Duration of Equilibrium Reaction

In summary, the question is asking for the duration of a reversible reaction where 10 moles of A and zero moles of B are involved. After 1 minute, 25% of A turns into B, and 50% of B turns into A. The class calculated the duration to be 5 minutes by determining the concentrations of A and B at each minute until equilibrium. However, it is unclear if this is the correct answer as the data provided is not enough to determine the order of the reaction. A possible solution was suggested using equations and the number of minutes passed.
  • #1
SciDude85
2
0
I am wondering the answer to the following question, and what equation you would use to solve it:
What is the duration of the following reversible reaction?

A <--> B
You have 10 moles of A and zero moles of B.
After 1 minute, 25% of A turns into B, and 50% of B turns into A.

My class calculated it to be 5 minutes by calculating how much A and B there will be after each minute until it reached equilibrium (6.667 moles A, 3.333 moles B), but I believe the correct answer will require calculus, but I don't know how.
 
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  • #2
This depends on what you mean by "duration". The reaction keeps occurring even in equilibrium and the approach to equilibrium is asymptotic (the difference from equilibrium decays exponentially).
 
  • #3
Actually there is not enough data to answer the problem. You are given two points - concentrations at the beginning and concentrations after one minute. That's not enough to determine the order of the reaction, and depending on what the order is, equation required to calculate reaction progress is different.

In most cases the concentration changes - as Dale said - asymptotically. The only case when it is not true is for the 0th order reactions, where the reaction speed is not dependent on the concentration (although this can get complicated, as for low concentrations such reactions often stop following the 0th order kinetics).

Compare https://en.wikipedia.org/wiki/Rate_equation
 
  • #4
I think what they meant for you to do was this:
$$A^{n+1}=A^n+(-0.25A^n+0.5B^n)$$
$$B^{n+1}=B^n+(0.25A^n-0.5B^n)$$
where n is the number of minutes that have passed. These equations reduce to:
$$A^{n+1}=0.75A^n+0.5B^n$$
$$B^{n+1}=0.25A^n+0.5B^n$$subject to ##A^0=1## and ##B^0=0##, so

After 1 minute:
##A=0.75##
##B=0.25##

After 2 minutes:
##A=0.6875##
##B= 0.3125##

ETC
 

1. What is the definition of "duration of equilibrium reaction"?

The duration of equilibrium reaction refers to the amount of time it takes for a chemical reaction to reach equilibrium, or a state of balance between the reactants and products.

2. How is the duration of equilibrium reaction determined?

The duration of equilibrium reaction is determined by the rate at which the forward and reverse reactions occur. It also depends on factors such as temperature, pressure, and concentration of reactants and products.

3. Can the duration of equilibrium reaction be changed?

Yes, the duration of equilibrium reaction can be changed by altering the conditions of the reaction. For example, increasing the temperature or concentration of reactants can speed up the reaction and decrease the duration, while decreasing the temperature or concentration can slow down the reaction and increase the duration.

4. What is the significance of knowing the duration of equilibrium reaction?

Knowing the duration of equilibrium reaction is important for understanding and controlling chemical reactions. This information can help scientists optimize reaction conditions, predict the outcome of reactions, and determine the amount of time needed for a reaction to reach completion.

5. How does the duration of equilibrium reaction affect the amount of product formed?

The duration of equilibrium reaction does not directly affect the amount of product formed. However, a longer duration may result in a higher yield of product, as the reaction has more time to proceed towards completion. Conversely, a shorter duration may result in a lower yield of product.

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