Kinetics with Total Gas Pressures

[flybynight]

Homework Statement

I am considering the reaction 2C₄H₆ --> C₈H₁₂ at 320 degrees C. Both the product and the reactant are gases.
I have the data:
Time (minutes): 0.00 3.25 12.18 24.55 42.50 68.05
Total P (torr): 632.0 618.5 584.2 546.8 509.3 474.6

Find the reaction order and the rate constant.
Assume that only C₄H₆ is present at the start of the reaction.

Homework Equations

rate=k[C₈H₁₂]^x
Perhaps PV=nRT?

The Attempt at a Solution

I tried to apply PV=nRT to the initial amount, hoping to find moles of reactant. However, I don't have a volume, so I don't know how to start. Any advice would be greatly appreciated.

 

[flybynight]

Any help?

 

[Borek]

Why does the pressure goes down? Can you use this change to calculate how much C₄H₆ reacted?

Your rate equation is wrong.

 

[flybynight]

I got it. Every time the reactant is changed into product, the pressure is one half for that molecule. So I found the values of the reactants and the products, and found the order is 1.

Thanks for the help,
Peter

 

[DeeNos]

I would approach this problem by first analyzing the given data and identifying any patterns or relationships. From the given information, we can see that the total pressure decreases over time, indicating that the reactant (C4H6) is being consumed and converted into the product (C8H12). This suggests that the reaction is not at equilibrium.

Next, I would consider the rate equation for this reaction, which is given as rate=k[C8H12]^x. From the provided data, we can see that the concentration of C8H12 increases over time, while the concentration of C4H6 decreases. This suggests that the reaction is first-order with respect to C8H12 and second-order with respect to C4H6.

To determine the rate constant (k), we can use the initial amount of C4H6 and the initial rate of the reaction. Since we are assuming that only C4H6 is present at the start of the reaction, we can use the initial pressure of 632.0 torr to calculate the initial concentration of C4H6. From the given rate data, we can also calculate the initial rate of the reaction (R0) at time t=0.

Using the equation rate=k[C4H6]^2, we can rearrange it to solve for k, which gives us k=R0/[C4H6]^2. Plugging in the values for R0 and [C4H6] at t=0, we can calculate the rate constant (k) for this reaction.

In conclusion, the reaction order is first-order with respect to C8H12 and second-order with respect to C4H6, and the rate constant (k) can be calculated using the initial amount of C4H6 and the initial rate of the reaction.