Laboratory 7 Procedure : The Chemistry of Metals: Exploring ReactivityBackground:Let’s consider single displacement reaction, where one element displaces another in a compound. This reaction can be summarized by the following general equation:A(s) + BC(aq) => B(s) + AC(aq)Figure 1: A is a free metal (s), BC is an ionic compound dissolved in water (aq), B is a free mental (s), and AC an ionic compound dissolved in water (aq).In this type of reaction, there is a competition between the two elements (A and B). During this single displacement, redox reaction one element loses electron (or electrons) to the other element.We can simplify the reaction by writing net ionic equation, that will show only the electron exchange between elements:A(s) + B+ (aq) => A+(aq) + B(s)Figure 2: A(s) is a free metal that is donating an electron and dissolving into the solution-forming cation A+(aq), a cation B+ (aq) is accepting an electron and converting to the free metal B(s).Above reaction occurs when free metal A(s) is more reactive then ion B+ (aq) in the solution.However, in cases where free metal A(s) is less reactive then ion B+ (aq) the reaction does not occur.There are four signs to look for, when analyzing a chemical reaction:Dramatic color changeGas evolution (formation of bubbles)Precipitate formation (formation of the solid)Temperature change In this lab you will determine order the relative reactivity of four metals: copper, magnesium zinc and led by performing series of redox reactions.The main objective of this lab is to enhance your understanding of relative reactivity of metals.Before you start this laboratory assignment, you are encouraged to research relative reactivity series and read pages 651-653 in your Textbook. Throughout this laboratory assignment, you will be required to analyze a chemical reaction in terms of single displacement redox reaction. Be sure to record all observations and any relevant notes that you think you will need to include in your laboratory report.Take a moment to formulate and write down a hypothesis answering the question what group of metals is more reactive alkaline earth metals or transitional metals?Pre-Lab questions:1.Using your own words, explain what is a relative reactivity?What is a redox reaction?What happens to the electrons during a redox process? Procedure:Preparing the Lab 5From the course home page, click on the Virtual Lab Tutorial link to watch the overview of using the virtual lab.From the course home page, access the lab environment by clicking on the Virtual LabAfter the lab environment loads, click ‘File’ then ‘Load an Assignment.’Select the ‘Redox’ category,Select the ‘Redox Reaction Series’ assignment.If you haven’t already done so, formulate a hypothesis what group of metals is more reactive alkaline earth metals or transitional metals? as you will need to include this in your final report.Select the ‘Solids’ tab in the stockroom. Then, select the container with ‘Cu’ metal and move it to theworkbench.Transfer 5 mL of ‘magnesium nitrate’ to the empty 250 mL Erlenmeyer flask. Record its temperature.Record the temperature, and any other possible changes to the reaction mixture.After you record your data, clear the workbench, and start again for the next solution/metal combination listed in the table in the Data Table.Carefully analyze the Data collected in the Data Table.Write details justification for your selection of the order.link.5.At this point, you have prepared the laboratory for the first experiment with the require supplies to complete your experiments.Performing the Experiment7.Select the ‘Solutions’ tab in the stockroom if it is not already selected. Then, select the Erlenmeyer flask containing the ‘0.1M magnesium nitrate solution’ to move it to the workbench.9.From ‘Glassware’ select 250 Erlenmeyer flask, and 5 mL pipette.11.Transfer 1.0 g of ‘Cu’ to the 250 mL Erlenmeyer’s flask containing magnesium nitrate solution. Data Collection Data Table:SolutionTemperatureMetalSigns of ReactionNet Ionic EquationMg+2CuZn+2CuPb+2CuCu+2MgZn+2MgPb+2MgCu+2ZnMg+2ZnPb+2ZnCu+2PbMg+2PbZn+2PbData Analysis15.Arrange the four metals in order of their increasing relative reactivity. From least reactive to the most reactive. NotesThis section should include notes about any observations or data collected during the lab.Report RequirementsThis section contains key information that must be included in your typed report.1.Define the problem in a manner that is clear and insightful.Identify the strategies and procedures used during the lab.Clear presentation of data including any tables or other figures that are relevant to understanding your stated conclusions at the end of the report. Include any relevant calculations performed during the lab.Clearly stated results and discussion of possible improvements to the procedure.Conclusive statements arguing in favor of your findings.3.Clear hypothesis statement and other potential solutions that identify any relevant contextual factors (i.e. real-world costs).Note: All reports will be graded using the rubric embedded within the course.Here are some questions to consider as you write your report:Does my problem statement make sense?Have I summarized my strategies/procedures well enough to be replicated by an outsider?Did I have a valid hypothesis at the start of the lab? Have I expressed this in my report?Do my tables and/or graphs make sense?Are my conclusions valid based on my supplied data?6.Did I thoroughly summarize my laboratory experience in a concise, factual way such that the reader can understand my processes and findings in the conclusion section alone?

**How do we characterize the rate of chemical change? **

The goal of *Lab Assignments 5* and *6* is to characterize the degradation kinetics of a new drug in the human stomach. You will accomplish this by determining the drug’s rate of decomposition at room temperature in an aqueous (water-based) acidic solution similar to the environment of the human stomach. In particular, your objective is to determine the reaction order and rate constant for this degradation. With the order and rate constant known you can then infer the half-life of the drug (at room temperature) in an acidic solution similar to that encountered inside the stomach. You are further expected to analyze experiments that investigate how the degradation depends on temperature, and from the data, infer the activation energy for the decomposition reaction. With the activation energy known, you should be able to *predict* the half-life at physiologic (body) temperatures and estimate the amount drug remaining after 8 hours in the stomach.

# Degradation Kinetics

Assume we are developing a new drug “Y” that must be taken orally, and we wish to explore its degradation in the presence hydrochloric acid (HCl) at the levels normally encountered in the human stomach. From lecture, you should understand that HCl in aqueous solutions exists as H^{+} and Cl** ^{–}**. That is, HCl completely dissociates into H

^{+}and Cl

**ions. The hydrogen ion, H**

^{–}**, is the reactive species here, whereas Cl**

^{+}^{–}remains a “spectator ion.” The rate of drug “Y” degradation by H

**follows the rate law:**

^{+}𝑅𝑎𝑡𝑒 = −𝑘[𝑌]^{𝑛}[𝐻^{+}]^{𝑚} **(1) **

Where *k *is the rate constant for the overall reaction, *n *the rate order with respect to the molar concentration of drug Y, [*Y*], and *m *the rate order with respect to the molar concentration of the hydrogen ion [*H***^{+}**].

Drug Y has a characteristic *λ _{max}* at 254 nm. At this wavelength, HCl does not absorb. Hence, measuring drug Y at low concentrations in the presence of high H

^{+}concentrations via spectrophotometry is possible, and we can follow the degradation of drug Y directly.

Now, if the hydrogen ion concentration remains in vast excess over the drug Y concentration, which we can symbolize as [*H***^{+}**] >> [

*Y*], the proportional decline in [

*Y*] will be far greater than the corresponding decline in [

*H*

**]. Stated another way, the relative percent change in [**

^{+}*H*

**] will be so small compared to the percent change of [**

^{+}*Y*] that for all practical purposes [

*H*

**] may be considered constant and thus combined with**

^{+}*k*to give a new constant

*k*:

_{obs}𝑘_{𝑜𝑏𝑠 }= 𝑘[𝐻^{+}]^{𝑚} **(2) **

In this definition, *k _{obs}* is the

*observed*rate constant given the assumption [

*H*

**] remains fixed. Substitution of**

^{+}**(2)**into the rate law for the hydrogen ion mediated degradation of Y

**(1)**results in:

𝑅𝑎𝑡𝑒 = −𝑘_{𝑜𝑏𝑠}[𝑌]^{𝑛} **(3) **

Expression **(3)** suggests that by maintaining [*H***^{+}**] constant, a condition met when [

*H*

**] >> [**

^{+}*Y*], the rate order

*n*and observed rate constant

*k*can be determined by measuring the drug Y molar concentration as a function of time and graphically analyzing the data.

_{obs}# Graphical Analysis of Kinetic Data

Let us now consider the graphical determination of *n* and *k _{obs}* more closely. From lecture you should understand that different rate orders correspond to different trends in the change of reactant and/or product concentrations as a function of time. In particular, there are three possible rate orders for this system: zeroth order (

*n*= 0), first order (

*n*= 1) and second order (

*n*= 2), each of which corresponds to a specific relationship between [

*Y*] and

*t*that gives a linear plot. For example, if the reaction is zeroth order in drug Y (

*n*= 0), then a graph of the drug Y molar concentration versus time ([

*Y*] vs.

*t*) should be a straight line with

*k*= – slope, while

_{obs}*ln*[

*Y*] vs.

*t*(for

*n*= 1), and 1/[

*Y*] vs.

*t*(for

*n*= 2) would return non-linear plots. (In practice, the

*R*value from EXCEL can assist in determining the most “linear” plot; the plot featuring a trend-line with a

^{2}*R*closest to 1.000 can be considered the most linear.) Hence, plotting the drug Y molar concentration as a function of time data as [

^{2}*Y*] vs.

*t*,

*ln*[

*Y*] vs.

*t*and 1/[

*Y*] vs.

*t*can reveal the rate order

*n*of the reaction and permit determination of the observed rate constant

*k*.

_{obs}Thus, the rate order *n* and observed rate constant *k _{obs}* can be experimentally determined by measuring the molar concentration of Y as a function of time.

*However, we cannot measure concentration directly.*Instead, we take advantage of the fact that Y uniquely absorbs at a particular wavelength (that is, no other chemical species in the reaction mixture has an appreciable absorbance at this wavelength). Hence, one collects absorbance measurements as a function of time

*A*(

*t*).

As you have learned in the past, at low concentrations the light absorbed by a substance (absorbance *A*) tends to be proportional to its molar concentration *C*:

*A* = *ε b C*

Using this relationship and the molar absorptivity, you can transform the absorbance collected as a function of time *A*(*t*) into the molar concentration as a function of time [*Y*(*t*)]. Graphical analysis of the [*Y*(*t*)] data set (*e.g.*, [*Y*] vs. *t*, *ln*[*Y*] vs. *t* and 1/[*Y*] vs. *t*) and NOT the absorbance versus time (*e.g.*, *A* vs. *t*, *ln*(*A*) vs. *t* and 1/*A* vs. *t*) should be done to properly determine the rate order *n* and the observed rate constant *k _{obs}*.

# Half-life

For all kinds of practical reasons, it is desirable to know the half-life of a drug. So, we need some way of quantitating half-life. From equation **(3)** you might suspect *k _{obs}* could serve the purpose. But the problem is how do you go from

*k*to determining the half-life of a drug?

_{obs}Integrated Rate Laws: For n = 0:[𝑌] For [𝑌] 𝑙𝑛 = −𝑘 [𝑌] 1 1 = 𝑘 [𝑌]𝑡 𝑜𝑏𝑠𝑡 + [𝑌]0 |

First, let’s define *half-life*. Half-life, *t _{1/2}*, is the length of time for a substance’s concentration to decrease from its original value to half of this original value. For drugs, this half-life is the time at which the product retains 50 % of its original potency (or the time at which 50 % of the drug has decomposed and 50 % of the active drug still remains). In other words, at

*t*=

*t*the Y molar concentration must be half that of the initial molar concentration, or [

_{1/2}*Y*]

*= 0.5[*

_{1/2}*Y*]

_{0}. This suggests that if we know the rate order

*n*of the degradation reaction, we can use the integrated form of the rate law, substitute in [

*Y*]

*= 0.5[*

_{1/2}*Y*]

_{ 0}when

*t*=

*t*, and solve for

_{1/2}*t*to derive an equation for half-life (

_{1/2}*t*) in terms of

_{1/2}*k*.

_{obs}At this point we should have the means to determine half-life from *k _{obs}*. But we wish to know the

*t*of a drug Y at various temperatures. For various reasons, the initial degradation experiments will be carried out at 23.5

_{1/2}^{o}C (room temperature), but we wish to know

*t*at physiologic temperatures (37

_{1/2}^{o}C). Hence, we seek a relationship between

*k*and temperature

_{obs }*T*. Enter the Arrhenius equation:

## 𝐸𝑎

𝑘𝑜𝑏𝑠 = 𝐴𝑒− 𝑅𝑇 **(4) **

In which *A* is the frequency factor, or frequency of collisions with the proper configuration, *E _{a}* the activation energy,

*R*the ideal gas constant (8.314 J/K·mol) and

*T*the temperature in K (kelvins). So, now we have a relationship between

*k*and temperature.

_{obs }# Arrhenius Plot,* ln*(*k*_{obs}) vs. *1/T*

_{obs}

Equation **(4)** can be written in a logarithmic form which is more convenient to apply and graphically interpret.

Taking the natural logarithm of both sides and rearranging yields:

## 𝐸_{𝑎 }1 𝑅 𝑇

𝑙𝑛(𝑘_{𝑜𝑏𝑠}) = −+𝑙𝑛(𝐴) **(5) **

By now you should recognize that equation **(5)** is linear with the activation energy *E _{a}* for hydronium ion mediated drug Y degradation determined from the slope (you may find

**Unit 5 Module 4**,

*Activation Energy*of your

*Chemical Thinking*text helpful).

Considering **(5)**, apparently you need to know *k _{obs}* for many

*T*. But, notice that temperature does not appear in equation

**(3)**. This is because

**(3)**assumes

*T*is constant. Put another way, when finding

*k*, you must use

_{obs}**. This means the resulting data should be parsed (segregated) into**

*A*vs.*t*data at the same temperature**whole degree temperature blocks**. To obtain

*k*for each temperature block, you then transform the

_{obs}*A*(

*t*) data for that whole degree temperature block into [

*Y*(

*t*)] and plot to find

*k*. Since you know the order

_{obs}*n*from previous work, you should know whether to plot the [

*Y*(

*t*)] data as [

*Y*] vs.

*t*, or

*ln*[

*Y*] vs.

*t*, or 1/[

*Y*] vs.

*t*, to find

*k*. Hence, if there are five whole degree temperature blocks, five graphs need be prepared (not 15!). Subsequently, the resulting

_{obs}*k*vs.

_{obs}*T*data can be worked up into a

*ln*(

*k*) vs.

_{obs}*1/T*plot that should permit determination of

*E*.

_{a}# Two-Temperature Arrhenius Equation

Let us continue our development of an equation that relates *k _{obs}* to

*T*. With

*E*known, and given

_{a}*k*at one temperature

_{obs}*,*you can obtain

*k*corresponding to another temperature. To see how, write

_{obs}**(5)**for two different temperatures,

*T*and

_{1}*T*:

_{2}𝐸_{𝑎 }1

𝑙𝑛(𝑘_{𝑜𝑏𝑠,1}) = − +𝑙𝑛(𝐴)

## 𝑅 𝑇_{1 }𝐸_{𝑎 }1

𝑙𝑛(𝑘_{𝑜𝑏𝑠,2}) = − +𝑙𝑛(𝐴) 𝑅 𝑇_{2}

Where *k _{obs,1}* is the observed rate constant at

*T*, and

_{1}*k*the observed rate constant at

_{obs,2}*T*. Note that

_{2}*E*and

_{a}*ln(A)*are assumed to be constants for a given chemical process, hence we have a system of two equations with two unknowns that yields with some algebra:

𝑘𝑜𝑏𝑠,2 [−^{𝐸}_{𝑅}^{𝑎}(_{𝑇}^{1}_{2}−_{𝑇}^{1}_{1})] **(6) **

=𝑒

𝑘𝑜𝑏𝑠,1

(see **Unit 5 Module 3**, *Temperature Effects* of your *Chemical Thinking* text). Thus, with *E _{a}* for the system and

*k*at

_{obs,1}*T*known, you can find

_{1}*k*at a desired

_{obs,2}*T*by

_{2}**(6)**and from the

*t*equation use

_{1/2}*k*to predict drug Y’s halflife at temperature

_{obs,2}*T*. Further, knowing

_{2}*k*at temperature

_{obs,2}*T*, the percent of drug Y remaining after a specific time period

_{2}*t*, can be predicted for temperature

*T*via the appropriate integrated rate law. In this characterization, solving the integrated rate law for the ratio [Y]

_{2}_{t}/[Y]

_{o}and then multiplying by 100% would give the percent of drug Y remaining at time

*t*.

**Lab Assignment 5**

Your name: ___________________________________ Your section: ________ **GRADE ____ /25 p **

*All work must be **very neat** and **organized**. Significant figures must be reasonable, and correct units (where applicable) must be present.*

Table 1 Absorbance at λ = 254 nm for _{max}Y at Various Time Points | |||||||

Time (hours) | 0.00 | 24.0 | 48.0 | 72.0 | 96.0 | 120 | 144 |

Absorbance | 0.678 | 0.549 | 0.446 | 0.366 | 0.299 | 0.245 | 0.201 |

Studying the degradation kinetics of Y in the presence of excess H^{+} so that [H^{+}] >> [Y] at 23.5 ^{o}C, you collect the following absorbance data at a * _{max}* = 254 nm as a function of time from a sample of

*Y*with a starting (initial) concentration of 1.49 x 10

^{-4}M. The molar absorptivity

*ε*of

*Y*is 4.55 x 10

^{3}cm

^{-1}M

^{-1}at 254 nm and the optical path length can be taken as

*b*= 1.00 cm.

**1. Graphical Analysis to Determine n and k_{obs} (16p).** Using EXCEL transform (convert) the above absorbance values into concentration (mol/L or M). Perform a graphical analysis with EXCEL to determine

**the rate order “**and

*n*”**the observed rate constant “**for the reaction. Paste-in ALL THE GRAPHS for the analysis, giving the linear trend-line equation with

*k*”_{obs}*R*value (from EXCEL) for each. Title the plots and label the axes correctly. Clearly explain how you derived the values of

^{2}*n*and

*k*.

_{obs}**2. Half-Life (7p).** Use the results from **Question 1** to calculate the **half-life ( t_{1/2}) of Y at 23.5 ^{o}C**. First show the derivation of a

*t*equation based on the order you have determined for the reaction (

_{1/2}*hint*: start by substituting [

*Y*]

_{t1/2}= 0.5[

*Y*]

_{0}when

*t*=

*t*into the appropriate integrated rate law). To receive credit, you must show all work in a way that justifies the mathematical relationships you are using.

_{1/2}**Lab Assignment 6**

Your name: ___________________________________ Your section: ________ **GRADE ____ /25 p **

*All work must be **very neat** and **organized**. Significant figures must be reasonable, and correct units (where applicable) must be present.*

Continuing with your study of the degradation kinetics of Y in the presence of excess H^{+} so that [H^{+}] >> [Y], you are interested in finding the activation energy, *E _{a}*

_{,}. Recall Y has a unique

**at 254 nm, with a molar absorptivity

_{max}*ε*of 4.55 x 10

^{3}cm

^{-1}M

^{-1}at 254 nm and the optical path length of

*b*= 1.00 cm. The following data is collected from samples of Y with a starting (initial) concentration of 1.49 x 10

^{-4}M:

Time
| Absorbance(at | Temperature (°C) | Time
| Absorbance(at | Temperature (°C) | |

1.0 | 0.668 | 16 | 1.0 | 0.669 | 18 | |

2.0 | 0.664 | 16 | 2.0 | 0.662 | 18 | |

3.0 | 0.660 | 16 | 3.0 | 0.654 | 18 | |

4.0 | 0.656 | 16 | 4.0 | 0.647 | 18 | |

5.0 | 0.652 | 16 | 5.0 | 0.640 | 18 | |

6.0 | 0.648 | 16 | 6.0 | 0.633 | 18 | |

7.0 | 0.643 | 16 | 7.0 | 0.626 | 18 | |

8.0 | 0.639 | 16 | 8.0 | 0.619 | 18 | |

9.0 | 0.635 | 16 | 9.0 | 0.612 | 18 | |

10.0 | 0.630 | 16 | 10.0 | 0.605 | 18 | |

11.0 | 0.626 | 16 | 11.0 | 0.598 | 18 | |

12.0 | 0.622 | 16 | 12.0 | 0.592 | 18 | |

13.0 | 0.618 | 16 | 13.0 | 0.586 | 18 | |

14.0 | 0.614 | 16 | ||||

15.0 | 0.610 | 16 | 1.0 | 0.669 | 19 | |

16.0 | 0.606 | 16 | 2.0 | 0.659 | 19 | |

17.0 | 0.602 | 16 | 3.0 | 0.649 | 19 | |

18.0 | 0.598 | 16 | 4.0 | 0.639 | 19 | |

19.0 | 0.594 | 16 | 5.0 | 0.630 | 19 | |

6.0 | 0.621 | 19 | ||||

1.0 | 0.665 | 17 | 7.0 | 0.612 | 19 | |

2.0 | 0.659 | 17 | 8.0 | 0.603 | 19 | |

3.0 | 0.653 | 17 | 9.0 | 0.594 | 19 | |

4.0 | 0.647 | 17 | 10.0 | 0.586 | 19 | |

5.0 | 0.642 | 17 | 11.0 | 0.577 | 19 | |

6.0 | 0.636 | 17 | 12.0 | 0.568 | 19 | |

7.0 | 0.631 | 17 | ||||

8.0 | 0.625 | 17 | 1.0 | 0.664 | 20 | |

9.0 | 0.620 | 17 | 2.0 | 0.652 | 20 | |

10.0 | 0.614 | 17 | 3.0 | 0.639 | 20 | |

11.0 | 0.609 | 17 | 4.0 | 0.627 | 20 | |

12.0 | 0.604 | 17 | 5.0 | 0.615 | 20 | |

13.0 | 0.599 | 17 | 6.0 | 0.603 | 20 | |

14.0 | 0.594 | 17 | 7.0 | 0.591 | 20 | |

15.0 | 0.589 | 17 | 8.0 | 0.581 | 20 | |

16.0 | 0.584 | 17 | 9.0 | 0.569 | 20 | |

10.0 | 0.559 | 20 |

**1. Rate Constant k_{obs} vs. Temperature T (12p).**

**Build a summary table**based only on the data from the previous page

**. In the table present the observed rate constant**. Show all the graphical work, by pasting in all five EXCEL graphs (one for each temperature) below. Remember to properly title the plots, label the axes correctly and include the linear trend-line equations and

*k*values at the five different temperatures,_{obs}*T**R*values. The summary table requires a title and properly labeled columns.

^{2}**2. Activation Energy E_{a} (5p).**

**Using EXCEL prepare an**for the system. Paste-in this plot below and give the linear trend-line equation and

*ln*(*k*) vs. 1/_{obs}*T*plot from the Question 1*k*vs._{obs}*T*summary table that can be used to determine the activation energy*E*_{a}*R*value (from EXCEL). State the

^{2}*E*thus obtained. Show all work, explaining clearly how you derived the value of

_{a}*E*from this plot.

_{a}**3. Half-Life at 37.0 °C (5p).** For the experimental conditions of the degradation study, calculate the ** t_{1/2} (half-life) for Y at 37.0 ^{o}C**. Use equation

**(6)**from the accompanying guide and the

**. Show all work. Symbolically state the**

*k*at 23.5_{obs}^{o}C from*Lab Assignment 5**equations*you are using. (Hint, the material in

**Unit 5 Module 3**under “Temperature Effects” may prove helpful.)

**4. Percent of Drug Y Remaining (3p).** For the experimental conditions of the degradation study, calculate the **percent of drug Y remaining after 8.00 hours at 37.0 ^{o}C**. Show all work. Symbolically state the

*equations*you are using.