Lab 3_Periodic Table Trends_Fa23

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Santa Fe College *

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CHM2045

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Chemistry

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Dec 6, 2023

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NATURAL SCIENCES DEPARTMENT-CHEMISTRY CHM 2045- College Chemistry I 1 Laboratory # 3 Graphical Analysis of Data Understanding Relationships in Periodic Table Graphical Data Analysis INTRODUCTION Part of science literacy is developing the tools that are needed to effectively employ the scientific method . Our first lab focused on making accurate observations and measurements as a set of key skills in the scientific method. Our second lab focused on interpreting the world around us in terms of scientific models and theories . In this lab, we will focus on another tool scientists need to use, data analysis . Data analysis is used to look for patterns and relationships between variables in an experiment or a set of data. To understand how the world works, scientists perform experiments and observe changes in variables. We can define a variable as any factor in an experiment that can be changed, and it in turn causes a change in another factor. For example, if I take a gas in a container, and I compress it to a smaller volume, I will find that pressure of the gas changes. In this case, the volume of the gas is my independent variable, the variable that I controlled its change. The second variable in this experiment is the pressure, and we call it the dependent variable . It is the variable that responds to the change in the independent variable. As I decreased the volume of the gas, the pressure responded by increasing. As a scientist, I can make the simple qualitative observation that as the volume of a gas is decreased, its pressure will increase. Doing several such experiments with different volumes will confirm that this result is a continuing trend. The smaller the volume the gas is compressed to, the higher its pressure increases. Trends are most easily seen when we visually graph our data. Knowing how to display data to reveal trends is a key skill for the scientifically trained individual to master. In order to graph our data consistently, we choose a convention where the independent variable is always on the x-axis, and the dependent variable is graphed on the y-axis. A simple graph of our above experiment is shown below. We can analyze this trend by noting that as the volume increases, the pressure continues to decrease. We have identified an inverse trend: as one variable increases, the other decreases. Experiments are designed with a specific purpose in mind, to try to understand the relationships between variables. Often, we want to find a quantitative or mathematical relationship between variables, so that we can use it to predict the outcome of future experiments exactly. At other times, a qualitative relationship is enough to understand general trends. In qualitative analysis, we look to see if a dependent variable increases or decreases as we increase the independent variable. In both cases, we have to consider that there may be more than just two variables that will impact

2 our results. A good experiment will attempt to hold other variables constant , or unchanging, so that we can observe only the effect of the two variables of interest. In the example gas experiment, temperature is another variable that could be considered. In order to make sure that we don’t confuse effects, we have to make sure tha t the temperature of the compressed gas is always the same when we take our data. As long as the temperature is constant, it is not affecting the outcome. Identifying variables that should be held constant is important both when setting up experiments, and when analyzing data. We will learn how to do this as we graph data in excel. Computer spreadsheets are powerful tools for manipulating and graphing data. In this exercise, the spreadsheet program Microsoft Excel will be used to explore trends in the periodic table. We will follow a step by step process in analyzing this data for trends. The end goal will be to display these trends graphically. Pre-lab Procedures: Download the excel spreadsheet from Canvas titled “Lab_3_Periodic Table Spreadsheet”. Open the file in excel and work through just the first tab on the spreadsheet. SAVE YOUR WORK, you will continue using this file in Lab. Lab Procedures: 1) Compile a data set. The characteristics of the chemical elements are already well known, and so we will use a data set that has already been compiled instead of trying to do all the measurements ourselves. This data set is already available as an Excel file, and can be downloaded from Canvas. What is missing from the data set is the effective nuclear charge. You will calculate this data set yourself. As we increase in element number, we are adding just two charged particles to create a new element, one proton and one electron. The new electron however is shielded from the full charge of the nucleus by the inner core electrons, but not by the electrons in its own orbital. For each element you will take the full nuclear charge (number of protons) and subtract the charge of the inner core electrons plus any completely filled d orbitals. This will give you the effective nuclear charge. Save this as a column in your data set. Excel Hint: Using formulas allows you to do many calculations quickly in excel. You can quickly create data columns and then create a formula to calculate the effective nuclear charge. Copy this formula in a column to the end of your data, and you have completed all the calculations. See your instructor if you are not sure how to do this step. 2) Perform “experiments” with the data. To perform experiments, we need to identify our independent, dependent, and constant variables. We are interested in knowing how certain properties of elements change as we move both horizontally across a period of the periodic table, and vertically up and down a group. The properties we are interested in are the effective nuclear charge (Z eff ), the atomic radius (AR), and the energy needed to take away an electron, ionization energy (IE). We will select each of these one at a time as a dependent variable . We will conduct two sets of experiments . In the first we will use periods as an independent variable (we will change the period number) while holding the group number constant . This will reveal how the dependent property changes as we move down a group. A second experiment will use group numbers as the independent variable, while holding the period constant. This will reveal how the independent property changes as we move across a period. Excel Hint: Being able to organize your data quickly in excel is of great help in data analysis. You will want to understand how to sort data using the custom sort feature of the program. Highlight all the data set you are interested in – the control, independent, and all dependent variables. Select custom sort, and then sort first by your control variable, and secondly by your independent variable. This will quickly organize your data for graphing. 3) Generate graphs of your experiments. For each dependent variable you will generate two different graphs, one for each experiment you conducted. The first graph will show how the dependent variable changes as you move across a period (Periods 1-5 only, there is not enough data to complete 6 and 7). The second graph will show how the dependent variable changes as you move down a main group (1A- 8A only, we won’t do the transition metals) Each graph will therefore be displaying multiple series. An example of how to organize your data is included in the spreadsheet. You will paste each of your graphs into the spreadsheet page along with your data so you can view both trends simultaneously. You will print each set of graphs on a single page and attach them to your report.

3 Excel Hint: This is one of the rare times you might want Excel to connect your data points with straight lines. This will let you see the change from one data point to the next. You are interested in overall trends, but it can also be instructive to be able to pick out exceptions in the trend. You can enable this feature when you select what kind of graph to use. USE THIS PART OF THE LAB AS YOUR REPORT 4) Analyze the trends qualitatively. You should now be able to look at the trends in a graph and qualitatively state the trend for each variable, whether it increases or decreases as you move across periods or down groups. Report those trends on this Data Sheet. Effective Nuclear Charge (Z eff ): Across periods 1-5 Down groups #13 (3A) Atomic radius (AR): Across periods 1-5 Down groups #2 (2A)

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4 . Ionization Energy (IE): Across periods 1-5 Down groups #16 (A6)

5 5) Explanation from law and theory. Finding a mathematical relationship. Now that the trends are clearly visible, we would like to be able to explain why they increase or decrease. We understand that each new element adds an additional proton to its nucleus, and adds an additional electron to its electron configuration. Coloumb’s law will give us the force that exists between these two particles. Coulomb’s Law: F = -kq 1 q 2 /r 2 where F is the force between the charged particles, k is a constant, q 1 in this case is the “effective nuclear charge” and q 2 is the charge of the electron (-1). R is the distance between the nucleus and the electron, and we can use the atomic radius as this distance. We can use these interactions to hypothesize about why we observe the trends that we do. In order to visualize the effects of increasing effective nuclear charge or increasing distance, we can hold all other variables constant and only increase the effective nuclear charge and see how the Force changes. This has been done for you on the excel spreadsheet. As you think about how this graph relates to the periodic trends, It will be helpful to realize that as the force between the nucleus and the electron increases, the electron is being pulled tighter and the potential energy is decreasing.

6 State the mathematical relationship between the effective nuclear charge and the force of attraction? The effective nuclear charge is the attractive positive charge of the nuclear protons acting on the valence electrons. With the increase of Zeff, the force of attraction between the nuclear protons and the valence electrons increases. Hence why the graph between Zeff and force is a straight line, a direct relationship. Now you will build a second graph of how the force changes with increasing distance. You can pick any succession of increasing distances to build the graph. This graph is analogous to what happens as you move down a group: the effective nuclear charge stays constant, but the electron is being placed in a further and further orbital. State the mathematical relationship between the force of attraction and the distance. As the distance increases, the force decreases. This makes sense because the farther the distance the less attraction and therefore less Zeff. Now use these relationships in Coulomb’s Law to provide a possible explanation (called a hypothesis ) for the trends that you observed in first ionization energy in the periodic table. Make sure you explain what is happening to both a) Zeff and to b) the distance of the valence electrons as you move across a period (row number is the independent variable) and as you move down a group (period number is the independent variable). Now explain how those trends relate to the force on the valence electrons, and how that helps to explain the IE trends we observe. Provide this in a well-written paragraph (4-8 sentences in length). If you worked with anyone on this

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7 paragraph, provide their name as one of the authors at the end of the paragraph. In scientific writing, you must credit the people you work with and not claim work that is not wholly yours as your own!! The trends observed in each category were distinct, and some differed when comparing periods to groups. In terms of the Effective Nuclear Charge, across the periods and groups the Zeff increased as the periods moved from left to right and as the groups moved from top to bottom. In terms of Atomic Radii, across the periods the atomic radii decreased as the periods moved from left to right, and the atomic radii increased across the groups as it moved from top to bottom. In terms of Ionization Energy, across the periods the ionization energy increased as the periods moved from left to right, and the ionization energy decreased across the groups as it moved from top to bottom.