I'm supposed to calculate the rate equation, including k, for the reaction whose data is given in the table:
Experiment: 1 2 3
Initial Concentration X: 0.10, 0.10, 0.60
Initial Concentration Y: 0.20, 0.10, 0.10
Measured Initial Rate: 2.57, 1.25, 1.27
(I hope the formatting turned out okay)
Here's what I have so far:
When the concentration of X is kept constant and the concentration of Y is doubled (comparing experiment 2 to experiment 1), the rate increases by a factor of 2.056.
When the concentration of Y is kept constant and the concentration of X is multiplied by a factor of 6, the rate increases by a factor of 1.27.
Now I'm not sure what this means for the orders of the reactions. I've only worked with whole numbers so far. Any advice would be greatly appreciated. Once I get those cleared up, I know how to find k.
Thank you!
Ahh never mind, I just remembered logarithms exist . . . oops
OK but be careful. I think changing the (X) by a factor of 6 and the change in rate is only 1.25 to 1.27 this tells me that experimentally there is no change in rate. Also I might be inclined, since this is experimental, to round that 2.06 off to 2.0
So essentially, the order of X is 0 and the order of Y is 1? Which would mean k is equal to 12.85? That seems like a big k, but mathematically it fits.
A couple of thoughts although I didn't do the math for calculating k.
1.
1,27/1.25 = 1.02 and if you do the orders math wise and not "logical" as we've done, you would have 2.06/1.02 = 2.02 which is even easier to use founding as an excuse to get a whole number of 2.0.
2. You might want to calculate k for the three samples you have, then average for a final answer. Also, why do you question 12.5 as being too large? This could be a made up problem for all we know.
To determine the rate equation and the orders of the reactions, you can compare the rate changes when the concentration of each reactant is changed while keeping the other constant. In your case:
1. Comparing experiment 2 to experiment 1:
Concentration of Y is doubled, and the rate increases by a factor of 2.056:
This suggests that the rate is directly proportional to the concentration of Y raised to the power of 1, i.e., rate ∝ [Y]^1.
2. Comparing experiment 3 to experiment 1:
Concentration of X is multiplied by a factor of 6, and the rate increases by a factor of 1.27:
This suggests that the rate is directly proportional to the concentration of X raised to the power of some order, let's call it m.
Combining these observations, the rate equation can be expressed as:
rate = k * [X]^m * [Y]^1
To solve for the order of X, you can compare the rate changes between experiments 2 and 3 while keeping the concentration of Y constant. In this case, the concentration of X increases by a factor of (6/0.10) = 60, and the rate increases by a factor of (1.27/2.056).
(1.27/2.056) = (60^m)
Simplifying this equation, you'll find the value of m.
Once you determine the order(s), you can substitute the rate, concentration values, and the order(s) into the rate equation to find the value of the rate constant k.
Let me know if you need any further assistance with the calculations!