Questions: A chemical engineer is studying the following reaction: BF3(aq) + NH3(aq) -> BF3NH3(aq) At the temperature the engineer picks, the equilibrium constant Kc for this reaction is 1.4. The engineer charges ("fills") three reaction vessels with boron trifluoride and ammonia, and lets the reaction begin. He then measures the composition of the mixture inside each vessel from time to time. His first set of measurements are shown in the table below. Predict the changes in the compositions the engineer should expect next time he measures the compositions. reaction vessel compound concentration expected change in concer entration A BF3 0.99 M O increase 0 decrease O (no change) A NH3 0.53 M increase decrease O (no change) A BF3NH3 0.76 M increase decrease (no change) B BF3 0.56 M increase decrease O (no change) B NH3 0.10 M O increase 0 decrease (no change) B BF3NH3 1.19 M increase decrease O (no change) C BF3 1.37 M increase decrease O (no change) C NH3 0.74 M increase decrease O (no change) C BF3NH3 1.46 M increase decrease (no change)

A chemical engineer is studying the following reaction:
BF3(aq) + NH3(aq) -> BF3NH3(aq)

At the temperature the engineer picks, the equilibrium constant Kc for this reaction is 1.4.
The engineer charges ("fills") three reaction vessels with boron trifluoride and ammonia, and lets the reaction begin. He then measures the composition of the mixture inside each vessel from time to time. His first set of measurements are shown in the table below.

Predict the changes in the compositions the engineer should expect next time he measures the compositions.

reaction vessel  compound  concentration  expected change in concer  entration
A  BF3  0.99 M  O increase 0 decrease  O (no change)
A  NH3  0.53 M  increase decrease  O (no change)
A  BF3NH3  0.76 M  increase decrease  (no change)
B  BF3  0.56 M  increase decrease  O (no change)
B  NH3  0.10 M  O increase 0 decrease  (no change)
B  BF3NH3  1.19 M  increase decrease  O (no change)
C  BF3  1.37 M  increase decrease  O (no change)
C  NH3  0.74 M  increase decrease  O (no change)
C  BF3NH3  1.46 M  increase decrease  (no change)
Transcript text: A chemical engineer is studying the following reaction: \[ \mathrm{BF}_{3}(a q)+\mathrm{NH}_{3}(a q) \rightarrow \mathrm{BF}_{3} \mathrm{NH}_{3}(a q) \] At the temperature the engineer picks, the equilibrium constant $K_{c}$ for this reaction is 1.4. The engineer charges ("fills") three reaction vessels with boron triffuorlde and ammonia, and lets the reaction begin. He then measures the composition of the mixture inside each vessel from time to time. His first set of measurements are shown in the table below. Predict the changes in the compositions the engineer should expect next time he measures the compositions. \begin{tabular}{|c|c|c|c|c|} \hline reaction vessel & compound & concentration & expected change in concer & entration \\ \hline \multirow{3}{*}{A} & $\mathrm{BF}_{3}$ & 0.99 M & O $\uparrow$ increase $0 \mid$ decrease & O (no change) \\ \hline & $\mathrm{NH}_{3}$ & 0.53 M & $\dagger \uparrow$ increase $\bigcirc \downarrow$ decrease & O (no change) \\ \hline & $\mathrm{BF}_{3} \mathrm{NH}_{3}$ & 0.76 M & $\dagger \uparrow$ increase $\bigcirc \downarrow$ decrease & (no change) \\ \hline \multirow{3}{*}{B} & $\mathrm{BF}_{3}$ & 0.56 M & $\dagger \uparrow$ increase $\bigcirc \downarrow$ decrease & $O$ (no change) \\ \hline & NH3 & 0.10 M & O $\uparrow$ increase $0 \downarrow$ decrease & (no change) \\ \hline & $\mathrm{BF}_{3} \mathrm{NH}_{3}$ & 1.19 M & ○ $\uparrow$ increase $\bigcirc \downarrow$ decrease & O (no change) \\ \hline \multirow{3}{*}{c} & $\mathrm{BF}_{3}$ & 1.37 M & ○ $\uparrow$ increase $0 \downarrow$ decrease & O (no change) \\ \hline & $\mathrm{NH}_{3}$ & 0.74 M & ○ $\uparrow$ increase $0 \downarrow$ decrease & O (no change) \\ \hline & $\mathrm{BF}_{3} \mathrm{NH}_{3}$ & 1.46 M & $0 \uparrow$ increase $0 \mid 1$ decrease & (no change) \\ \hline \end{tabular}
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Solution

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Solution Steps

Step 1: Understanding the Reaction and Equilibrium Constant

The reaction given is: \[ \mathrm{BF}_{3}(aq) + \mathrm{NH}_{3}(aq) \rightarrow \mathrm{BF}_{3}\mathrm{NH}_{3}(aq) \]

The equilibrium constant \( K_c \) for this reaction is 1.4. The equilibrium constant expression for this reaction is: \[ K_c = \frac{[\mathrm{BF}_{3}\mathrm{NH}_{3}]}{[\mathrm{BF}_{3}][\mathrm{NH}_{3}]} \]

Step 2: Analyzing Reaction Vessel A

For vessel A, the concentrations are:

  • \([\mathrm{BF}_{3}] = 0.99 \, \text{M}\)
  • \([\mathrm{NH}_{3}] = 0.53 \, \text{M}\)
  • \([\mathrm{BF}_{3}\mathrm{NH}_{3}] = 0.76 \, \text{M}\)

Calculate the reaction quotient \( Q_c \): \[ Q_c = \frac{0.76}{0.99 \times 0.53} = \frac{0.76}{0.5247} \approx 1.448 \]

Since \( Q_c > K_c \), the reaction will shift to the left, decreasing \([\mathrm{BF}_{3}\mathrm{NH}_{3}]\) and increasing \([\mathrm{BF}_{3}]\) and \([\mathrm{NH}_{3}]\).

Step 3: Analyzing Reaction Vessel B

For vessel B, the concentrations are:

  • \([\mathrm{BF}_{3}] = 0.56 \, \text{M}\)
  • \([\mathrm{NH}_{3}] = 0.10 \, \text{M}\)
  • \([\mathrm{BF}_{3}\mathrm{NH}_{3}] = 1.19 \, \text{M}\)

Calculate the reaction quotient \( Q_c \): \[ Q_c = \frac{1.19}{0.56 \times 0.10} = \frac{1.19}{0.056} \approx 21.25 \]

Since \( Q_c > K_c \), the reaction will shift to the left, decreasing \([\mathrm{BF}_{3}\mathrm{NH}_{3}]\) and increasing \([\mathrm{BF}_{3}]\) and \([\mathrm{NH}_{3}]\).

Step 4: Analyzing Reaction Vessel C

For vessel C, the concentrations are:

  • \([\mathrm{BF}_{3}] = 1.37 \, \text{M}\)
  • \([\mathrm{NH}_{3}] = 0.74 \, \text{M}\)
  • \([\mathrm{BF}_{3}\mathrm{NH}_{3}] = 1.46 \, \text{M}\)

Calculate the reaction quotient \( Q_c \): \[ Q_c = \frac{1.46}{1.37 \times 0.74} = \frac{1.46}{1.0138} \approx 1.440 \]

Since \( Q_c > K_c \), the reaction will shift to the left, decreasing \([\mathrm{BF}_{3}\mathrm{NH}_{3}]\) and increasing \([\mathrm{BF}_{3}]\) and \([\mathrm{NH}_{3}]\).

Final Answer

  • Vessel A: \([\mathrm{BF}_{3}]\) and \([\mathrm{NH}_{3}]\) will increase, \([\mathrm{BF}_{3}\mathrm{NH}_{3}]\) will decrease. \[ \boxed{\text{BF}_3 \uparrow, \text{NH}_3 \uparrow, \text{BF}_3\text{NH}_3 \downarrow} \]

  • Vessel B: \([\mathrm{BF}_{3}]\) and \([\mathrm{NH}_{3}]\) will increase, \([\mathrm{BF}_{3}\mathrm{NH}_{3}]\) will decrease. \[ \boxed{\text{BF}_3 \uparrow, \text{NH}_3 \uparrow, \text{BF}_3\text{NH}_3 \downarrow} \]

  • Vessel C: \([\mathrm{BF}_{3}]\) and \([\mathrm{NH}_{3}]\) will increase, \([\mathrm{BF}_{3}\mathrm{NH}_{3}]\) will decrease. \[ \boxed{\text{BF}_3 \uparrow, \text{NH}_3 \uparrow, \text{BF}_3\text{NH}_3 \downarrow} \]

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