no longer change, which occurs at 80 seconds and onwards. Hence, the equilibrium concentrations are: \([PCl_5] = 0.29 \, \text{mol/L}\), \([PCl_3] = 0.71 \, \text{mol/L}\), and \([Cl_2] = 0.71 \, \text{mol/L}\).

05

Identifying Equilibrium Time

The equilibrium is reached when the concentrations of reactants and products remain constant. Based on the data, this occurs at 80 seconds since the concentrations from 80 seconds to 120 seconds remain constant.

06

Analyzing Reaction Rate at Given Times

At 20 seconds, \(PCl_5\) is forming (increasing from 0 to 0.10 mol/L), so the forward reaction is faster. At 100 seconds, the system is at equilibrium, and both reactions proceed at the same rate.

07

Analyzing Substances' Amount Disparity

\(PCl_5\) does not equal \(PCl_3\) or \(Cl_2\) at equilibrium because the initial condition had 1 mol/L of each product. The products were initially present, while \(PCl_5\) started from zero.

08

Equality of Product Concentrations

\(PCl_3\) and \(Cl_2\) always have equal concentrations as they are produced together in a 1:1 ratio according to the balanced equation, ensuring their concentrations increase equally over time.

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Key Concepts

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

Dynamic Equilibrium

Dynamic equilibrium is a fascinating concept in chemistry. It takes place in reversible reactions, where the forward and reverse reactions happen simultaneously. In such reactions, the change is continuous, even though it may seem like everything has stopped once equilibrium is reached.
For our reaction, when phosphorus pentachloride ( PCl_5(g) ) decomposes into phosphorus trichloride ( PCl_3(g) ) and chlorine ( Cl_2(g) ), dynamic equilibrium is achieved when the rates of the forward and reverse reactions are equal. This balance means that the concentrations of reactants and products remain constant, even though the molecules continue to react.
It's important to note that dynamic equilibrium does not mean that reactants and products are present in equal concentrations. Instead, it indicates that the forward and reverse processes happen at the same rate, keeping their concentrations steady.

Reaction Rates

Reaction rates play a crucial role in understanding dynamic equilibrium. They indicate how quickly reactants are transformed into products and vice versa.
Initially, when PCl_5 starts breaking down, the forward reaction is faster as products PCl_3 and Cl_2 form rapidly. Meanwhile, PCl_5 is still being produced, but at a slower pace. As time progresses, the reverse reaction accelerates, reforming PCl_5 until the system achieves equilibrium.
At equilibrium, the reaction rates of the forward and reverse reactions are equal. That's why the concentrations remain constant. However, changes in conditions, such as temperature or pressure, can affect these rates, shifting the equilibrium and altering the proportions of reactants and products.

Plotting Graphs in Chemistry

Graphing is a powerful tool for visualizing chemical reactions and understanding equilibrium. By plotting data points representing concentrations over time, you can observe how a reaction proceeds.
On the graph, time is placed on the x-axis, while concentration appears on the y-axis. When dealing with the decomposition of PCl_5 , marking the plotted line points will reveal how concentrations of PCl_5 , PCl_3 , and Cl_2 shift as the reaction progresses.
At the beginning of the reaction, you will notice a change in slope, especially with the reactants being consumed and products being formed. As equilibrium sets in, the slopes of these lines flatten, indicating constant concentrations. Being able to interpret these graphs is crucial, as it helps clarify the equilibrium state and the overall reaction dynamics.

Le Chatelier's Principle

Le Chatelier's Principle is essential to understanding how a chemical reaction responds to external changes. It predicts how the position of equilibrium will shift when conditions like pressure, temperature, or concentration change.
If you increase the concentration of reactants ( PCl_5 ), the system will favor the forward reaction to form more products ( PCl_3 and Cl_2 ), trying to lower the concentration of the added reactant. Similarly, altering the temperature or pressure can lead to shifts in equilibrium, often aiming to counteract the change introduced.
For instance, if the system is exothermic, raising the temperature will shift the equilibrium towards the reactants, as the system seeks to absorb excess heat. Understanding Le Chatelier's Principle helps chemists predict how reactions will behave under different conditions, making it a vital tool in chemical manufacturing and applications.