GATHERING AND REPORTING QUANTITATIVE DATA | Study notes Chemistry

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Activity No.3

GATHERING AND REPORTING QUANTITATIVE DATA

For a student working in the chemistry laboratory, gathering of data is always a

part of his task. The term data refers to measurements of a particular characteristic,

or variable, which may be classified as quantitative.

Qualitative: where individual values are assigned a descriptive category, e. g

the detection of the presence and absence of a chemical by a color test or

precipitate. This kind of data describes the properties and changes in matter.

Quantitative: where the individual values are described on a numerical scale

which may be either (i) continuous, taking any value on the measurement scale, or (ii)

discontinuous (or discrete), where only integer values are possible. Many of the

variables measured in chemistry are continuous and quantitative, e.g. weight,

temperature, time, amount of product form in an enzyme reaction.

Variables may be independent or dependent. An independent variable is

typically under the control of the experimenter, e.g. the time, reagent concentration,

ph among others, while dependent variable is the variable being measured.

In this exercise, the student will be (1) taught how to gather and report

quantitative data scientifically such that the results to be obtained are understandable

and reproducible. He is expected to consider the accuracy of his measured values

that are, in themselves, limited by the precision of the instruments used. He is also

expected to (2) learn how to compute numerical values from measured quantities.

I. GATHERING OF QUANTITATIVE DATA

A. Accuracy of Measurement

The accuracy of a measurement is the degree of agreement between the

measured value and the true value. It is properly indicated by the number of digits

used in expressing the numerical value. Each digit in the numerical value of a

measurement should be trustworthy or significant. A significant figure may be

defined as a number that is believed to be correct within some specified limit of

error. For example, if the height of a man is reported as 5.38 ft, it is assumed that

only the figure 8 (the last digit) may be in error and that the true value lies

between 5.37 ft and 5.39 ft. It would be wrong to report the man’s height as 5.380

ft because this would mean that the true height lies between 5.379ft and 5.381ft.

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Activity No. GATHERING AND REPORTING QUANTITATIVE DATA For a student working in the chemistry laboratory, gathering of data is always a part of his task. The term data refers to measurements of a particular characteristic, or variable, which may be classified as quantitative. Qualitative: where individual values are assigned a descriptive category, e. g the detection of the presence and absence of a chemical by a color test or precipitate. This kind of data describes the properties and changes in matter. Quantitative: where the individual values are described on a numerical scale which may be either (i) continuous, taking any value on the measurement scale, or (ii) discontinuous (or discrete), where only integer values are possible. Many of the variables measured in chemistry are continuous and quantitative, e.g. weight, temperature, time, amount of product form in an enzyme reaction. Variables may be independent or dependent. An independent variable is typically under the control of the experimenter, e.g. the time, reagent concentration, ph among others, while dependent variable is the variable being measured. In this exercise, the student will be (1) taught how to gather and report quantitative data scientifically such that the results to be obtained are understandable and reproducible. He is expected to consider the accuracy of his measured values that are, in themselves, limited by the precision of the instruments used. He is also expected to (2) learn how to compute numerical values from measured quantities. I. GATHERING OF QUANTITATIVE DATA A. Accuracy of Measurement The accuracy of a measurement is the degree of agreement between the measured value and the true value. It is properly indicated by the number of digits used in expressing the numerical value. Each digit in the numerical value of a measurement should be trustworthy or significant. A significant figure may be defined as a number that is believed to be correct within some specified limit of error. For example, if the height of a man is reported as 5.38 ft, it is assumed that only the figure 8 (the last digit) may be in error and that the true value lies between 5.37 ft and 5.39 ft. It would be wrong to report the man’s height as 5. ft because this would mean that the true height lies between 5.379ft and 5.381ft.

It is important that the student should know how to count the number of significant figures in a measured value. The following are the guidelines:

To count the number of significant figures, read the number from left to right starting from the digit that is not zero. The zeros after the decimal point but before other digit are not significant. They are there only to indicate the position of decimal point. 0.0034 cm 2 sig. fig. 0.000200 cm 3 sig. fig.
Final zeros after a decimal point are significant. 1.000 m 4 sig. fig. 20.000 km 5 sig. fig.
Final zeros in a whole number are not significant. They are only written to indicate the magnitude of the value. 800 g 1 sig. fig. 55000 kg 2 sig. fig.
The exponential form in a measured value which indicates the number of decimal places that the decimal point was moved is not significant. 8.50 x 10^2 s 3 sig. fig. 3.641 x 10-^1 min 4 sig. fig.
Numbers which are not the results of measurements are not considered significant figures. 48 Quezon Avenue 12:00 a.m. P 500 (if not the result of a mathematical calculation) B. Precision of an Instrument The accuracy of any measured value is limited by the precision of the instrument used. The precision of an instrument signifies the smallest quantity that the instrument could be sensitive to or is able to detect. It is defined as half of the smallest graduation or calibration on the instrument. Precision = ± Smallest calibration, SC 2 The Smallest Calibration, SC, is given by the equation below.

2400 s = 2.4 x10^3 346.0 x 10¯^6 m = 3.460 x10¯6+2^ m = 3.460 x10 ̅^4 m

If the number is less than zero (0), move the decimal point to the right until only one integer remains to the left of the decimal point. The exponent n increases by one for every place that the decimal point is moved to the right. 0.00283 km = 2.83 x10¯^3 km 0.000340 x10 ̅^2 kg = 3.40 x10¯2¯4^ kg = 3.40 x10 ¯^6 kg B. Rounding off significant Figures If the number of digits in a measured value exceeds the required number of significant figures, rounding off is necessary. The following points are considered:
When the number to be dropped is greater than or equal to five (≥ 5) the last significant digit is increased by one. Consider when the following examples are rounded off to three significant figures (3 SF). 0.7625 L 0.763 L Last significant digit number to be dropped 23.893 mm 23.9 mm 1.214 cm 1.21 cm
When the number to be dropped is less than five (< 5), the last significant digit is not changed. Consider when the following examples are rounded off to two significant figures (2 SF) 0.0283 g 0.028 g 1.7268 mg 1.7 mg C. Mathematical Operations Involving Significant Figures
1. Addition and Subtraction In addition, and subtraction, the answer must contain the same number of digits to the right of the decimal point as that term containing the least number of digits to the right of the decimal point. In number expressed in scientific notation, the exponents must be made equal first before addition or subtraction is performed. Examples: a. 257.1325 g + 3.091 g + 50.36 g = 310.58 (answer) Solution:

50.36 contains the least number of digits after the decimal 310.5835 point. The final answer is then reduced to 310.58 g b. 2.48 x 10^2 mL – 0.02 x 10^3 mL = 2.28 x 10^2 mL Solution: Convert 0.02 x 10^3 to 102 0.02 x 10^3 → 0.20 x 10^2 Thus, 2.48 x 10^2 – 0.20 x 10^2 Finally, the answer is rounded off to 2.28 x 10^2 mL.

Multiplication and Division In multiplication and division, the answer must contain the same number of significant figures as that term with the fewest number of significant figures. For scientific notations, in multiplication, the exponents are added, while that in division, the exponents are subtracted from the numerator. Examples: a. (1.58 m) (13.613 m) = 21.50854 m^2 = 21.5 m^2 b. (2.6 x 10^2 in) (1.350 x 10^3 in) = 3.5 x 10^5 in^2 c. 1.25 g = 0. 39 g/mL 3.2 mL d. 6.04 x 10-^2 mol = 2.00 10-^4 mol/L 3.02 x 10 2 L Density of Water
Weigh a clean and dry 250-mL beaker.
Measure 5.00 mL of water (see Figure 1 for technique in pipetting) and transfer it into the beaker.
Determine the weight of the beaker with water using a top loading balance.
Take note of the room temperature.
Compute the density of water using the equation below. Express the answer with the correct number of significant figures.

GATHERING AND REPORTING QUANTITATIVE DATA, Study notes of Chemistry

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