UNIVERSITY OF TECHNOLOGY

AnalyticalChemistry

Laboratory ReportExperiment 1b –Sampling statistic

BLab partners: Yanique Jerry, Velesha Frater, Johnross James

5/28/2014

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Experiment 1b

Title: Sampling Statistics B

Aim:

To determine the effects of grinding to improve homogeneity on

the absorbance of solutions prepared from grounded samples and

ungrounded samples using a mixture of salt (NaCl) and dichromate

ion (Cr2O72) with the aid of a spectrophotometer to detect

absorbance.

Abstract:

The laboratory exercise involve the investigation of a mixture

containing NaCl and dichromate ion, samples were investigated as

grounded and as ungrounded with the aid of a spectrophotometer to

record the absorbance values of each set of samples; These values

obtained were then utilized along with statistical information

(mean, standard deviation, relative standard deviation), to

determine the most precise results. The procedure involves the

coning and quartering of a bulk sample of the NaCl and dichromate

ion. A portion of the mixture was collected and made into a

solution using distilled water to be analyzed in the

spectrophotometer. A second portion of sample was grounded and

also made into a solution to be analyzed. Both methods used gave

rise to variation for precision. The accuracy of the

spectrophotometer was unaffected by the sampling methods. The

absorbance of both the grounded and ungrounded samples concluded

that indeed grinding did improve precision with a standard

deviation of 0.2513 for ungrounded sample and 0.0623 for grounded

sample. Accuracy of the spectrophotometer was merely unaffected

as the mean for ungrounded was 3.548 and that for grounded was

3.238 not much of a difference.

Statistics can be defined as the collection, classification,

analysis and interpretations of numerical data and facts. In

order for data to be analyze using statistics, data must first be

collected which is simplified using what is term sampling.

Sampling is the obtaining of a subset of the population to be

examined which is representative of the whole. Coning and

quartering was the process employed in order to obtained a

representative sample. The method of sampling aims at separating

and reducing a sample size without a bias in particle size

distribution. Granular or powdered sample is reduced via this

method and it involves forming a conical heap which is divided

into quarters. Opposing quadrants are combines and other

quadrants are discarded. This procedure can be repeated as many

times as needed to obtained the desire working sample size. This

exercise however uses three of the final quarters to make up the

solutions for observations.

To measure absorbance of the solutions, the spectrophotometer

was used. The principle of the spectrophotometer is that it

allows for the passing of a beam of light through a coloured

sample and measure the light intensity that reaches a detector.

The intensity of the light passes through a blank (distilled

water was use as the blank in this lab) which is used as a

standard which have a zero absorbance to light. This zero

absorbance to light is as a result of the blank not having any

analytes or colour hence 100% of light is transmitted. The

samples are then measure following blanking of the instrument and

the absorbance readings noted and recorded. Absorbance is the

expression of total amount of light being absorbed.

A mixture of NaCl and dichromate will have absorbance that

is proportional to the dichromate ions since its has colours and

can therefore absorb visible lights. An increase in

concentration in directly portional to an increase in absorbance

and vice versa if there is a diluted solution as the colour is

less thus the absorbance will decrease. Taking into consideration

Beer’s law which states that the concentration of a substance is

directly proportional to the amount of light absorbed. It is

represented by:

A= €.b.c

Where A is the absorbance, C is the concentration; b is the

optical path length of the cuvette and € is a constant specific

to the coloured analyte A and C are therefore proportional.

The obtaining of the absorbance value for each of the two

solution (grounded and ungrounded) can allow for the calculation

of the mean, standard deviation, relative standard deviation and

percentage relative standard deviation. The mean depicts the

accuracy of the spectrophotometer, while other data collected as

well as statistical tables can which sample will yield better

results interms of precision. Standard deviation gives the

precision of the experiment results and tells how much they

deviate from the mean. Increase standard deviation is indicative

of imprecision while low standard deviation values conclude

precision. RSD is a ratio of standard deviation of a data set, to

its mean and is used to compare the error in different data sets.

The statistical used were the F and T tests. The F test is

used to compare the known standard deviation of two independent

samples while the t test is used to assess whether the means of

two groups are statistically different from each other. It is

used in the comparison of the two means and thus is ideal to

determine whether grinding before or not affects accuracy and

precision of results. The equation below illustrates that the t-

test assesses the difference between the mean of data obtained

and the estimated standard error of the differences between the

means.

t=((x ̅_1-x ̅_2 ))/√((S_1^2)/n_1 +(S_2^2)/n_2 )

The calculated T value is compared with the T-table value

(critical value) using the degree of freedom. If the calculated

value is greater than the critical value then the results will be

significant and the reverse is true. When the calculated T value

is less than the critical value, this indicates that there is no

significant difference in the means and any difference seen may

be due to chance or errors.

Method:

Refer to experiment 1b; Sampling Statistics B; in Analytical

Chemistry (CHY3022) Lab book

Results:

Table 1.0: Mass table for sample collection for three quadrants

ungrounded

Sample 1 2 3

Mass of

Container +

sample(g)

32.5007g 34.1146g 33.3262g

Mass of

Container (g)

32.2505g 33.8645g 33.0760

Mass of 0.25g

samples

0.2502g 0.2507g 0.2502g

Table 1.1: Mass table for sample collected from two quadrants 1

and 4- grounded sample

Sample 1 2 3

Mass of

container +

sample(g)

24.1329g 33.2859g 24.2481g

Mass of

container

23.8820g 33.3456g 24.0024g

Mass of 0.25g

sample

0.2509g 0.2407g 0.2457

Table 1.2: Table showing absorbance of solution preparation from

quadrants 1-3 for ungrounded sample

Flask Mass Absorbance at 430nm

1 0.2502 0.95

4

0.955 0.954

2 0.2507 0.882

3 0.2502 0.829

Table 1.3: Absorbance of solution preparation from quadrants 1

and 4 for grounded sample

Flask Mass (g) Absorbance at 430nm

1 0.2509 0.822

2 0.2407 0.762

3 0.2457 0.804

Table 1.4: Absorbance of solution per gram preparation from

ungrounded sample

Sample Absorbance per gram (430)

Run 1 Run 2 Run 3

1 3.813 3.817 3.813

2 3.518

3 3.313

Table 1.5 Absorbance of solution per gram preparation from

grounded sample

Sample Absorbance per gram (430nm)

1 3.276

2 3.166

3 3.272

Calculations

1. To determine the absorbance per gram for each value

measured:

Absorbance per gram is given by the following equation:

Absorbance per gram= (Absorbance measured for solution)/(Mass of

sample used for corresponding solution)

Using Solution 1

Run 1

Absorbance=0.954

Mass of Sample=0.2502g

Absorbance per gram=0.954/0.2502

=3.813g-1

Therefore finding the mean absorbance per gram for solution 1

Absorbance per gram=(Run 1+Run 2+Run 3)/3

=

(3.813+3.817+3.813)/3

=3.814 g-1

2. Using Table 1.4

To determine the mean and standard deviation, scientific

calculator is used in the statistical mode:

x ̅=3.814g-1

S=2.309×10-3 g-1

Recall:

Relative Standard Deviation(RSD) = (standard deviation/

mean) S/x ̅

Therefore

RSD=2.309×10-3/3.814

=6.054×10-4

Hence,

%RSD=S/x ̅ ×100

=2.309x10-3 x 100 =

_____________

3.814

= 0.0605 %

Therefore the error or measure of uncertainty of the

spectrophotometer is 0.0605%

3.

Themean,standarddeviation,RSD∧%RSDofthetwodifferentsamplesets

(before∧aftergrinding)werefoundusingthesamemethodasabove.

Thefirstrunofabsorbancepergramofthethreerunsforsolution1wasused

TABLE 1.6: VALUES CALCULATED FOR THE STANDARD DEVIATION (S),

RELATIVE STANDARD DEVIATION (RSD), PERCENTAGE RELATIVE STANDARD

DEVIATION (%RSD) AND MEAN (x¿OF THE TWO DIFFERENT SAMPLE SETS

(SAMPLE USED AS GROUNDED AND UNGROUNDED PRIOR TO ANALYSIS)

Values Ungrounded grounded

Mean, x (g-1) 3.548 3.238

Standard Deviation,

S (g-1)0.2513 0.0623

Relative Standard 0.0708 0.0192

Deviation, RSD

%RSD

7.082%1.924%

4. From table 1.6 by obvious calculated values, it can be seen

that the %RSD value for ungrounded sample was greater than

that of the grounded sample. Since the %RSD represent the

measure of the error of uncertainty, these values shows that

grounded samples are more precise than ungrounded samples.

Since also grinding brought about even consistency

(homogeneity),it further proves that mixtures of the same

consistency yield more precise values than those of uneven

consistency. The value of %RSD obtained from ungrounded

sample that were measured three times in a row was found to

be a smaller value of 0.0605%. This value can conclude as

being precise, but is only due to the three in a row run of

the sample.

5. To determine if the two sets have different standard

deviation, an F-test was performed.

Null Hypothesis, Ho: There is no significant difference between the

variance of the absorbance per gram of the bulk sample and that

of the grounded sample.

Fcalculated=S12

S22

WhereS1isthevarianceofthevaluesforungroundedsample

¿S2isthevarianceofvaluesforthegroundedsample

NB Variance=(standarddeviation)2

Fcalculated=(0.2513 )2

(0.0623 )2

¿ 0.06323.881×10−3

Fcal=16.28

Fcritical

UsingFtablesAtthe95 %confidencelimit,with2degreesof freedomforbothnumerator∧¿

denominator.

Fcritical=19.00

SinceFcalculated<Fcriticalthenthenullhypothesisisaccepted

Conclusion:There is no significant difference between the

variance of the absorbance per gram of the bulk sample and that

of the grounded sample.

6. Since there is no difference in the variance of the

absorbance per gram of the two samples, T test which

incorporates Spooled calculation for the use of the equation

will be used.

Null Hypothesis, Ho: There is no significant difference between

the mean of the results obtained for grounded and ungrounded

samples.

tcal=(x2−x1 )

√ (s1 )2

N +(s2)

2

N

tcal=(3.238−3.548 )

√ (0.2513 )2

3+

(0.0623 )2

3

tcal=(−0.31 )0.1493

¿−2.076

From the t- table

Tcrit=4.303

Since tcal<tcrit Accept Ho

Therefore, there is no significant difference between the means

of the results of grounded and ungrounded samples.

Discussion:

The goal of this experiment was to decide on whether or not

grinding affected precision or accuracy. This was done with the

use of Nacl with dichromate in a solution and taking absorbance

reading using a spectrophotometer. The calculation of the mean,

standard deviation, relative standard deviation from absorbance

reading from the spectrophotometer aid in making this decision.

The very first test conducted on the instrument was used to

determine the degree of error. This involved taking absorbance of

solution time repeatedly (thrice) and then by calculating the

standard deviation. The ungrounded sample 1 was used for this

test. It was noted that there was no significant difference

between the absorbance values for all three samples as there was

only a 0.001 difference in one of the values. The relative

standard deviation was also calculated and the values obtained

reflected imprecision was low thus the spectrophotometer was

therefore precise. These tests were repeated on a sample

that was grounded which assess whether or not accuracy and

precision is affected by grinding. The ungrounded value had an

increase standard deviation in comparison to the grounded sample

as well as the RSD and %RSD values were increase for the

ungrounded sample. The standard deviation for the grounded sample

was 0.0623 while that of the ungrounded was 0.2513 and the RSD

was 0.0192 and 0.0708 respectively. This therefore indicates that

grinding does affect precision.

The F- Test compared the standard deviation of the sample

before and after grinding. Fcalculated was (16.28) and less than the

Fcritical (19.00 ¿ and so the null hypothesis was accepted So there

was no significant difference between the variance of the

absorption per gram of the bulk sample compared to that of the

ground sample.

In the t-test, tcalculated was less than the tcritical,

thus the null hypothesis which states there is no significanct

between the mean of the results obtained for grounded and

ungrounded samples was accepted

Precautions were taken throughout the experiment to

eliminate systematic errors, these precautions include zeroing of

the analytical balance, prior to weighing, cleaning of cuvettes

using soft tissues to ensure that light will not pass through the

sample with any form of hindrance thus more accurate results

Conclusion:

Base on all the absorbance reading obtained for grounded and

ungrounded sample, it can be concluded that grinding affects the

precision of the sampling but leaves the accuracy of the sampling

unaffected as the mean values for both sample only varied by 0.30

differences.

Post Lab question:

1. To sample a train load of coals for its sulphur content the

use of systemic sampling can be done in which each car could

be sampled. A sample of the individual car can be taken from

different areas in the car for example a sample from the

top, a sample from the bottom and from the centre and other

areas underneath the surface. The different particle sizes

in the present in the coal can be managed by crushing of the

larger coals particles into smaller pieces, then followed

through with coning and quartering for equal and fair

distribution until the desired sample size is obtained

Reference

Taylor, C. (n.d) Statistical Sampling- What is statistical

sampling. Statistics- Learn about Statistics. Retrieved June

11, 2013 from

http://statistics.about.com/od/HelpandTutorials/a/What-Is-

Statistical-Sampling.htm

Turgeon, M.L., Rungsrud, K.M., & Linnel, J.J. (2012). Linne

and Ringsrud clinical laboratory science:the basic and

routine techniques. (6th ed). Maryland Heights, MO: Mosby

Elsevier