Bichemistry Summer Packet Science Basics Metric Cnversins All measurements in chemistry are made using the metric system. In using the metric system yu must be able t cnvert between ne value and anther. Yu must memrize the factrs, prefixes and symbls in the chart belw. There are numerus ways t d metric cnversin. I present ne methd belw that I have used in my Hnrs and Chemistry I classes. Example: Cnvert 1.83 x 10-1 kilgrams t centigrams. Step 1. Subtract the pwer f ten value yu are slving fr frm the pwer f ten value yu are given. In this prblem yu are given 1.83 kilgrams and yu are cnverting t centigrams. Kilgrams have a pwer f ten value f 3; centigrams have a pwer f ten value f -2. 3-(-2) = 5 Step 2. Write yur result as the pwer f ten value f yur answer. In this prblem ur answer is 1.83 x 10-1 x 10 5. Step 3. Put yur answer in prper scientific ntatin. 1.83 x 10-1 x 10 5 is cnverted t 1.83x10 4. Remember that when multiplying using pwers f ten yu add. Factr Prefix Symbl 1 x 10 12 tera- T 1 x 10 9 giga- G 1 x 10 6 meg - M 1 x 10 3 kil- k 1 x 10 2 hect- h 1 x 10 1 deca- D 1 x 10 0 --- --- 1 x 10-1 deci- d 1 10-2 centi- c 1 x 10-3 milli- m 1 x 10-6 micr- μ 1 x 10-9 nan- n 1 x 10-10 angstrm Å 1 x 10-12 pic- p Uncertainty in Measurement Depends n the precisin f the measuring device Fr example a measurement f 1 682956 grams is a mre precise measurement than 1.7 grams Reliability in Measurements Accuracy clseness t the actual scientific value Precisin getting repeated measurements in repeated trials Types f Errrs Randm: errr in measurement has equal prbability f being high r lw Systematic: errrs all ccur in the same directin General Rules fr determining if a Number is Significant 1. Draw a bx arund all nnzer digits beginning with the leftmst nnzer digit and ending with the rightmst nnzer digit in the number. 2. If a decimal is present, draw a bx arund any trailing zers t the right f the riginal bx. 3. Cnsider any all bxed digits significant. Example 1: 20406: 5 significant digits Example 3: 4000: 1 significant digit Example 5: 0.002500: 4 significant digits Example 2: 0.0045: 2 significant digits Example 4: 4000. : 4 significant digits Example 6: 3.00: 3 significant digits Additin r Subtractin using Significant Figures The answer can nly be as precise as the least precise measurement. Example 2.8701 (precise fur places t the right f the decimal) 0.0673 (precise fur places t the right f the decimal) + 301.520 (precise three places t the right f the decimal) 304.4574 runds ff t 304.457 (answer must be precise three places after the decimal)
Multiplicatin r Divisin using Significant Figures The answer can have n mre ttal significant figures than there are in the measurement with the smallest ttal number f significant figures. Example: 12.257 (5 ttal significant figures) x 1.162 (4 ttal significant figures) 14.2426 runds ff t 14.24 (4 ttal significant figures) As a general rule, if yu are unsure hw many significant figures t us n the AP exam, use 3 significant figures. This may nt always wrk but it will wrk mst times. Hwever yu shuld always pay clse attentin t using the crrect number f significant figures in all calculatins. Scientific Ntatin In chemistry, we ften use numbers that are either very large (1 mle = 602 200 000 000 000 000 000 000 atms) r very small (the mass f an electrn = 0.000 000 000 000 000 000 000 000 000 000 910 939 kg). Writing numbers with s many digits wuld be tedius and difficult. T make writing very large and small numbers easier, scientists use an abbreviatin methd knwn as scientific ntatin. In scientific ntatin the numbers mentined abve wuld be written as 6.022 x 10 23 and 9.10939 x 10-31. Cnverting a number t r frm scientific ntatin If yu mve the decimal place t the left, the pwer f 10 value increases. If yu mve the decimal place t the right, the pwer f 10 value decreases. Example 1: Lk at the first number frm abve: 602 200 000 000 000 000 000 000 T put this number in scientific ntatin yu wuld mve yur decimal place until there is ne number t the left f the decimal. T d this, we must mve ur decimal 23 places t the left. When yu mve the decimal t the left, the pwer f 10 value increases. It increases frm 0 t 23. Thus, the answer is 6.022 x 10 23 Lk at the secnd number frm abve: 0.000 000 000 000 000 000 000 000 000 000 910 939 T put this number in scientific ntatin we must mve ur decimal 31 places t the right. REMEMBER: Yu shuld always have ne digit t the left f the decimal when writing numbers in scientific ntatin. Since we are mving ur decimal t the right, we must decrease ur pwer f 10 value. It decreases frm 0 t 31. The answer is 9.10939 x 10-31 Rules fr multiplying & dividing using scientific ntatin: When multiplying tw numbers in scientific ntatin, ADD their pwer f 10 values. Fr example: (3.45 x 10 6 )(4.3 x 10 5 ) = 14.835 x 10 11. But, we must als remember t express ur answer in significant figures. Thus, the final answer is 1.5 x 10 12 When dividing numbers in scientific ntatin, SUBTRACT the denminatr s pwer f 10 value frm the numeratr s pwer f 10 value. Fr example: (2.898 x 10 12 ) (3.45 x 10 15 ) = 0.840 x 10-3 (I had t add the zer at the end t get the three significant figures needed.) I gt 10-3 because 12 15 = 3. Make sure yur answer is in prper scientific ntatin (ne number t the left f the decimal). In this prblem we have t mve the decimal ne place t the right. When we mve ur decimal t the right, we decrease ur pwer f 10. 3 decreases by 1 t 4. Our fi al answer is: 8.40 x 10-4 Dimensinal Analysis Used t cnvert a number frm ne system f units t anther. Understanding dimensinal analysis is crucial. This prcess will help yu when perfrming difficult calculatins later in the year. Yu will find a cmplete listing f English/Metric Equivalents n the last page f yur text bk. Cnversin factrs d nt need t be memrized.
Example: Calculate hw many kilmeters there are in 5 miles. Slutin: (Needed Equivalents: 1 mile = 1760 yards, 1 meter = 1.094 yards) 5 miles x 1760 yards x 1 meter x 1 kilmeter = 8.04 (runded t) 8 kilmeters 1 mile 1.094 yards 1000 meters Example: Cnvert 55.0 miles/hur t meters/secnd Slutin: (Needed Equivalents: 1 mile = 1760 yards, 1 meter = 1.094 yards, 1 hur = 60.0 minutes, 1 minute = 60.0 secnds) 55.0 miles x 1760 yards x 1 meter x 1 hur x 1 minute = 24.5785 (runded t) 24.6 m/s hur 1 mile 1.094 yards 60.0 minutes 60.0 secnds General Rules fr Runding Numbers in Chemistry Rule 1. If the digit fllwing the last significant figure is less than 5, the last significant figure remains unchanged. The digits after the last significant figure are drpped. Example: Rund 23.437 t three significant figures. Answer: 23.4 Explanatin: 4 is the last significant figure. The next number is 3. 3 is less than 5. Thus, 4 remains unchanged and 37 is drpped. Rule 2. If the digit fllwing the last significant figure is 5 r greater, then 1 is added t the last significant figure. The digits after the last significant figure are drpped. Example: Rund 5.383 t tw significant figures. Answer: 5.4 Explanatin: 3 is the last significant figure. The next number is 8. 8 is greater than 5. Thus, 1 is added t 3 making it 4. The 83 is drpped. As a rule, when perfrming a series f calculatins, wait until the very end t rund ff t the prper number f significant figures instead f runding ff each intermediate result unless yu are changing frm additin /subtractin t multiplicatin/divisin r vice versa. Example 1: 10.82 + 2.5 + 2.64 = WRONG: 10.82 + 2.5 = 13.32 (runded t 13.3) 13.3 + 2.64 = 15.94 (runded t) 15.9 CORRECT: 10.82 + 2.5 + 2.64 = 15.96 (runded t) 16.0 (precise t 1 place after the decimal) Example 2: (12.00 10.00) 12.00 = In this case yu shuld subtract and ROUND t the prper number f significant figures and then divide because yu are changing between significant figure rules. CORRECT: (12.00-10.00) = 2.00 (precise t 2 places after the decimal) 2.00 12.00 = 0.167 (runded t 3 ttal significant figures)
Practice Prblems Measurements Recrd the measurements fr each f the fllwing pieces f equipment. Be sure t include the number with the crrect number f significant figures and the label n the number. Assume the rulers are in centimeters (cm), the thermmeters in Celsius (C), the graduated cylinders in milliliters (ml), and the triple beam balance in grams (g). 1. 2. 3. 4. 5. 6. 7. 8. 9.
Metric t Metric Cnversins 1) 2000 mg = g 6) 5 L = ml 2) 104 km = m 7) 198 g = kg 3) 480 cm = m 8) 75 ml = L 4) 5.6 kg = g 9) 50 cm = m 5) 8 mm = cm 10) 5.6 m = cm Scientific Ntatin Cnvert the fllwing numbers int scientific ntatin: 1) 3,400 2) 0.000023 3) 101,000 4) 0.010 5) 45.01
Cnvert the fllwing numbers int standard ntatin: 6) 2.30 x 10 4 7) 1.76 x 10-3 8) 1.901 x 10-7 9) 8.65 x 10-1 10) 9.11 x 10 3 Unit Cnversins A nurse weighs a patient. The patient s weight is 70.67 kg. Hw many punds is this? A man is rushed t the emergency rm after a severe accident. He is given 7.2 unces f bld. Hw many pints is this? A 140 pund wman is ging int surgery. She is given a sedative, and the anesthesilgist injects 1 unce fluid fr every 1000 grams f the patient s mass. Hw many unces des the anesthesilgist need t inject int the IV? A child has strep thrat and is administered amxicillin. The crrect dsage is fr every 50 kg, 1 teaspn is needed. The child weighs 60 lbs. Hw many teaspns shuld the child take? Significant Figures 1. Hw many sig figs des each value have? 3.00 6.0900 100000 12.60.0009000 2.600 x 10 5 0.0045 0.120003 1.01080 x 10-3
2. Perfrm the calculatins with the crrect sig figs. 10.0369 + 1.23 = 6010 + 17.78 3.0963 x 2.682 = 5890/120.2 = 3. Rund t 3 sig figs. 8.01603 m 4.5992 g 7 L The Scientific Methd Scientists use an experiment t search fr cause and effect relatinships in nature. In ther wrds they design an experiment s that changes t ne item cause smething else t vary in a predictable way. These changing quantities are called variables. A variable is any factr, trait, r cnditin that can exist in differing amunts r types. An experiment usually has three kinds f variables: independent, dependent, and cntrlled. The independent variable is a factr that is changed r manipulated by the scientist. T insure a fair test, a gd experiment has nly ne independent variable. As the scientist changes the independent variable, he r she bserves what happens. The scientist fcuses his r her bservatins n the dependent variable t see hw it respnds t the change made t the independent variable. The dependent variable is measured t determine if the manipulatin f the independent variable had any effect. The dependent variable depends n the independent variable. Experiments als have cntrlled variables. A cntrl grup r a cntrl is quantities that a scientist wants t remain cnstant r unchanged. Mst experiments have mre than ne cntrlled variable. Lastly, in a gd experiment, the scientist must be able t measure the values fr each variable. Weight r mass is an example f a variable that is very easy t measure. Example: T test a hypthesis that eating carrts imprves visin, the experimenter wuld manipulate whether r nt subjects ate carrts. Thus, eating carrts is the independent variable. Each subject s visin wuld be tested t see if carrt eating had any effect. Thus, visin is the dependent variable. The subjects assigned t eat carrts are in the experimental grup, whereas subjects nt eating carrts are in the cntrl grup.
Identify the independent variable, dependent variable, experimental and cntrl grups in the fllwing studies. 1. The cmpany Office Max thinks that a special juice will increase the prductivity f its wrkers. The cmpany creates tw grups f 50 wrkers each and assigns each grup the same task (in this case, they're suppsed t staple a set f papers). Grup A is given the special juice t drink while they wrk. Grup B is nt given the special juice. After an hur, the cmpany cunts hw many stacks f papers each grup has made. Grup A made 3,587 stacks, Grup B made 1,113 stacks. Independent variable: Dependent variable: Experimental grup: Cntrl grup: What shuld the cmpany s cnclusin be? 2. A grup f cllege students were given a shrt curse in speed-reading. The instructr was curius if a mnetary incentive wuld influence perfrmance n a reading test taken at the end f the curse. Seventy students were ffered $15 fr btaining a certain level f perfrmance n the test, and anther seventy students were nt ffered any mney. The students that were ffered $15 scred an average f 75% n the test. The students that were nt ffered any mney scred an average f 86%. Independent variable: Dependent variable: Experimental grup: Cntrl grup: What shuld the instructr s cnclusin abut mnetary incentive be?
Practice: Write a hypthesis fr each f the questins and identify the variables, cntrl grup, and experimental grup. 1. Des cigarette smking increase the risk f lung cancer? Hypthesis: If, then Independent Variable: Dependent Variable: Cntrl Grup: Experimental Grup: 2. Des eating breakfast increase perfrmance in schl? Hypthesis: If, then Independent Variable: Dependent Variable: Cntrl Grup: Experimental Grup: