MEASUREMENT AND PROBLEM SOLVING Chapter 3 & 4
Importance of Measurements 1. Fundamental to all sciences 2. In chemistry you use the International System of Measurements (SI units).
Qualitative vs. Quantitative Measurements Qualitative -- descriptive, nonnumeric Quantitative -- results in a definite form, usually as numbers and units.
Scientific Notation 3.6 x 10 4 = 36,000 8.1 x 10 3 = 0.0081
Numbers less than 1 the exponent is negative and represents the number of places the decimal has been moved to the right. Numbers greater than 1, the exponent is positive and represents the number of places the decimal is moved to the left.
Manipulation of Exponents: Multiply -- multiply the coefficients and add the exponents. Ex: (3.0 x 10 4 ) (2.0 x 10 2 ) = 6.0 x 10 4 + 2 = 6.0 x 10 6
Division -- Divide coefficients and subtract denominators from the numerator. Example: 3.0 x 10 4 = 3.0 X 10 4 2 = 1.5x 10 2 2.0 x 10 2 2.0
Addition & Subtraction make exponents the same, by moving the decimal Example: 5.4 x 10 3 + 6.0 x 10 2 = 5.4 x 10 3 + 0.60 x10 3 6.0 x 10 3
Accuracy How close a measurement comes to the actual or true value. To evaluate the accuracy of a measurement, it must be compared with the correct value.
Precision -- A measure of how close a series of measurements are to one another. Depends on more than one measurement.
Error the difference between what you get and the actual value. 1. Actual (True) Value The correct value based on reliable references. 2. Experimental value measured in the lab.
Error = Actual Experimental a.can be positive or negative b. Percent error is the absolute value divided by the accepted value, multiplied by 100%.
SIGNIFICANT DIGITS To determine the number of significant digits in a written number complete one of the following:
1. Qualifying statement: The numerical value has no decimal place written. Action to take: Count from the first nonzero digit to the last non-zero digit. Examples: 18,004-5 significant digits 10,040,000 4 sig digs 10 1 sig dig
2. Qualifying statement: The numerical value contains a decimal place. Action to take: Count from the first nonzero digit to the end of the number. Examples: 100.00 5 sig digs 1,050. 4 sig digs 0.000 145 00 5 sig digs
Using Significant Digits in problems: Addition and Subtraction Answer the problem then round to the same number of decimal places as the measurement with the least number of sig digs. Example: 14.05 + 21.3 = 35.35 = 35.4
Multiplication and Division -- answer the problem and round the answer to the same number of sig. digs. As the measurement with the least number of sig. digs. Example : 24.55 x 52.3 x 14.235 = 18277.24178 = 18300
Units : 1. All measurements depend on units 2. Science uses the metric system. 3. Each type of measurement has a base unit.
Length (distance) = meter Volume (the amount of space occupied by matter) = liter Mass (weight) = gram
Prefixes are added to the base unit in order to measure in different amounts.
Common prefixes 1. Kilo ( K ) = 1000 2. Hecta ( H ) = 100 3. Deka ( D ) = 10 4. deci ( d ) = 1 /10 5. centi ( c ) = 1 / 100 6. milli ( m ) = 1/ 1000 7. micro (μ ) = 1 / 1x10-6 8. nano ( n ) = 1 / 1x 10-9
Density the relationship between an objects mass and its volume. Density = Mass / Volume (D = M / V) Example: D =? If the mass of an object is 114 g and takes up a volume of 10.0 ml. D = 11.4 g/ml.
If the mass of an object stays the same, but the volume changes then the density will change. Typically as the volume gets smaller the density gets larger. Water is an exception to this.
Temperature of an object determines the direction of heat transfer. - Heat moves from the object of higher temperature to the object of lower temperature.
- Almost all substances expand with an increase in temperature (thermal expansion).
Scales Celsius -- uses two reference points to set it, the freezing point ( 0º C ) and the boiling point of water ( 100 º C ).
Kelvin ( absolute scale ) the freezing point of water is 273.15 K and the boiling point is 373.15 K. -No degree sign is used. -The zero point is equal to 273.15 º C, and is called absolute zero.
Conversion Formulas: K = º C + 273.15 K = 20 C + 273.15 = 293.15K º C = K 273.15 C = 118K 273.15 = -155.15 C
Problem Solving Three steps to solving problems 1. Analyze a.identify the known ( what is given ). b.identify the unknown c. Plan a solution ( choose appropriate equation )
2. Calculate a. Substituting known quantities b. Arithmetic manipulation c. Convert the units 3. Evaluate Does the answer make sense? Is it written in the correct units?
Conversion Factors a ratio of equivalent measurements. Example: 100cm = 1m 1 m 100cm
The numerator (top) is equal to the denominator (bottom). Dimensional Analysis a way to analyze and solve problems using the units, or dimensions, of the measurements.
Multistep Problems 1. Solve by breaking the solution into steps. 2. Convert complex units, using dimensional analysis. Practice Problems on board.