Determination of an Equilibrium Constant

Introduction

The purpose of the experiment was to determine the equilibrium constant for the reaction of iron (III) with thiocyanate (eq 1).

Fe⁺³(aq) + SCN^-(aq) FeSCN²⁺ (1)

The equilibrium constant K_eq of this solution is represented by eq 2.

(2)

According to the Beer-Lambert law (eq 3) the intensity of the color directly depends on the concentration of the solution.

A=abc (3)

In eq 3, A is the absorbance, a is the absorptivity, b is the path length of the cuvette, and c is the concentration [FeSCN^2+] of the solution.

Procedure

10.00 mL of 2.00 x 10^-3 M potassium thiocyanate and 25 mL nitric acid were measured and diluted to 100 mL. 1.00 mL of 0.100 M iron (III) nitrate was added to the solution. A sample of the solution was added to a spectrophotometer cuvette and the absorbance was measured at 445 nm with a Spectrum SP-1105 spectrometer that was adjusted to zero absorbance (100% T) with diluted water.  The solution sample in the cuvette was poured back into the solution and another 1.00 mL of 0.100 M iron (III) nitrate was added to the solution and the absorbance of the new solution concentration was measured. There were a total of ten additions of iron and absorbance was measured after each. The data was put into Microsoft Excel where calculations done and a plot was created.

Results

The data was plotted in linear form in Figure 1 where the x axis is 1/(mol/L) and the y axis is 1/(mol/L)². The first three data points were omitted from the plot because they were obvious outliers.  

Figure 1. Modified equilibrium constant expression plotted in linear form.

The line of best fit in Figure 1 had the equation of y = -235.27x + 794687. The equilibrium constant was determined from the slope of the line to be K= 235.27.

Discussion

The equilibrium constant was found to be K=235.27, which has a 70% error when compared to the literature¹ value of K=138. Reasons for this error may be because the experiment was carried out at 20° C and the literature value was carried out at 25 ° C.  There were large outliers in the data because two different spectrometers were used in this experiment, which caused inconsistent data.

References

1. Ramette, R.W. J. Chem. Ed. 40, 71 (1963).

Application of LeChatelier’s Principle to Chemical Equilibria

Introduction

The purpose of this lab was to use LeChatelier’s Principle to determine the direction of equilibrium shifts in reactions. LeChatelier’s Principle states that change in any of the parameters that determine equilibria will result in a system change, which will cause a change in the equilibria. The equilibria of three solutions were found by executing and observing a variety of experiments for each. 

Observations

For the first reaction an initial solution was prepared by adding crystal NaHSO₄ and Thymol Blue as a pH indicator to five test tubes. When the pH is less than two Thymol Blue is red, when it is greater than two Thymol Blue is a red-yellow color. The first test tube was used as a standard. Na₂SO₄ was added to the second test tube and NaHSO₄ was added to the third until there was a color change. The fourth test tube was heated in a hot water bath, and the fifth was cooled in a ice water bath. Observations and the determined direction of equilibrium shift can be seen in Table 1. It was determined that this was an exothermic reaction, because the equilibrium shifted to the reactants when the solution was heated and shifted to the products when cooled.

Table 1. Observation and interpretation of chemical and physical perturbations to the aqueous bisulfate equilibrium.

HSO4-(aq) + H2O (l) ⇌  H3O+(aq) + SO42- (aq)
Perturbation	Change in Appearance	Equilibrium Shift
Na2SO4 Added	Lightened to Pink/Yellow	Reactants
Crystal NaHSO4 Added	Darkened to Purple	Products
Heated Solution	Lightened	Reactants
Cooled Solution	Darkened	Products

For the second reaction the initial solution was created in five test tubes with MgCl₂ and NaOH. The first test tube was used as a standard, HCl was added to the second, and Na₄EDTA was added to the third. The fifth test tube was cooled and the sixth was heated. Observations and the determined direction of equilibrium shift for this reaction can be seen in Table 2. It was determined that this reaction was exothermic.

Table 2. Observation and interpretation of chemical and physical perturbations to the __ equilibrium.

Mg2+(aq) + 2OH-(aq) ⇌  Mg(OH)2(s)
Perturbation	Change in Appearance	Equilibrium Shift
NaOH Added	Precipitate	Products
HCL Added	Precipitate disappeared	Reactants
Na4EDTA Added	More Precipitate Formed	Products
Heated Solution	Less Precipitate	Reactants
Cooled Solution	More Precipitate	Products

The initial solution for the third reaction comprised of water and CoCl₄^2-. The first test tube was a standard, ethyl alcohol was added to the second, silver nitrate to the third, and HCl to the fourth. The fifth test tube was cooled and the sixth was heated.

The observations and the direction of the equilibrium shift can be found in Table 3.

Table 3. Observation and interpretation of chemical and physical perturbations to the __ equilibrium.

CoCl42-(alc) + 6H2O(l) ⇌  Co(H2O)62+(aq) + 4Cl-(aq)
Perturbation	Change in Appearance	Equilibrium Shift
H2O Added	Pink	Products
Ethyl Alcohol Added	Blue	Reactants
Silver Nitrate Added	Pink and Precipitate Formed	Products
HCl Added	Blue	Reactants
Heated Solution	Blue	Reactants
Cooled Solution	Pink	Products

Discussion

LeChatelier’s Principle states that when the parameters of a reaction are changed, the equilibrium will shift in order to counteract the change. In this lab we changed many parameters in the reactions and used LeChatelier’s Principle to aid in determining which side of the reaction the equilibrium lied on.

All three reactions were found to be exothermic. 

Reading Summaries

Women and the Poor: The Challenge of Global Justice
Third world countries are now dominated by the New World Order, in which corporations primarily from the rich countries are exploiting their economies and governments. Africa is becoming poorer and living standards are getting worse in many areas, but corporations such as the world bank are profiting and becoming stronger. Africa needs to properly diagnose it’s problems in order to make a solution. Inequality between countries, inequality between sexes, and the gap between the rich and poor are all interconnected and all part of the problem.

Under Western Eyes
We have made stereotypes and generalizations about women in different cultures and of women in general. When the oppression of women as a group is assumed it effects our view of average third world women. Westerners tend to generalize women from third world countries as being more uneducated, traditional, ignorant victimized, etc. But Western women tend to see them selves as educated, modern and in control of themselves.

On The backs of Women and Children
State employment services affect women directly because women tend to have government funded jobs such as medical care and education. Women work many jobs that are not accounted for as a source of income, such as sex workers, house keepers, and taking care of the family. Development is dependent on the cheap labor of women.

Being South Asian in North America
Chandra Mohanty has had to deal with racism throughout the last fifteen years that she has lived in the USA. Most of the racism is mild, mostly just generalizations. People assume that she is here on a student visa and that she will be returning home to India, even though she has a PHD and some signs of aging. She points out that if you were not a U.S. citizen that you are an alien, weather your illegal or a legal resident. Having a U.S. passport means that you can breeze through most borders and that you are not an alien, but it doesn’t prevent racism within the borders of the U.S. When she went back to India she found that her family and friends were envious of her green card. They also didn’t value her opinion on political topics in india saying that she couldn’t understand because she doesn’t live there. Racism/sexism was normalized and violence was high. She finds it important to her that she works for grassroots organizations in both of her homes- the U.S. and India.

Rate Law Determination of the Crystal Violet Reaction

Introduction

The purpose of this experiment was to determine if the reaction of crystal violet with sodium hydroxide was a first order, second order, or third order reaction. This was achieved by the measurement of the absorbance of two solutions of sodium hydroxide and crystal violet of different concentrations over a length of time. The absorbance and time data was plotted and analyzed to find which order best linearized the data. 

Procedure

Two 10 mL graduated cylinders were used to obtain 10 mL of 0.020 M sodium hydroxide and 10 mL of 2.0 x 10^-5 M crystal violet solution. The two solutions were combined in a beaker and stirred while data collection was started on Logger Pro. After three minutes of stirring the solution some of it was poured into a cuvette and placed into a calibrated colorimeter. The absorbance versus time data was collected every minute for twenty minutes. These steps were repeated using a dilute solution of 5.0 mL crystal violet, 5.0 mL water, and 10 mL sodium hydroxide. The data was exported into Microsoft Excel and was plotted and analyzed. The kinetic rate constant was was determined from the slope of the trendline of the plot that best linearized the data, then the half-life was determined.

Detailed procedures can be found in reference 1.

Results 

In Figures 1, 2, and 3 the blue data is of the first crystal violet solution, and the red data is the diluted solution. Absorbance versus time for both concentrations of crystal violet was plotted in Figure 1 to determine if the reaction was 0^th order. 

Figure 1. Absorbance versus time

The data sets of the natural log of absorbance versus time for both concentrations of crystal violet were plotted in Figure 2 to determine if the reaction was 1^st order. The data sets plotted are linear, which means that it was a 1^st order reaction.

Figure 2. Natural log of absorbance versus time

Figure 3 shows 1/absorbance versus time for both concentration of crystal violet, which was plotted to determine if the reaction was 2^nd order. The data is not linear so it is not a 2^nd order reaction.

Figure 3. 1/absorbance versus time 

The rate constant was found to be to be 0.0381 1/min.  The half-life was calculated to be 18.2 min.

Discussion

The plot that best linearized the data was the natural log of absorbance versus time, which means that it was a 1^st order reaction. The rate constant is not dependent of the concentration of crystal violet, because the rate constant is always constant. The rate constant was found to be to be 0.0381 1/min.  The half-life was calculated to be 18.2 min.

References

1. General Chemistry Experiments: A Manual for Chemistry 204, 205, and 206, Department of Chemistry, Southern Oregon University: Ashland, OR, 2010

Fitting Nonlinear Data in the Absence of a Physical Model Function

Introduction

The purpose of this lab was to linearize the data and determine the parameters of unknown number 35 by linearizing six two-parameter functional relationships and determining which of them best fit the data.  Unknown number 35 was entered into Microsoft Excel and plotted. The functional relationship between X and Y variables of the unknown were investigated by linearizing six common two-parameter functional relationships. Equation 1 is the basic linear form that the functions were put in.

y=mx+b (1) 

The slope (m) of the linear form of the function allowed for the determination of the a and c values.

Procedure

Unknown number 35 data was entered into Microsoft Excel and was plotted. There were six common two-parameter functions given to be tested, one of which would fit the data. The six functions were linearized and the data plotted accordingly. From the linear plot the values of the a and c parameters were determined from the slope and intercept of the best-fit line. The values of the parameter were substituted into the appropriate function and a curve was calculated by the data set.

Detailed procedures can be found in reference 1.

Results 

The raw x and y data of unknown number 35 was can be found in Figure 1.

Figure 1. Raw data of unknown 35. 

Table 1 shows six trial functions in both linear and nonlinear form, along with how the data was plotted, and values of a and c as calculated from the slope of mx+b.

Table 1. Trial functions in linear and nonlinear form, how they were plotted, and their a and c values.

Nonlinear Form	Linear Form	Plot	a	c
y=ae±cx	lny=±cx+lna	x vs. lny	eb	m
y=acx	lny=lna+xlnc	x vs. lny	eb	em
y=axc	lny=lna+clnx	lnx vs. lny	eb	em
y=a+cx2	y=a+cx2	x2 vs. y	1/m	b(1/m)
y=a/(c+x)	1/y=(a/c)+(x/a)	x vs. 1/y	1/m	b/a
y=ax/(1+cx)	1/y=1/ax+c/a	1/x vs. 1/y	1/m2x	b/c

The function y=a/(c+x) was found to best linearize the data in Figure 1. The linearized plot is shown in Figure 2, where the data plotted were the original x values versus the inverse of the y values.

Figure 2. The unknown 35 data plotted in linear form.

From the equation of the best-fit line the parameter a was calculated to be 0.9051 and c was calculated to be 0.2170. The values of a and c were used to calculate a set of y values. These were then plotted with the original y values, which is shown in Figure 3.

Figure 3. The original unknown number 35 data (Series 1) plotted with the calculated y values (Series 2).

Discussion

The function that best linearized the data was y=a/(c+x). The parameter a was calculated to be 0.9051 and the parameter c was calculated to be 0.2170. The calculated y values were consistent with the original y values when plotted in Figure 2.

References

1. General Chemistry Experiments: A Manual for Chemistry 204, 205, and 206, Department of Chemistry, Southern Oregon University: Ashland, OR, 2010