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

Step 1 - THE PROBLEM Read the problem Be sure you understand what is being asked 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 Problem solving in chemistry

Step 3 - SOLVE FOR THE UNKNOWNS Determine the correct equation Plug in knowns to solve for unknowns Don’t forget the conversions Step 4 – EVALUATE Look at the answer and units... Do they make sense? Check your work! Problem solving in chemistry

Measurement = A quantity that has a number and a unit Qualitative vs. Quantitative Color Texture Time Temperature Mass Measurements

Base Unit = System of measurement that is based on an object or event in the physical world SI Base Units (Table 2.1) Units of Measurement

Prefixes used with SI base units Units of Measurement Kilo (k) – 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

 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 Units of Measurement

 Use thermometers to get quantitative data  Celsius scale (C)  Freezing water = 0 degrees C  Boiling water = 100 degrees C  Kelvin (K) - SI base unit for temperature  Freezing water = 273 K  Boiling water = 373 K Temperature

 Accuracy – how close a measured value is to an accepted value  Precision – how close a series of measurements are to one another How Reliable are Measurements? Section 2.3

Error  Error = Accepted value – Experimental value  Ignore + or – signs  Percent Error = l error l /accepted value x 100  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 ?  Practice problems on handout!

Dimensional Analysis Dimensional Analysis = method of problem-solving that focuses on the units used to describe matter Goal: To convert from one unit to another Uses conversion factors == 1 Let’s do the examples on the notes pages!

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 teaspoons/1 tablespoon = 1 tablespoon/3 teaspoons = 1 == 1 Let’s do the examples on the 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?  Practice and example problems!

Significant Figures  Scientists indicate the precision of measurement by the number of digits they report  Sig. Figs. include all known digits plus one estimated digit  Answer can’t be more precise than the numbers given in the problem Let’s practice on notes pages!

Significant Figures  Sig Fig Rules (VERY IMPORTANT!!!):  1. Non-zero numbers are always significant.  2. Zeros between non-zeros are always significant  3. All final zeros to the right of the decimal place are significant  4. Zeros that act as placeholders are not significant (use scientific notation)  5. Counting numbers and defined constants have an infinite number of sig figs.

Using Sig Figs in Math  Add/subtract: Calculate and then round so that there is the same number of decimal places as the value with the lowest number of decimal places.  Multiply/divide: Calculate and then round so that there is the same number of sig figs as the value with the lowest number of sig figs.  Rules of rounding  Use only one digit to the right of the last sig fig to determine if round up or stay same.  Practice Problems!