# Math is the language of science Data Analysis Ch. 2.1, 2.2, 2.3.

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Math is the language of science Data Analysis Ch. 2.1, 2.2, 2.3

Problem solving in chemistry  Step 2 – ANALYZE THE PROBLEM  Re-read problem. What do you know? What is unknown? Make a list.  Consider units, gather info from graphs, tables, figures  Plan steps to take in problem solving  Step 1 – THE PROBLEM  Read problem.  Be sure you understand what is being asked

Problem Solving in Chemistry  Step 3 – SOLVE FOR THE UNKNOWNS  Determine equation needed  Plug in the knowns to solve for the unknowns  Solve the problem  Don’t forget your conversions  Step 4 – EVALUATE  Think about your answer – does it make sense?  Consider units – do they make sense?  Check your work!

Measurements  Measurement – a quantity that has a number and a unit  Qualitative vs. Quantitative measurements  What’s the difference?  EXAMPLES:  Hot and cold – qualitative or quantitative?  Temperature scale (degrees Celsius or Kelvin) – qualitative or quantitative?

Units of Measurement  Base Unit – defined unit in a system of measurement that is based on an object or an event in the physical world SI Base Units Table 2-1, p. 26

Units of Measurement  Metric use of prefixes to alter base units:  Kilo (k) – 10001000 m = 1 km  Deci (d) – 1/101 m = 10 dm  Centi (c) – 1/1001 m = 100 cm  Milli (m) – 1/1,0001 m = 1000 mm  Micro (μ) – 1/1,000,0001 m = 1,000,000 μm

Units of Measurement  Derived Units – a unit that is defined by a combination of base units  Volume – the space occupied by an object (cm 3 or L)  Volume of an irregular object – water displacement  Density – a ratio that compares the mass of an object to its volume (g/cm 3 )  Density = mass  volume Practice Problems, p. 29 1, 2

How Reliable are Measurements?  Accuracy – how close a measured value is to an accepted value  Precision – how close a series of measurements are to one another

Error  Error = Accepted value – Experimental value  Ignore + or – signs  Percent Error = l error l x 100  accepted value  We use absolute value because we want the % error to be a positive value. Example p. 37: Calculate Student A’s percent error Practice: Calculate Student B’s percent error

Scientific Notation  Exponential notation is used as shorthand for writing very large or very small numbers  3.6 x 10 4  3.6 is the coefficient and 4 is the exponent (power of ten)  What is the difference between 3.6 x 10 4 and 3.6 x 10 -4 ?  Refer to notes in packet!

Dimensional Analysis A CONVERSION FACTOR is a ratio of equivalent values used to express the same quantity in different units. Ex. 3 teaspoons = 1 tablespoon Conversion Factors: 3 teaspoons1 tablespoon 1 tablespoon3 teaspoons == 1 Let’s do the examples on the notes pages!

Significant Figures  Scientists indicate the precision of measurement by the number of digits they report  Sig Fig Rules (VERY IMPORTANT!!!):  1. If the number has a DECIMAL: Start counting with the first non-zero (1-9) and count ALL THE WAY TO THE END.  2. If the number has NO DECIMAL: Start counting with the FIRST non-zero (1-9) and count to the LAST non-zero Let’s practice on notes pages!

Rules for conversions  1. To convert from one unit to another, use the equivalence statement that relates the two units - a ratio of the two parts of the equivalence statement.  2. Choose the appropriate conversion factor by looking at the direction of the required change (Remember algebra class and make sure unwanted units cancel)  3. Multiply the quantity to be converted by the conversion factor to give the quantity with the desired units.  4. Check that you have the correct number of significant figures.  5. Check your work. Does your answer make sense?

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