Unit 2 Scientific Measurement
Qualitative vs quantitative Qualitative measurementsgive results in a descriptive, non-numerical form Ex. Observations taken in the demo lab Quantitative measurementsgive results in a definite form, usually as numbers and units Ex. Measurements taken in Measurement Activity.
Accuracy vs Precision Accuracyis a measure of how close a measurement comes to the actual or true value of whatever is measured. Somewhat tied to the price of the instrument making the measurement (remember my make believe meter sticks) Precisionis a measure of how close a series of measurements are to one another. Tied to the person making the measurements (can you repeat measurements)
Scientific Notation In scientific notation, a number is written as the product of two numbers: a number (between 1 & 9) times 10 raised to some power. Correct form: 3.2 10 5 not 32 10 4 Both represent 320000, but only 3.2 10 5 is in the correct form.
Practice scientific notation 4500000000.0000045 4.5 x 10 9 4.5 x 10-6 Both start out 4.5 x 10 raised to some power The number on the left is bigger than one and will have a positive exponent. The number on the right is less than one and will have a negative exponent.
Top of Scientific Notation Worksheet 39000000 3.9 x 10 7 3900000000 3.9 x 10 9.000039 3.9 x 10-5.0000039 3.9 x 10-6.0039 3.9 x 10-3 39000 3.9 x 10 4 390 3.9 x 10 2.039 3.9 x 10-2 39 3.9 x 10 1.00039 3.9 x 10-4 (must show the one)
Rules for simple math operations ( + -)
Multiplication When multiplying, add exponents (4 x 10 8 )(7 x 10 5 ) = 28 x 10 8+5 = 28 x 10 13 (must fix the 28) = 2.8 x 10 1 x 10 13 = 2.8 x 10 14 Must show work when solving these problems.
Division When dividing, subtract exponents (must show work) 8 10 4 x 10 9-5 8 10 2 10 4 x 10 4 2 10 4 x 10-9-5 4 x 10-14 8 10 4 x 109- (-5) 8 10 2 10 4 x 10 9+5 2 10 4 x 10 14 4 x 10-9-(-5) 4 x 10-9+5 4 x 10-4
Adding or subtracting When adding or subtracting, the exponents must be the same 6 x 10 4 60 x 10 3 +2 x 10 3 +2 x 10 3 62 x 10 3 (now fix the 62) 6.2 x 10 1 x 10 3 6.2 x 10 4 6 x 10 4 is the same as 6x10x10x10x10. You need to take a power of 10 away from the 10 4 and give it to the 6. It becomes 60 x 10 3.
Significant Digits The significant digits in a measurement include all of the digits that are known, plus a last digit that is estimated. (remember making measurements using a scale)
Rules for determining significant digits All nonzero numbers are significant Final zeros in a decimal are significant Zeros stuck between significant numbers are significant All other zeros are not significant
Special Cases A counting number has an infinite number of significant digits. A definition (such as: 1 min = 60 sec) both numbers have an infinite number of significant digits. Sometimes zeros are significant based on a calculation and need to be marked. Put number in scientific notation Use a decimal point at the end of the number
Examples 456 3 sig digs.00450600 6 sig digs (all non-zero numbers) (4,5,6,final zero in decimal, and two 0s trapped) 4560 3 sig digs 0.4560 4 sig digs (4,5,6, and the 0 does not count) (the 4,5,6 and the final zero in the decimal) 4506 4 sig digs 4500.00 6 sig digs (the 4,5,6 and the trapped 0) (the 4,5, the final zero in the decimal, rest trapped).000456 3 sig digs 4500. 4 sig digs (only the 4,5,6, zeros don t count) (the 4,5, the last 0 is marked, the other 0 trapped) 4.50 10 6 3 sig digs (the 4,5, and the final zero in the decimal only the numbers before the x)
Top of Significant Digit Worksheet a. 4.65 3 k. 54.52 4 b. 0.3246 4 l. 0.12090 5 c. 85.00 4 m. 2.890 4 d. 93000 2 n. 53.0 3 e. 0.0040 2 o. 3700.00 6 f. 50.003 5 p. 6200 2 g. 0.601 3 q. 6200. 4 h. 0.00390 3 r. 6.20 10 3 3 i. 0.02300 4 s. 6020 3 j. 26.5090 6 t. 6002 4
Addition or Subtraction Least number of decimal places. 356.2765 (4 decimal places) + 4.5 (1 decimal place) 360.7765 (can only have 1 decimal place in the answer answer becomes 360.8
Multiplication or Division Least number of significant digits. 3 sig dig 1 sig dig (can only have 1 sig dig in the answer) 456 x 100 = 45600 = 50000 (must keep the magnitude of the answer) 3 sig dig 2 sig dig ( can have 2 sig digs in the answer) 456 x 1.0 x 10 2 = 45600 = 46000 3 sig dig 3 sig digs (can have 3 sig digs in the answer) 456 x 100. = 45600 = 45600
Base Units of the SI System Quantity SI base unit Symbol Example Length Meter m ~ length of a yard (36 in) Volume Cubic meters m 3 ~ volume of cubic yard Mass Kilogram kg ~ mass of small text Temp Kelvin K Same size as C Energy Joule J moves apple 1 meter Time Second sec nothing beats time!! Amt of substance Mole mol unfathomable!!
Mass vs Weight Massof an object is the amount of matter the object contains. It is not affected by gravity Weightis the force that measures the pull on a given mass by gravity.
Temperature The temperature of a substance is the degree of hotness or coldness of an object. When two objects at different temperatures are in contact, heat moves from the object at the higher temperature to the object at the lower temperature.
Temperature Scales Fahrenheit used in the US * mp= 32 F and bp= 212 F Celsius used by everybody else * mp= 0 C and bp= 100 C Kelvin scale devised once absolute zero was theorized (no in unit) * mp= 273 K and bp= 373 K K = C + 273 C = K 273 Note: K can never be negative!
Density Density is the ratio of the mass of an object to its volume. Density = mass volume mass units are usually g ml or g cm 3 D vol
Ex 1 What is the density of a solid that has a mass of 45.7 g and occupies 7.6 cm 3? Mass = 45.7 g Vol 7.6 cm 3 D =? g/cm 3.. = 6.013157895 (Now we must look at significant digits; 3 sig digs up top and 2 sig digs down below. Since division, the rule is least number of significant digits. So, I can only have 2 sig digs in the answer. The answer becomes 6.0 g/cm 3 )
Ex 2 Aluminum has a density of 2.70 g/cm 3. What is the mass of 35.0 cm 3? Mass =? g Vol 35.0 cm 3 D = 2.70 g/cm 3 rearrange for mass mass = D x volume Mass 2.70 g/cm 3 x 35.0 cm 3 94.5 g (Now we must look at significant digits; 3 sig digs in the density and 3 sig digs in the mass. Since we are multiplying, the rule is least number of significant digits. So, I can have 3 sig digs in the answer. The answer remains 94.5 g)
Specific Heat Capacity Specific heat capacity is the amount of energy needed to raise one gram of a substance by one degree Celsius. For water, the specific heat capacity can be represented by two numbers, depending upon the energy unit used. J cal 4.18 or 1.00 g C g C
The formula used for specific heat capacity problems is Q = mδtc p where Q stands for energy and the unit is joules m stands for mass and the unit is grams Δt stands for change in temp and the unit is C C p stands for specific heat capacity and the unit is Q m t C p
Ex 1 How much energy is needed to raise the temperature of 49.6 grams of aluminum from 24.0 C to 57.5 C? (Cpfor aluminum =.900 Δt = 57.5 24.0 = 33.5 C Q =? J Mass = 49.6 g t = 33.5 C C p =.900 Q = m tc p = (49.6 g)(33.5 C)(.900 ) = 1495.44 J We can have 3 sig digs in the answer 1498.44, cut off for three becomes 1500. However the 1500 should show 3 sig digs, so the answer must be placed into scientific notation to show the 3 significant digits. The answer becomes 1.50 x 10 3 J
Ex 2 387 J of energy are needed to raise the temperature of 57.4 g of a metal by 37.5 C. What is the specific heat capacity of the metal? Q = 387 J Mass = 57.4 g t = 37.5 C C p =? C p = = t (57.4 g)(37.5 C) =.1797909408 We can have 3 sig digs in the answer. The 7 will round the 9 which also rounds the 7 in front of the 9. The answer becomes.180
Ex 3 An unknown metal with a mass of 46.5 g was heated to 100.00 C and then dropped into 35.0 g of water at 23.00 C. The final temperature of the system is 25.75 C. What is thespecific heat capacity of the unknown metal? Must make a table of information Energy lost by metal = energy gained by water Q metal = Q water Metal water m tc p = m tc p *m =46.5 g * m = 35.0 g T i = 100.00 C T i = 23.00 C T f = 25.75 C T f = 25.75 C now plug in the numbers from the table (do not * t = 74.25 C * t = 2.75 C need the temperatures any more) *C p =? *C p = 4.18 (46.5 g)(74.25 C)(C p ) = (35.0 g)(2.75 C)(4.18 3452.625 g C)(C p ) = 402.325 J C p = 402.325 J 3452.625 g C C p =.11652728 Looking at original set up, you can have 3 significant digits. The answer becomes.117