The Tools of Quantitative Chemistry Let’s Review

Units of Measurement Metric System (International System of Units – SI) All units are derived from base units; quantities expressed using prefixes Unit Mass kilogram kg Lengthmeterm Timeseconds TempkelvinK Amount molemol CurrentampereA

SI units kilo-k10 3 deci-d10 -1 centi-c10 -2 milli-m10 -3 micro-μ10 -6 nano-n10 -9

Temperature Scales Celsius –zero is the freezing point of pure water –100 is the boiling point of pure water Kelvin –same size unit as Celsius –zero is the lowest temp that can be achieved (absolute zero) –no degree symbol is used with kelvin

Length, Volume, and Mass SI unit for length is the meter, but usually in chemistry it is necessary to use smaller divisions, such as micrometer or nanometer. SI unit for volume is m 3, but liters are commonly used in chemistry. 1 mL = 1 cm 3 1 L = 1000 mL = 1000 cm 3

Length, Volume, and Mass SI unit for mass it the kilogram, but smaller masses in chemistry are often used such as grams or milligrams.

Making Measurements Precision indicates how well several determinations of the same quantity agree. –often expressed as standard deviation Accuracy is the agreement of a measurement with the accepted value of the quantity. –often expressed as percent error

Making Measurements Experimental Error Error = experimental value – accepted value % Error = (Error/accepted value) x 100% Standard Deviation = the square root of the sum of the squares of the deviations for each measurement from the average divided by one less than the number of measurements.

Practice Problem Two students measured the freezing point of water. Student A used an ordinary thermometer calibrated in 0.1 o C units. Student B used a thermometer certified by NIST and calibrated in 0.01 o C. A: -0.3 o C; 0.2 o C; 0.0 o C; -0.3 o C B: o C; 0.02 o C, 0.00 o C; 0.04 o C Calculate the average value, the percent error, and standard deviation for each student. Which is more precise? Which has a smaller error?

Exponential or Scientific Notation Scientific (or exponential) notation is a way of presenting very large or very small numbers in a compact and consistent form that simplifies calculations. N x 10 n exponent is positive if the number is greater than 1 and negative if the number is less than 1

Significant Figures A result calculated from experimental data can be no more precise than the least precise piece of information that went into the calculation. Significant figures are the digits in a measured quantity that were observed with the measuring device.

Determining Significant Figures Rules on page 36 Arrow Method Addition/Subtraction –The number of decimal places in the answer is equal to the number of decimal places in the number with the fewest digits after the decimal. Multiplication/Division –Number of sig figs in answer is equal to the quantity with the fewest sig figs.

Dimensional Analysis Uses the dimensions of each unit to guide you through calculations. Conversion factors are used to change measured quantities to chemically useful information.

Graphing Goal is to obtain an equation that may help us obtain new results. y = mx + b “y” is the dependent variable; “x” is the independent variable; “m” is the slope of the line (Δy/Δx); “b” is y- intercept

Practice Problem To find the mass of 50 jelly beans, we weighed several samples of beans. (see Exercise 8 on page 41) Plot these data with the number of beans as independent variable and mass as dependent. What is the slope of the line? Use your equation of a straight line to calculate the mass of exactly 50 jelly beans.

Homework After reading the “Let’s Review” section, you should be able to do the following problems… pp (3-6, 15-18, 21-24)