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Measurement & Calculations

Measurement & Calculations. Honors Chemistry Chapter 2. Scientific Notation Shorthand way of expressing very large or very small numbers. Consists of two factors: Coefficient - a number between 1 and 10 (only 1 digit to the LEFT of the decimal point)

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Measurement & Calculations

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  1. Measurement & Calculations Honors Chemistry Chapter 2

  2. Scientific NotationShorthand way of expressing very large or very small numbers Consists of two factors: • Coefficient - a number between 1 and 10 (only 1 digit to the LEFT of the decimal point) • Base - a power of 10  “power of 10” shows the number of 10’s that are to be multiplied together • Examples on the number line: 1x102 4x101 1x100 1x10-10 1x10-1

  3. Place numbers on the line:4x101 1x10-10 1x100 1x102 1x10-1 0

  4. Uncertainty in Measurement – due to instrument flaw and estimation • Measurements are uncertain because • Instruments are not free from ERROR. • Measuring always involves some ESTIMATION. • Estimating with a scale • Estimate ONE digit more than the instrument measures.

  5. Length - Rulers

  6. How to use a graduated cylinder Read the meniscus

  7. How to use a graduated cylinder

  8. Triple Beam Balance

  9. How to read a triple beam balance

  10. Temperature

  11. Uncertainty • Precision – represents agreement between several measurements of the same quantity • Precise data vs. Imprecise data • Accuracy – represents agreement between a measurement & the true value (within the limits of the instrument); enhanced with calibration • Accurate data vs. Inaccurate data • % Error = measured value –accepted value accepted value x 100%

  12. Accuracy vs. Precision

  13. Exact numbers– numbers with no uncertainty • Significant Digits– certain digits plus 1 uncertain digit in a measurement; indicative of precision • Rounding– 0.5

  14. Nonzero Digits • Every nonzero digit is assumed significant. • 24.7 m • 0.743 g • 714 m

  15. Captive Zeros • Zeros appearing between nonzero digits are significant. • 7003 m • 40.79 g • 1.503 m

  16. Leading Zeros • Leftmost zeros appearing in front of nonzero digits are NOT significant. They are placeholders. • 0.0071m = 7.1 x 10-3m • 0.42m = 4.2 x 10-1m • 0.000099m = 9.9 x 10-5m

  17. Trailing Zeros • Zeros at the END of a number AND to the RIGHT of a decimal point are always significant. • 43.00 m • 1.010 m • 9.000 m

  18. Trailing Zeros • Zeros at the rightmost end of a measurement that lie to the left of an understood decimal point are NOT significant if they serve as placeholders to show the magnitude of the number. • 300 m 7000 m 27,210 m • Use decimal point at end to signify that the last 0(s) are significant. • 300. m or 3.00 x 102 m

  19. Significant Digits Use Atlantic-Pacific Rule – imagine a US map decimal point decimal point Pacific Atlantic resent bsent

  20. 1100 1100. 11.010000 0.025 0.00035000 1,000,100 Decimal Absent Start counting with the 1st nonzero digit and count all the rest. Decimal Present Start counting with the 1st nonzero digit and count all the rest.

  21. Calculations • Multiplication and Division (fewest sig digits) • 2.2 x 0.36 x 3.21 = • 3.6 ÷ 4.20 = • Addition and Subtraction (least number of decimal places) • 28.75 – 17.5 = • 125.7 + 1.86 + 0.074 =

  22. 140mm 20mm Using a Manometera device used to measure pressure • When a gas is produced during the reaction, the gas can be pumped into the bulb of the manometer and the pressure of the gas can be determined. • There are 2 types of manometers – closed & open. • Closed: the difference in the height of the Hg columns is the pressure of the gas in the bulb. Gas has no pressure Gas has a pressure of 120 mm Hg

  23. 140 mm 70mm 20mm 20mm Using a Manometer • Open: To use an open manometer, you must also have a barometer to determine the atmospheric pressure. In an open manometer, the gas pressure is working against atmospheric pressure. • Assume the atmospheric pressure is 760 mm Hg.

  24. Measurements: basic to all sciences & all are comparisons to a standard • English – still used in US • Metric – devised in the late 1700’s in France • SI – Le Système Internationale d’Unités • Modern metric system (1960) • Based on 7 base units • Base units are modified by prefixes

  25. SI Base Units meter (m) • Length • Mass (SI standard unit) • Time • Temperature • Amount of a substance mole (mol) • Electric current ampere (A) • Luminous intensity candela (cd) kilogram (kg) second (s) Kelvin (K)

  26. Metric Conversion

  27. Derived Units • Area: 2-D • L x W (m2) • Volume: 3-D • Solid - L x W x H (m3) • Liquid or irregular shaped object - graduated cylinder (L or cm3) • Density • mass/volume (kg/m3)

  28. The Liter • The liter is 1000 mL • 10cm x 10cm x 10cm • 1 liter= 1000 cm3 = 1 dm3 • 1 milliliter = 1 cm3 = 1 cc = 20 drops =

  29. Length Relationships

  30. Conversions between units • Factor-label method or dimensional analysis – based on using unit equalities _____ km = _____ m 1 km OR 1000 m 1000 m 1 km 60 s = 1 min 60 s OR 1 min 1 min 60 s 1 1000

  31. V. Tools for Analysis • Organize data into tables • Ascending values for independent variable • Present data in a graph • Independent variable is graphed on the x-axis • Dependent variable is graphed on the y-axis • Best-fit line or curve • Used to see a relationship • Develop a relationship from the graph • Direct • Indirect or inverse • Develop an equation to relate the variables

  32. The characteristic plot for a Direct Relationship is a straight line graph. • Indirect Relationship • The characteristic plot for an Inverse Relationship is a curve of the type illustrated here. As one of the variables increases, the other decreases. Note: It is not a straight line sloping downward.

  33. Examples • Determine the density of aluminum from the analysis of data from 5 samples. • 54.0-g sample has a volume of 20.0 mL • 14.0-g sample has a volume of 5.0 mL • 41.0-g sample has a volume of 15.0 mL • 27.0-g sample has a volume of 10.0 mL • 19.0-g sample has a volume of 7.0 mL HINT: Graph the data with volume as the independent variable. Find the slope of the line! • Convert the density of benzene, 0.8787 g/cm3, to kg/m3. • Calculate the density of mercury if 1.00 x 102 g occupies a volume of 7.36 cm3.

  34. Density Graph BACK

  35. Specific Heat • Amount of energy required to raise the temperature of 1 g of substance by 1°C or 1K. q = mCT q – heat (J) m – mass of substance (g) C – specific heat capacity constant (J/g·°C) - different for every substance T – change in temp (Tf– Ti) (°C) Specific heat capacities of substances in reference packet.

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