Concentration and Temperature Dependence of Reaction Rates PDF

Preview

Summary

Complete essay on concentration and temperature dependence of reaction rates....

Description

Joshua Farley Chem 1252L-912 3/5/2015

Concentration and Temperature Dependence of Reaction Rates Introduction The average rate of a reaction can be defined as the change in the concentration of reactants or products over a certain period of time (M/s):

eq. 1:

rate=

− Δ[ A ] , where [A] is the concentration of the reactant in any concentration unit Δt

and t is time in seconds (s). When finding the rate of product being formed, a positive signed is used in the equation instead. Chemical kinetics is a branch of chemistry that studies the measureable properties of reactions, such as the speed of a reaction, the concentration dependence of the reactants, how temperature affects a reaction rate, and what mechanisms drive the reactions. The reactants must be oriented correctly and moving at a high enough speed (with enough kinetic energy) in order to collide and form into products. As the reaction proceeds, the amount of reactants decreases at a certain rate while the amount of product increases. The change in concentration over a period of time can be observed various ways—in this experiment, a spectrophotometer (or Spec-20), was used to record the absorbance values over a period of 5-6 minutes. Concentration dependence of a particular reactant can be determined by finding its rate order. A zeroth order reactant reveals a relatively constant slope in comparison to first and second order, making it useful for isolating the concentration values of phenolphthalein.

Joshua Farley Chem 1252L-912 3/5/2015

eq. 2:

a b rate=k [ A ] [ B] , where [A] and [B] are the concentrations of reactants or products, k

is the rate constant, and ‘a’ and ‘b’ represent their respective rate orders. This equation is known as the rate law. Each molecule taking part in a reaction must contain enough thermal heat to overcome the activation energy barrier, which is unique for each reaction and always found during the slowest step. The relationship between temperature, activation energy, and the rate constant is known as the Arrhenius equation:

eq. 3:

( RTEa )

−

k =A e

, where k is the rate constant, A is a constant related to collision

frequencies and orientation of reactants, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin. This equation takes different forms in order to be made into a straight line on a graph or to determine the rate change if the temperature were to change. Procedure To begin, the spectrophotometer to be used was set to transmittance mode at 550 nm. The transmittance was set to 0.0 and 4.0 mL of a 0.2 M sodium hydroxide solution was transferred to a cuvette. After wiping it clean with a kimwipe, the cuvette was placed in the spectrophotometer and the transmittance was set to 100.0. Now that the Spec-20 had been calibrated it was turned over to absorbance mode for recording the data. In order to measure the change in concentration of the pink phenolphthalein compound with respect to time, a data table was prepared for 360 seconds at 5-second intervals for two different experiments. In the first experiment, 1 drop of phph2- was placed into the cuvette used in the above step and inverted several times to mix. At t = 0 (initial time), the absorbance was

Joshua Farley Chem 1252L-912 3/5/2015

recorded using the spectrophotometer and was called out and recorded every 5 seconds for the following 6 minute. This data will be used in the analysis of the order of the reaction with respect to [phph2-]. The previous experiment was then similarly repeated; 2.0 mL of 0.2 M NaOH was mixed into a cuvette with 2.0 mL of 0.2 M NaCl. After repeating the spectrophotometer calibration, 1 drop of phenolphthalein was added to the solution and inverted multiple times to mix. Once again, the absorbance values were observed and recorded for the next 6 minutes to help determine the dependence of [OH-] since it is no longer being kept at a constant rate. To determine the temperature dependence of reaction rates, an ice water bath was created with ice and tap water where a cuvette containing 4.0 mL of 0.2 NaOH was placed for 10 minutes. After cooling the solution, 1 drop of phph2- was added to the mix and inverted several times. After 2 seconds, the absorbance value was recorded as accurately as possible. This experiment only required 6 data points, therefore the absorbance values were recorded at initial time, and then every 60 seconds afterwards for the next 5 minutes. Between each trial, the solution was to remain cooled in the ice bath. Analysis

Part 1: Order of Reaction with Respect to [phph2-] Rate = k[phph2-]a[OH-]b = kobs[phph2-]a Kobs = k[OH-]b

Joshua Farley Chem 1252L-912 3/5/2015

Graph 1: ln(absorbance) versus time; a straight line indicates that this is a first order reaction. Therefore, a = 1.

ln ( Absorbanc e) versus Time ln(Absorbance)

Linear (ln(Absorbance))

0

ln (absorbance)

-0.5 -1 f(x) = − 0 x − 1.04 R² = 1

-1.5 -2 -2.5 -3 0

50

100

150

200

250

300

350

Time (sec)

To find the initial rate of the reaction, the slope between t = 0 sec and t = 10 sec can be calculated using the following equation:

eq. 3: slope=

Δ(|.|) Δt

At t = 0 sec, the absorbance was 0.380. At t = 10 sec, the absorbance was 0.351. −0 sec 10 sec ¿ ¿ ¿ − (0.351 )− ( 0.380 ) initial rate = ¿

Joshua Farley Chem 1252L-912 3/5/2015

The initial rate of the reaction was 0.0029/sec, meaning the absorbance of the reactant phph2dropped about 0.0029 per second of the reaction initially occurring.

eq. 4: slope = -kobs -0.0046/sec = -kobs Kobs = 0.0046/sec Rate = kobs[A]a Rate = (0.0046/sec)[phph2-]

Part 2: Order of Reaction with Respect to [OH-] Graph 2: ln (absorbance) versus time; a straight line once again indicates that the rate order, b, is 1.

ln( Absorbance) versus time 0

0

50

100 150 200 250 300 350

ln (absorbance)

-0.2 -0.4

f(x) = − 0 x − 0.39 R² = 1

-0.6 -0.8 -1 -1.2 Time (sec)

ln(Absorbance) Linear (ln(Absorbance)) Linear (ln(Absorbance))

Joshua Farley Chem 1252L-912 3/5/2015

The R2 value of the “1/Absorbance versus Time” trendline is 0.9972; therefore, this graph exhibits the most linear version. Using equation 3, the initial rate can be found for this experiment as well:

initial rate=

( 0.672 )− (0.688 ) −0.016 −0.0016 = = sec 10 sec 10 sec−0 sec

And using equation 4, the k’obs value can be found for this reaction: -0.002/sec = -k’obs k’obs = 0.002/sec Rate = k’obs[A]a Rate = (0.002/sec)[phph2-] Although the two observed rate constants are different based on the experimental data, the true rate constant, k, is the same. This value is found using the following equation: eq. 5: kobs = k[OH-]b 0.0046/sec = k(0.2 M)1 k = 0.0023/(sec x M) Rate = 0.0023/(sec x M)[phph2-][OH-]

Part 3: Low Temperature Effect on Reaction Rates From the previous experiments, the value of k at room temperature was 0.0023/(sec x M).

Joshua Farley Chem 1252L-912 3/5/2015

Graph 3: ln (absorbance) at a low temperature versus time

ln (absorbance) at 8.0 C versus time ln (absorbance) at 8.0 C Linear (ln (absorbance) at 8.0 C)

Linear (ln (absorbance) at 8.0 C)

0.1 ln (Absorbance)

0 -0.1

0 f(x) = − 0 x5+00.01 R² = 0.99

100

150

200

250

300

350

-0.2 -0.3 -0.4 -0.5 Time (sec)

Slope = -klow -0.0015/sec = -klow Klow = 0.0015/sec

Because temperature is directly proportional to the rate constant, the value of k dropped when the temperature was lowered using the ice water bath.

Joshua Farley Chem 1252L-912 3/5/2015

Graph 4: ln (k) versus 1/T

ln (k) Versus 1/T ln (k) -5.8 -5.9

0

0

Linear (ln (k)) 0

0

Linear (ln (k)) 0

0

0

-6 ln (k)

-6.1

f(x) = − 2150 x + 1.24 R² = 1

-6.2 -6.3 -6.4 -6.5 -6.6

1/T

eq. 5: slope=

−Ea R

-2150 K-1 (8.314 J/(mol x K) = -Ea Ea = 17875.1 J/mol Ea = 17.88 kJ/mol Discussion Determining rate orders can be solved in a variety of different ways, one of them being the use of graphs. Plotting experimental data on graphs can give many clues about the type of

Joshua Farley Chem 1252L-912 3/5/2015

reaction and the mechanisms that occur. If the graph exhibits a straight line without being altered, then it is zeroth order for that particular reactant. If taking the natural log of the concentration produces a straight line, then the reactant is first order for the reaction. And finally, taking the inverse of the concentration determines if it is a second order reactant based on the appearance of a straight line or not. In fact, sodium hydroxide (NaOH) was actually being used as a zeroth order reactant in part one of the experiment because it was added in such excess that it was being used up at the same rate. The phenolphthalein was added in a very minute amount (only 1 drop), but knowing the concentration of this compound was unnecessary because the recordings taken in this experiment are measured via absorbance, not a unit of concentration like molarity. In part one, adding an excess of NaOH accomplished the isolation of [phph2-] as the variable. To maintain the number of ions in part two, sodium hydroxide was mixed in equal amounts with sodium chloride. This allowed for the isolation of [OH-] as the main variable in part two. Using less NaOH in part two ultimately led to a decrease in the initial rate, indicating that [OH-] has an observable effect on the speed of a reaction. None of the actual concentrations of the species had to be determined because a spectrophotometer was used to measure the absorbance of wavelengths of light in the solutions. According the Beer-Lambert Law, absorbance is directly proportional to concentration, making it an accurate technique for determining concentration dependence. Since the rate orders for both reactants turned out to be 1, the reaction is second order overall. This simply means that as the concentrations of either reactant doubles, so will the rate of the reaction. Conversely, cutting the concentration in half will also divide the reaction rate in two.

Joshua Farley Chem 1252L-912 3/5/2015

Although the concentrations of reactants and products did not affect the true rate constant, k, changing the temperature did. As it turns out, the temperature and the rate constant of a reaction are directly proportional. If the temperature drops, so does the rate constant. Therefore, as the temperature increases, the rate constant increases and the reaction occurs more quickly. Activation energy acts as a barrier during a reaction that prevents all of the molecules from reacting. Only certain molecules with enough kinetic energy have the potential to overcome this barrier. Based on this, it can be concluded that having a higher activation energy will decrease the rate of a reaction by making it harder for molecules to overcome the barrier. If the same experiment were to be tested at a higher temperature, such as 50 degrees Celsius, the data would reveal a much quicker reaction. The absorbance values would have decreased at a much more rapid rate as the reactants are being used up and the rate constant would be much higher. Conclusion There are countless factors that affect the speed, mechanisms, and characteristics of a chemical reaction. Adding heat gives the molecules more kinetic energy to overcome the activation barrier and form into products. The concentration of species in a solution is another important factor. However, these are difficult to determine as all reactions occur with different mechanisms and have rate orders that must be determined experimentally. For most reactions, the rate at which it occurs slows down as the concentration of reactants steadily decreases. This is because there are less reactants to collide with one another and the likelihood of them colliding at the correct position with enough kinetic energy is significantly lower. The more we learn about the interactions of molecules in any solution (including air), the better we can understand the natural world in which we live....