Name CHM112 Lab Math Review Grading Rubric Criteria Points possible Points earned A. Simple Algebra 4 B. Scientific Notation and Significant Figures (0.5 points each question) C1. Evaluating log and ln and their reciprocals (0.25 points each question) 2 2 C2. Rules of Logarithms (0.25 points each question) 1.5 C3. Solve for the unknown y in each case (0.5 points each question) 4 D1 (0.5 points each question) 1.5 D2 (0.5 points each question) 1 D3 (0.5 points each question) 1.5 D4 (0.5 points each question) 1.5 D5 (0.5 points each question) 1 Total 20 Subject to other additional penalties as per the instructor
Math Review A. Scientific notation and Significant Figures While entering a number in scientific notation in your calculator, look for the EE or the exp key on your calculator. For example using the TI3-XA, one would enter 6.023 x 10 23 as 6.023 EE 23. Using a TI-84 plus, the same number would be entered as 6.023 2 nd EE 23. Using a TI-89, the same number would be entered as 6.023 EE 23 Practice entering the following numbers in your calculator a) 2.303 x 10 12 b) 9.11 x 10-31 c) 2.3 x 10 3 Rules for Counting Significant Figures: Example # S. F. 1. All nonzero integers are significant. 421.1 4 2. Leading zeros are never significant. 0.0034 2 3. Captive zeros are always significant. 205 3 4. Trailing zeros in a decimal number are significant. 25.0 3 5. Trailing zeros in a number with no decimal are not significant. 400 1 Exponential /Scientific Notation: The number of significant figures in a number written in exponential notation is easily determined as the leading and trailing zeros are removed. Examples: Decimal Exponential/Scientific notation # S. F. 0.0034 3.4 x 10-3 2 400 4 x 10 2 1 0.000505 5.05 x 10-4 3 530000 5.3 x 10 5 2 0.0100 1.00 x 10-2 3 Rules for sig figs in mathematical operations Multiplication and division The final answer must have the same number of sig figs as the number having the least sig figs Addition and subtraction The final answer must have the same number of decimal places as the number with the least decimal places Rules for Rounding: 1. In a calculation carry all of the significant figures through to the final result, then round to the correct number of significant figure based upon the data with the smallest number of significant figures. 2. If the digit to be removed is <5, the preceding digit remains unchanged. 25.44 rounds to 25.4. 3. If the digit to be removed is 5, then the preceding digit is incremented by 1. 25.46 rounds to 25.5
B. Logarithms to the base 10 (log) and Natural Logarithms (ln, to the base e) Logarithms are the opposite of exponentials. For example: Since 10 2 100, we can write log 10 2 2 or log 100 2 Since 10 0 1, then log 10. Similarly, e 0 1, therefore ln 1 0 e lnx x or lne x x Similarly, log10 x x or 10 log x x Look for the log and the 10 x key on your calculator to get the log and the antilog of a number. Similarly, become familiar with the ln and e x key on your calculator. Example: If log x 2, then x 10 2 Ex: If ln x 5, then x e 5 Some basic rules for logarithms are: log(a*b) log a + Log b log a log a log b b log a m m log a ln (a*b) ln a + ln b ln a ln a ln b b ln a m m ln a C. Graphs A graph is a visual representation of the relationship between two quantities. Usually, the x axis is the independent variable and the y axis is the dependent variable. This means that the quantity plotted on the y axis depends on the value plotted on the x axis. A graph of concentration against time implies that the concentration is on the y axis (dependent variable) and time is on the X axis (independent variable). If you are told to plot a graph of ph versus volume, then ph is plotted on the Y axis and the volume is plotted on the X axis. Chemists mostly like to deal with linear relationships and will choose y and x units such that the plot is a straight line. Consider the following graph of volume of a gas versus number of moles: From the graph, we can see that when the Volume of gas (cm 3 ) y 20x + 2E-14 R² 1 Moles of gas (n) moles of the gas changes from 0.5 to 1.0, the volume of the gas changed from 10 cm 3 to 20 cm 3. The Slope of this line can be calculated Δy as: Slope Δx change in y change in x 3 20 10 10 cm Slope 20 1.0 0.5 0.5 mol The equation of a straight line is of the form y m x + b, where m is the slope of the line and b is called the y intercept. Consider the linear form of the Clausius-Clapeyron equation ΔHvap 1 ln PVapor + ln β R T y m x + b A graph of ln (P vapor ) against 1 vap, will give a straight line with a slope T ΔH R and an intercept ln β
CHM 112: Math Review Name A. Simple Algebra Solve for the unknown (y) in each of the following cases. Show your work. 3y 6 12 6y 48-25 30 5y 1 0.02 y 25 125 y 1 1 1 + 6.25 23.9 y y 1.44 1 1 + 1 12 0.65 y 0.05 2y B. Scientific notation and Significant Figures Carry out the following calculations and report your answer in scientific notation with the correct sig figs a) 34 8 (6.634 10 )(3.0 10 ) 589 10 9 c) (1.00866.100728) 23 6.0225 10 b) 6.08 x 10-3 + 7.2 x 10-4 + 0.531x 10-2 d) (433.621-333.9) / 11.900 Report Page 1 of 4
C. Logarithms C. 1. Evaluating log and ln and their reciprocals. Calculate the following quantities. 1. ln (e) 2. log(1000) 3. ln (e) 4 4. e (18200/(8.314*290)) 5. ln (1) 6. - log (0.050) 7. 10-4.74 8. log (13) C. 2. Rules of Logarithms Complete the following calculations. (You can either use the rules of logarithms discussed earlier or evaluate these directly using your calculator. Try it both ways to see if you get the same answer) 1. log(20) log(2) 4. 0.53 ln 2.5 2. ln(80) + ln(20) 5. 1 log 10 3. 2.303 log 1.254 6. 1 ln 40 C3. Solve for the unknown y in each case (You can either use the Rules of logarithms discussed earlier or evaluate these directly using your calculator. Try it both ways to see if you get the same answer) 1. y log(100) 36 y 4. ln 7.234 0.0112 2. log(33) + ln(y) 2.250 5. ln(5 y ) 2.45 3. log y -6.26 6. log(12 y ) 2.303 Report Page 2 of 4
7. 2.3 log y 1.25 8. ln(125 y ) 4.248 D. Graphs D1. Complete the following table by comparing each equation to the equation of a straight line. Equation Slope Is the slope positive or negative? Intercept y 310. x + 18.5 y - 255 x + 1.003 y -1.203 + 0.17 x D2. Consider the equation y 0.035 x + 0.125 a. What will be the value of y when x 3.5? b. What is the value of x when y 0.754 D3. Complete the following table by comparing each of the equations to y m x + b Equation [A] t [A] 0 k t What is plotted on the y axis? What is plotted on the x axis? Slope Intercept E a 1 ln k + ln A R T 1 1 + kt [ A] [ A] t 0 Report Page 2 of 4
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ΔH vap 1 D4. The linear form of the Claussius Clapeyron equation is ln P vapor + ln β R T a) What is plotted on the X axis? b) What is plotted on the Y axis? c) What will be the slope the graph? D5. A student plotted a graph of ln (VP in torr) versus 1/T in Kelvin for dichloromethane and obtained the best fitting line as y -3805x + 18.8 a. What is the vapor pressure of dichloromethane at 85.0 C? b. What is the normal boiling point of dichloromethane? Remember that at the normal boiling point, the vapor pressure 1 atmosphere. Report Page 4 of 4