The solubility merchandise invariable of K H tartrate in H2O and it dependance of temperature were investigated in this experiment. The solubility merchandise invariable was determined at different temperature through acid-base titration against NaOH. A additive graph was obtained by plotting ln Ksp against 1/T and positive correlativity between temperatures and solubility merchandise invariable was observed. This survey concluded that solubility merchandise invariable of K H tartrate is dependent merely on temperature.

## Introduction

The purpose of this experiment is to look into the solubility merchandise invariable of K H tartrate in H2O and it dependance on temperature. Solubility is frequently defined the sum of substance required in obtaining a concentrated solution. Therefore, merely a little sum of K H tartrate ( KHC4H4O6 ) is needed to bring forth a concentrated solution as it has limited solubility in H2O.

In the concentrated solution, the rate of the dissociation of the solid is the same as the rate of the aqueous ions organizing the solid compound ; the solution is known to be at equilibrium.

The equilibrium equation for KHC4H4O6 in the solution can be written as:

The invariable for the equilibrium equation can be expressed as: Ksp = [ K+ ] [ HC4H4O6- ] .

This invariable is besides known as the solubility merchandise invariable ( Ksp ) which has a fixed value for a given system at changeless temperature. Therefore, by happening out the concentration of the ions dissolved, the solubility merchandise invariable for KHC4H4O6 can be determined.

From the equation above, the dissociation of KHC4H4O6 will bring forth equal sum of K ions ( K+ ) and hydrogen tartrate ions ( HC4H4O6- ) . Therefore, by obtaining the concentration of one of the ions, the concentration of the other ion can be derived and the solubility merchandise invariable can be calculated. As HC4H4O6- behaves like a weak acid, its concentration can be determined by acid-base titration utilizing NaOH, a strong base as the titrant, with phenolphthalein as the index. As NaOH and HC4H4O6- react with each other in 1:1 ratio, the sum of NaOH used in the titration will be equal to the sum of HC4H4O6- nowadays in the solution.

While Ksp is fixed at a certain status, alterations in temperature will impact the value of Ksp. Harmonizing to the Virginia n’t hoff equation, the value of Ksp is related to the alteration in Gibbs free energy and can be expressed as:

From the equation, the solubility merchandise changeless depends on three variables which are the alteration in heat content, the alteration in information and the temperature. The alteration in information and heat content with regard to temperature were stated to be undistinguished due to the similar heat capacities of the merchandise and reactants. This suggests a additive tendency between the staying variable and Ksp [ 1 ] . Therefore, a graph of natural logarithm of Ksp versus the reciprocal of temperature can be secret plan which the gradient of the graph can be used to cipher the heat content alteration and the y-intercept for the information alteration. Therefore, the relationship between Ksp and temperature can be observed.

## Experimental Procedure

Dried KHC8H4O4 ( 0.5002 g ) was prepared in a 250 milliliter conelike flask with the aid of an analytical balance. Deionized H2O ( 25.0 milliliter ) was added into the flask and a standard solution of KHC8H4O4 was obtained. The prepared solution was so titrated against an unknown concentration of NaOH to the end point, with phenolphthalein as the index. The volume of NaOH used was recorded. The full process was so repeated with different multitudes KHC8H4O4 ( 0.5039 g, 0.5033 g ) . The concentration of the NaOH was calculated from the volume of NaOH used and tabulated in Table 1.

A concentrated KHC4H4O6 solution was prepared by adding one gm of KHC8H4O4 into a 250 milliliter conelike flask, incorporating 100.0 milliliter of deionized H2O. The flask was swirled for five proceedingss and set to rest with occasional swirling for another five proceedingss at room temperature. At the terminal of 10 proceedingss, the solution was so filtered and the supernatant was collected in a dry 250 mL conelike flask. Concurrently, the temperature of the solution in the filter funnel was recorded. Two parts of 25.0 milliliter of the filtered solution were so pipetted into two separate 250 mL conelike flasks. The two solutions were titrated against the 0.7070M NaOH solution to the end point, with phenolphthalein as the index. The volume of the NaOH used was recorded. The process was so repeated for different temperatures.

For temperature above room temperature, a hot H2O bath was prepared in a one liter beaker on a hot plate scaremonger. The concentrated KHC4H4O6 solution was prepared in the same manner but was placed in a hot H2O bath with changeless stirring, utilizing a stir saloon. The solution was put aside with occasional monitoring until a changeless temperature was observed. Following, the solution was decanted in little sum into a dry conelike flask. The temperature of the solution in the filter funnel was recorded at the same time. Three parts of 25.0 milliliter of the filtered solution were so pipetted into three separate 250 mL conelike flasks.

For temperature below room temperature, an ice-water bath was prepared in a one liter beaker. The solution was besides prepared in the same manner as the old process and was placed into the ice-water bath. The solution was cooled until the solution stabilized at a certain temperature. The solution was so filtered and the temperature of the solution in the filter funnel was recorded. Three parts of 25.0 milliliter of the filtered solution were so pipetted into three separate 250 mL conelike flasks similar to the above room temperature apparatus.

The six solutions were so placed aside for it to return to room temperature and so titrated against the standardised NaOH. The solutions were titrated the same manner as the titration done at room temperature. The volume of NaOH used was recorded for the different solutions were recorded. The mean volume of NaOH used for the same temperature was so calculated and tabulated in Table 2.

## Data Treatment and Analysis

The computations of [ HC4H4O6- ] , [ K+ ] and Ksp at 302.15K:

[ NaOH ] = 7.070 ten 10-2 mol L-1

Sum of NaOH used = ( 7.070 x 10-2 mol L-1 ) ( 1.2825 x 10-2 L ) = 9.067 ten 10-4 mol

Sum of HC4H4O6- = Amount of NaOH used = 9.067 ten 10-4 mol

[ HC4H4O6- ] = [ K+ ] = 9.067 ten 10-4 / ( 0.0250 L ) = 3.63 ten 10-2 mol L-1

Ksp = [ K+ ] [ HC4H4O6- ] = ( 3.63 x 10-2 mol L-1 ) 2 = 1.32 ten 10-3

The deliberate value of [ K+ ] , [ HC4H4O6- ] and Ksp were tabulated into the tabular array below:

Table 2: Determination of Ksp of KHC4H4O6 at different temperature

## Temperature / K

## Average Vol. of NaOH used / L

## Sum of NaOH used / mol

## [ HC4H4O6- ] / mol L-1

## [ K+ ] / mol L-1

## Kspof KHC4H4O6

285.15

7.4750 x 10-3

5.327 x 10-4

2.13 x 10-2

2.13 x 10-2

4.54 x 10-4

294.15

1.0075 x 10-2

7.180 x 10-4

2.87 x 10-2

2.87 x 10-2

8.25 x 10-4

302.15

1.2825 x 10-2

9.067 x 10-4

3.63 x 10-2

3.63 x 10-2

1.32 x 10-3

309.15

1.6375 x 10-2

1.158 x 10-3

4.63 x 10-2

4.63 x 10-2

2.14 x 10-3

320.15

2.2375 x 10-2

1.582 x 10-3

6.33 x 10-2

6.33 x 10-2

4.00 x 10-3

Based on the temperature and Ksp value obtained in Table 1, values of 1/T and ln Ksp were calculated and tabulated in Table 3. A graph was plotted based on the values:

Figure 1: Graph of Ksp versus 1/T

From Figure 1, the gradient and y-intercept was obtained as shown in Table 4.

The heat content alteration and information alteration was calculated based on the Virginia n’t hoff equation:

Gradient = – ( / R ) = -5692.06

Standard divergence of gradient: ± 99.87

= – ( -5692.06 x 8.314 ) ± ( 99.87 x 8.314 ) = ( 47.32 ± 0.83 ) kJ K-1 mol-1

Y-intercept = ( / R ) = 12.25 ± 0.33

Standard divergence of Y-intercept = ± 0.33

= ( 12.25 x 8.314 ) ± ( 0.33 x 8.314 ) = ( 101.85 ± 2.74 ) J K-1 mol-1

The standard mistake of arrested development was found to be 0.0295.

( Number of measurings = 6, Degree of Freedom = 4 )

## Consequences and Discussion

From the informations obtained, the deliberate values of and were ( 47.3 ± 0.83 ) kJ K-1 mol-1 and ( 101.85 ± 2.74 ) J K-1 mol-1 severally. Ksp of KHC4H4O6 was found to be 1.32 ten 10-3 at 302.15K. It was observed that a additive graph was obtained upon plotting ln Ksp against the reciprocal of T. The addition in temperature was besides found to correlate with the addition of Ksp values. The literature Ksp value for KHC4H4O6 is 3.8 ten 10-4 at 291.15K. [ 2 ] The approximated Ksp value that corresponds to 291.15k based on experimental information was calculated to be 6.755 ten 10-4 as shown in the Appendixs.

Linear Relationship between T and Ksp

Based on figure 1, a additive theoretical account was observed between the reciprocal of T and the natural logarithm of Ksp. This was supported by the R-square value of 0.99 which greatly suggests a additive tendency from the experimental information plotted. The standard mistake of arrested development obtained from the experiment was found to be 0.0295, which indicates a good tantrum among the experimental values obtained, matching to a good preciseness of the experimental information. Therefore from the additive tendency, the claim of undistinguished alterations of heat content and information due to temperature alterations was valid. Therefore, the premise that the value of Ksp is dependent merely on temperature at which the disintegration occurs can be established.

Comparison of Literature values

The estimated Ksp value based on experimental information was 6.755 ten 10-4 at 291.15K and was found to be 43.75 % higher than the literature value ( 3.8 x 10-4 ) [ 2 ] . The difference could be accounted to the restriction of this experiment. As the experiment was carried out in different temperature, one of the restrictions was due to the setup used. The volumetric glass pipette used was calibrated at 20, therefore at other temperature, enlargement or contraction might happen taking to the inaccurate volume transferred for titration after the filtering procedure. Another beginning of mistake was noted to be the temperature fluctuation during the filtering procedure. Although the solution were decant in little parts to minimise mistakes, rapid addition of the temperature for the cold temperature reading was observed. This corresponds to the addition in the ions concentration dissolved in the solution, therefore ensuing in a higher value of Ksp. Despite the per centum difference of 43.75 % , the difference between both values was really little due to the fact that the Ksp of KHC4H4O6 is a really little value. When the uncertainness of the enthalpy alteration and information alteration was taken into history, the experimental Ksp value was assumed to be between 3.446 ten 10-4 and 1.324 ten 10-3 ( Refer to Appendices ) . The literature value was noted to be within this scope, therefore the experimental informations do hold with the theoretical value of KHC4H4O6.

Change of Enthalpy and Entropy

The alteration of heat content from the reaction was found to be ( 47.3 ± 0.83 ) kJ K-1 mol-1. The positive heat content alteration means that the disintegration of KHC4H4O6 was an endothermal procedure where heat was absorbed during the procedure. This was expected as the disintegration breaks up the stronger ionic bonds within KHC4H4O6 and weaker bonds between the H2O molecules and the ions was formed. These resulted in a positive net alteration for heat content for the reaction, which is consistent with the positive heat content alteration derived from the experimental information. The alteration of information was found to be ( 101.85 ± 2.74 ) J K-1 mol-1. As information was frequently defined as a step of upset, the positive information can be explained with the increased upset brought about when the when KHC4H4O6 dissolved into ions.

As the value of enthalpy alteration was much larger than the information alteration, in order to acquire a larger value of ln K based on the Virginia n’t hoff equation, higher temperature was required. This coincide with high temperature favours endothermal procedure such as disintegration of KHC4H4O6, therefore it can be concluded that temperature have a positive correlativity with Ksp.

## Decision

Ksp have a additive relationship with temperature for KHC4H4O6. The temperature dependant of enthalpy alteration and information alteration was found to be undistinguished for the disintegration of KHC4H4O6. As disintegration is an endothermal procedure, temperature has a positive correlativity with Ksp, therefore higher temperature allow more KHC4H4O6 to fade out. This concluded that solubility merchandise invariable of K H tartrate is dependent merely on temperature.