Find the Relationship: An Exercise in Computer-Based Graphing Analysis, Lab Reports of Chemistry

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New Jersey City University Chemistry Lab 1106

Find the Relationship: An Exercise in Computer-Based Graphing Analysis

I. Introduction In chemistry, the skills and knowledge of graphing analysis are very important because it allows you to make mathematical methods to be able to compare the relationship of two variables. In this experiment, for instance, the variables that were observed were the volume and the pressure. The logger pro was used to generate the graphs needed for this experiment. For instance, one of the graphical relations that were learned in this experiment, was the direct relationship because the line was a straight line that passed to the origin (0,0). This relationship can be expressed as y=k*x. Another graph that was observed while performing the experiment was the concave-up graphs, however, based on the data that was given to group 8, no graphs concave-up were collected. The idea of this experiment was to be able to determine some mathematical relationships using computer-based graphical methods, to measure the pressure of an air sample at different volumes by using a Gas Pressure Sensor and a syringe, be able to differentiate the relationship between pressure and volume of the gas, and finally be able to describe the relationship between gas pressure and volume in a mathematical equation. Now, it is important to analyze the graphical relations and express the data in a simple direct relationship because it makes it easy to understand and allows us to use it in mathematical expressions. However, in this experiment, the groups were asked to perform three different types of graphs with variables given, each graph representing different relationship, and to further check if the graphs were correct, we then use a mathematical method to prove it right, then, the Boyle’s Law was performing to analyze the relationship between pressure and volume this was accomplished. II. Results

Data and Calculations Problem number 21 Problem number 22 Problem number 24 x y x y x y 7 82.3 14 5.36 4.5 0. 12 415 25 3.00 5 0. 10 240 19 3.95 7 0. 15 810 36 2.08 3 0. 3 6.48 48 1.56 8 0. n = 3 n =-1 n = - Problem number Slope (m) from Linear fit or (A) from the curve fit Equation (using x, y, & k) of the Final Linear Graph Solve for “k” (Show all calculations for k using the original data pairs). Calculated k must be the same as the slope (m or A) Final equation (x, y, and value of k) #1 16.1 y=k/x^2 K= y x •^2 K= (4)(2)^2 = 16 K = (1)(4)^2 = 16 Y = 16/x^2 #21 0.24 y= k x •^3 k= y/x^3 k= 82.3/(7)^3 = 0.24 y= 0.24 x •^3 #22 75.

y= k( )

1 𝑥 k= y x• k= 14 5.36= 75• y= 75(^ ) 1 𝑥 #24 14.

y= k( )

1 𝑥 3 k= y x •^3 k= 0.154 (4.5)• 3 = 14

y= 14( )

1 𝑥 3 Part II. Boyle’s Law: Pressure (P) - Volume (V) Relationship in Gases Slope (m or A) from the Linear Fit or Curve Fit: 1145 A. Mathematical relationship between P and V (from the curve fit or linear fit graphical analysis): Indicate which process you used (mark X): x_ Linear Fit; _____ Curve Fit Volume mL Pressure (kPa) Constant k (p/v or p * v)^1 10.8 103.00 10.8 x 103.00 = 1112.

5.8 195.36 5.8 x 195.36= 1133. 7.8 141.72 7.8 x 141.72 = 1105. 9.8 112.86 9.8 x 112.86 = 1106. 11.8 93.93 11.8 x 93.93= 1108. 13.8 79.76 13.8 x 79.76= 1100. 15.8 69.29 15.8 x 69.29 = 1094. 17.8 61.62 17.8 x 61.62= 1095. 19.8 55.26 19.8 x 55.26 = 1094. Average slope 9950.8/9 =1105.

2. Discussion Part I In this experiment, there were three problems given by the instructor, problems 21, 22, and 24, and in order to find the relationship for the data pair of each problem, the data was manipulated in order to get the line coinciding with the coordinates of y and x. This was accomplished by using the Vernier Software. For instance, the original graph for problem 21 was an inverse cube, the original graph for problem 22 was a reciprocal inverse and the original graph for problem 24 resulted in the reciprocal inverse cube. Now, the equation that represented the relation for problem 21 was y = k x•^3 when solving for k and plugging the values in x and y it resulted in k= 82.3/(7)^3 = 0.24. For problem 22, the equation that represented the relationship between x

and y was y= k( ). When solving for K, it resulted in k= 14 5.36= 75. For problem 24, the

1 𝑥

equation that represented the relationship between x and y was y= k( ). And when solving for k,

1 𝑥 3 the value resulted in k= 0.154 (4.5)•^3 = 14. Since all the original graphs were curved, they needed to be modif. To do so, a new calculation colum was created using Vernier Software in order to manipulate x and change it to xn^ or change it to 1/x. Which resulted in n= -1. Now, the two-point equation of the problems

were manipulating values for n in xn^ and expressing mathematically. After all, a practical application of graphical analysis is that if you are interested in knowing the linear graph of an inverse cube, inverse square, or negative inverse, by using Logger pro and the skills learned in this lab, it can be accomplished. Also if you want to know if a data set is x square or x cube. Questions

1. Why is it necessary to analyze graphical relationships and process the data to a simple direct relationship? Analyzing the graphical relationship and at the same time processing it to a simple relationship is important because it provides a better understanding of complicated data. It also helps to compared and to used mathematical equations to further prove the relationship between variables. 2. In this experiment, what were the three problems given by the instructor? What were the original shapes of the three graphs, and how did you use these graphs to obtain the relationship between y and x variables? The three problems that were assigned by the instructor were problems 21, 22, and 24. The original shapes of graph 21 were an inverse cube, for the number 22 graph, the original shape of the graph was also an inverse relationship, however, it was the reciprocal of x. Lastly, the original graph for 24 was inverse cube like the first one but this one was the reciprocal of x^3. To obtain the relationship between the y and x variables the graph was modified to fit into a linear graph by changing the variables in y vs xn^. For problem 21 the y vs x, the x was modified to become x^3 now, for problem 22, the x was

modified and became y vs 1/x in order for the graph to fit into the linear graph. For problem 24, in order to obtain the linear graph, the x was modified and became 1/x^3.

3. What computer-based graphical manipulations did you perform to derive the two-variable linear equation? Briefly describe the correlation between x and y variables for each of your assigned problem sets (Note: Make sure to identify the Problem Number in your answer). The computer-based graphical manipulations that were performed in order to be able to derive the two-variable linear equations was to find the correct value for n that way, turning it into a linear graph. For problem 21, the values were y and x^3 therefore the values in the new column were 3. In problem 22, the values were y and 1/x which resulted in -1 and for the last one problem 24, the values were 1/x^3 therefore resulted in -

4. What was the relationship between pressure and volume variables when you first plotted the data points? When the data points were first plotted, the relationship between pressure and volume, it indicated a negative inversed relationship.
5. What did you do to manipulate the data and arrive at a linear relationship? What is the general two-variable equation of this trendline? Using this equation, what is the calculated average slope value? What can you infer from the calculated slope and the one obtained using Vernier graphical method? In order to manipulate the data and arrive at the linear relationship, a new calculated colum was created, and then since it was a negative inverse, the reciprocal of x was

References Tro, N. (2019). Chemistry: A molecular approach, 5 th^ Edition. Boston, MA: Pearson. New Jersey City University (2013). CHEM 1105: General Chemistry I laboratory and recitation: miniscale experiments. Boston, MA: Pearson Learning Solutions. Vinier Software Logger Pro 3.16.