Rate Law Equation: Solving for m & k

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In summary, the Concentration of Hydrochloric Acid (mol/L), Reaction Rate (s/M), and Reaction Order (M) are all related. The equation for the rate law is r=k[H+]m. The Exponent, m, is found by taking the line of best fit slope of the recordings and using a random value in the recordings. The Unit for k is not found, but would be expected to be equal to 0.063 if plotted log(r) vs log(H+).
  • #1
TheExibo
55
1

Homework Statement



Concentration of Hydrochloric Acid (mol/L)

3

2

1.5

1

0.5

Reaction Rate (s/M)

1.333

13.30

38.67

73.00

1466

Homework Equations



r=k[H+]m (r is rate in M/s, k is constant, [ ] is concentration, m is order of reaction)

The Attempt at a Solution



I'm not entirely sure how to start off this problem. Using the concentration as the "x" value and the rate of reaction as the "y" value, I need to figure out m, the exponent, and if possible: k, which is the constant. How do I start?
 
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  • #2
Can you think of a mathematical way of converting the r=k[H+]m equation to the y=mx+a form (where m is the exponent you are looking for, and all other things - x, y, a - are easy to calculate from the given data?
 
  • #3
Borek said:
Can you think of a mathematical way of converting the r=k[H+]m equation to the y=mx+a form (where m is the exponent you are looking for, and all other things - x, y, a - are easy to calculate from the given data?

I am trying that right now. Here is where I've gotten so far:

*using line of best fit slope of the recordings (0.024s-1/M)
log(1/r)=(0.024s-1/M)[H+]+logk
*using random value in the recordings
log0.065=(0.024s-1/M)log3M+logk
-1.19854=logk
k=0.063

I'm also not sure how to get the units for k.
 
  • #4
What would you expect to get if you plotted log(r) vs log(H+)?

Chet
 
  • #5
To stop this being a very scholastic excercise please show the plot of your fit. We have no idea how good it is nor whether there are any systematic trends away from your line.
Also no one would be treating data of a reaction that he didn't know what it was, and what ws in the reaction mixture, so please tell us.
Does s/M mean the numbers in the second table are reciprocals of the reaction rate?
What does Log3M mean?
 
  • #6
Is there any way you could manipulate the given rate to fit the rate law?
 

1. What is the rate law equation and why is it important?

The rate law equation is a mathematical expression that describes the relationship between the rate of a chemical reaction and the concentrations of the reactants. It is important because it allows scientists to predict how changing the concentrations of reactants will affect the rate of a reaction.

2. What is the difference between m and k in the rate law equation?

M represents the reaction order, which is a measure of the dependence of the reaction rate on the concentration of a particular reactant. K is the rate constant, which is a constant value that depends on the temperature, pressure, and presence of a catalyst. It is unique to each reaction and remains constant at a given temperature.

3. How do you determine the reaction order (m) from experimental data?

The reaction order can be determined by plotting the rate of the reaction versus the concentration of a particular reactant. If the rate is directly proportional to the concentration, then the reaction order is 1 (first order). If the rate is proportional to the square of the concentration, then the reaction order is 2 (second order). If the rate is independent of the concentration, then the reaction order is 0 (zero order).

4. What factors can affect the rate constant (k)?

The rate constant can be affected by temperature, pressure, and the presence of a catalyst. Generally, an increase in temperature leads to an increase in the rate constant, as more particles have enough energy to overcome the activation energy barrier. Pressure and the use of a catalyst can also increase the rate constant by increasing the number of collisions between reactant particles.

5. How do you use the rate law equation to predict the rate of a reaction?

To predict the rate of a reaction using the rate law equation, you first need to determine the reaction order (m) and the rate constant (k) from experimental data. Then, you can plug in the concentrations of the reactants into the rate law equation and solve for the rate of the reaction. This allows you to predict how changing the concentrations of the reactants will affect the rate of the reaction.

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