CHEMISTRY: Measurements and Calculations

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The Scientific Method
A logical approach to solving problems by observing and collecting data, formulating hypotheses, testing hypotheses, and formulating theories that are supported by data.

System - that portion of matter in a given region of space that has been selected for study during an experiment or observation.

Scientific Method Activities

Observe
Collect Data
Formulate Hypotheses

Test Hypotheses

Theorize

The System Internationale (SI) - Metric System

1. Base Units (the MKS system: meter-kilogram-second)
length meter (m)
mass kilogram (kg)
time second (s)
temperature Kelvin (K)
amount of a substance mole (mol)
electric current ampere (amp)
luminous intensity candela (cd)


2. Derived Units

density mass / volume
velocity length / time
volume length x length x length


Conversion Factor - a ratio derived from the equality between two different units that can be used to convert from one unit to the other.

feet to inches 12 in = 1 ft
miles to feet 5280 ft = 1 mi.
inches to centimeters 1 in = 2.54 cm


Making Measurements

When making measurements with a measuring device (ruler, balance, burette,...), always estimate one place beyond the smallest calibration increment.

Accuracy and Precision (Error and Deviation)
See handout on Accuracy and Precision (on WebPage)Accuracy is a measure of how close the measurement is to the true or accepted value.Precision is a measure of how close individual measurements are to each other.
In this diagram, the X's are the individual measurements, M is the mean, d is the deviation of the measurement from the mean, E is the error of the individual measurement from the true value (or target) and Eavg is the average error.



Significant Figures
Rules

All non-zero digits are significant

All final zeros after the decimal point are significant

Zeros located between significant figures are significant

Zeros used solely for spacing the decimal point are not significant

*** The above rules can be reduced to only two rules:


All non-zero digits are significant

Zeroes are always significant unless they are used to space the decimal point (i.e., indicate the order of magnitude).

Math involving significant figures (Rules)

Rounding off -
the last significant digit is unchanged if the next digit is less than 5
the last significant digit is increased by one if the next digit is 5 or greater

Addition/Subtraction - the number of significant digits depends on the number with the largest uncertainty.

Multiplication/Division - the measurement with the smallest number of significant digits determines the number of significant digits in the answer.


Scientific Notation
Format: M x 10n


where: M is a number between 1.00 and 9.9999.....; and n is an integer (can be positive or negative)


Math involving scientific notation

addition/subtraction - ensure that the numbers have the same exponent, then add or subtract the numbers. If the exponents are different, change one of them so that they are the same, then add or subtract.

multiplication - multiply the numbers and add exponents

division - divide the numbers and subtract exponents

roots - taking the nth root of a number, divide the exponent by n

When in doubt, use three significant digits (x.xx, 0.00xxx, xxx00). Never just report all the digits that you get on your calculator.


Using Your Calculator - correctly! -

Always use EE (for exponents).


Problem-Solving Techniques

Analyze


read the entire problem carefully

define the answer required

identify the known facts and organize the information into a table or list

sketch a picture to help clarify the problem

Plan


Is the problem similar to any you have seen before?

write down any equations linking the unknown and the given information together

develop a plan for solving the problem (rearrange an equation, ??)

estimate the answer (What would be a reasonable answer?)

Compute - solve the problem - perform the mathematical steps you outlined above in your plan. Check your units and significant digits


Evaluate - does the result make sense???? Compare your answer with your estimate above.



Proportions
Direct Proportions

y is proportional to x

y/x = k or y=kx

if x increases, y also increases; when plotted, you get a straight line with a slope = k


Inverse Proportions

y is proportional to 1/x

xy = k

if x increases, y decreases; when plotted, the curve shape is a hyperbola.

Graphing

Always use graph paper! Linear or logarithmic. Select the appropriate graph paper such that you will be using about 2/3 - 3/4 of the paper for your data. This enables the reader to extrapolate.

Use a ruler to draw lines for the axes

Label the axes with appropriate descriptions, and units

Select a descriptive title for your graph.

In most cases you will draw the "best fit" for the data points you have. If the curve should be a straight line, then with a ruler draw the best fit. However, the best fit may be a curve. In such a case, draw a curved line - using French curves if they are available.


Always identify your data points clearly. If only one set of data is being plotted on the curve, use a dot with a circle around it. If additional data sets are also plotted on the same graph, select a different set of symbols for each data set. When other symbols are used, you must include a legend to explain what each set of symbols