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Measurements

Learn about qualitative and quantitative data in chemistry, the SI units system, density calculations, temperature conversions, precision, accuracy, and the significance of significant figures and significant figures rules. Practice problems and calculations included.

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Measurements

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  1. Measurements Measuring in Chemistry

  2. Qualitative or Quantitative? • Qualitative data describes the physical properties of matter in terms of a description, not a measurement. • Ex. Red ball, blue balloon • Quantitative data describes the physical properties of matter in terms of a measured or counted quantity • Ex. 25 eggs, 35.2 grams

  3. Measuring • Measurement is determining the size or magnitude of something using a device or accepted value. All measurements have • magnitude, • Units, and • Uncertainty

  4. Counting Numbers • Counting is never uncertain unless you estimate a very large number- counting is not a measurement • Exact numbers are obtained by counting or definition

  5. SI Units • Scientists have developed a system of standardizing units of measurement. • Systeme Internationale or SI

  6. SI Units

  7. Derived Units • Derived Units are those units that come from combining 2 or more SI units. • Volume is length x 3 and so is m3 • Density is mass per volume or kg / m3 • Energy is Joule or kg  m2 / s2

  8. Density • Density is a derived unit that describes the ration between both the mass and volume of matter. • D = m / v • What is the density of an object with a mass of 85.6 g and a volume of 17.99 mL? The density of tin is 7.265 g/mL. If a sample of tin has a mass of 13.6 g what is its volume?

  9. Temperature Conversions • In Chemistry, the temperature scale utilized is the Kelvin Scale • K = C + 273.15 • So, 100oC = 373 K

  10. Measurement Devices • devices have a limit on precision • zero a balance or correct for a measuring device • significant digits are part of a valid measurement depending on the divisions

  11. Uncertainty? • All measurements have a certain degree of uncertainty, because of instrument calibration and human bias. • Measurements should be made recording all certain digits plus one estimated digit.

  12. Reading a Volume • Always read the volume of a liquid at the bottom of the meniscus 50 40 30 20 10

  13. Error • Errors in chemistry are classified as systematic (determinate) and random (indeterminate). • Error - the result of a measurement minus a true value of the measure and (physical paramater being quantified by measurement) • Systematic Error – an error that can be identified and is repeated • Random Error – an error that occurs due to irreproducible conditions.

  14. Precision & Accuracy • accuracy is how well a measurement agrees with the true value • poor accuracy means poor equipment or flaw in procedures • relates to a chemical measure, qualitative concept • The error of an observation is the difference between the observation and the actual or true value of the quantity observed.

  15. Precision • precision is how well a measuring device can reproduce a measurement • The term precision is used in describing the agreement of a set of results among themselves. Precision is usually expressed in terms of the deviation of a set of results from the arithmetic mean of the set • devices have a limit on precision; precise measurements that are not accurate indicate an equipment error; zero a balance or correct for a measuring device • poor precision means poor technique

  16. Percentage Error • Percentage error is used to determine how far from the true value • Take the absolute value of the difference in the accepted value and the experimental value divided by the accepted or true value • Put the number into % form; Low % error indicates accuracy • % Error = true value – measured value true value

  17. Significance of Significant Numbers • Why do we need to know about significant numbers, what do they really mean? • When making a quantitative measurement, measure the length, volume, etc. to the closest measurement and estimate the last digit. • All digits in a measurement are significant; as is the estimated digit

  18. Significant Figure Rules • All non-zero numbers are significant. • (1, 2, 3 . . . 9) • All zeros between two non-zero numbers are significant. • 10,001 = 5 significant figures • Zeros that come to the right the decimal are significant ONLY if they follow a sig fig. • 0.000100 = 3 significant figures • Zeros that come before the decimal are significant ONLY if they are between 2 sig figs. • 10,100 = 3 significant figures

  19. Practice Problems 1. 4261 ml 4 sig figs 2. 207.32 g 5 sig figs 3. 0.58 cm 2 sig figs 4. 230 mol 2 sig figs • 5. 3.200 m • 4 sig figs • 0.00691 g/ml • 3 sig figs • 20.0 cm3 • 3 sig figs • 0.04500 kg • 4 sig figs

  20. Calculations • When adding or subtracting measured quantities the answer should contain only as many decimal places as the least number in the problem. • When multiplying or dividing measured quantities the answer should contain only as many significant figures as the least number in the problem

  21. Practice For each problem explain how to properly round the answer. • 5.27 ml + 83.5 ml • 18.362 g / 9.6 ml • 71.548 g – 70.882 g • 21.62 cm x 1.43 cm • 6.725 g / (25.82 ml – 21.4 ml)

  22. Scientific Notation

  23. Scientific Notation • Scientific Notation is a way to express very large or very small numbers. • Scientific notation expresses numbers as a multiple of two factors: a number between 1 and 9; and ten raised to a power, or exponent. • The exponent is the magnitude of the number of places you move the decimal. • When you decrease the exponent, you move the decimal to the left; increase moves to the right.

  24. Convert the following to scientific notation and then count the significant figures: • 1,392,000 g • 0.000 000 028 km • 0.000 000 000 000 050 ms • 472,920,000,000,000,000 mmol

  25. Calculations • Multiplication: add the exponents • (5.0 x 103) x (2.0 x 102) • Division: subtract the exponents • (6.0 x 103) ÷ (2.0 x 102) • Addition/Subtraction: exponents must be the same before you perform the function • (1.50 x 102) + (3.45 x 103)

  26. Chemistry Calculations

  27. Dimensional Analysis • Most calculations in the chemistry classroom will involve dimensional analysis • Dimensional analysis is a mathematical manipulation of variables used to solve for an unknown. • Factor – label method

  28. How do I use it? • We are going to start simple. How many dozen students do I have if I have 21? • Take the given information. This is your known variable. (21 students) • Determine what units your unknown variable will be in; this is what you are solving for. (dozen students) • Determine the relationship between the known variable and the unknown variable (this is called your conversion factor) (1 dozen = 12 students)

  29. Set up the problem • Known x conversion factor = unknown • All units should cancel out. • Your conversion factor is set up by putting the units of the unknown on top and the known on the bottom. • So: If I have 21 students and 12 students = 1 dozen Then 21 students x 1 dozen = 1.75 dozen 12 students

  30. Metric Prefixes • Mega 1,000,000 • Kilo 1,000 • Hecto 100 • Deka 10 • Base 1 • Deci 0.1 • Centi 0.01 • Milli 0.001 • Micro 0.000 001 • Nano 0.000 000 001 • Pico 0.000 000 000 001 There is a factor of 1,000 between these two prefixes Each new unit is a factor of 1,000 less from this point on

  31. Dimensional Analysis and Metric Conversions • Now, you can convert from one metric unit to another using dimensional analysis. • 5 km = ? Meters? • Known: 5 km • Unknown: meters • Conversion factor: 1 km = 1000 m • Problem: 5 km x 1000 m = 5000 m 1 km

  32. Try this one • How many feet are there in ½ a mile if 5,280 feet = 1mile? • A. 10,560 feet • B. 1,320 feet • C. 2,640 feet • D. 3,000 feet

  33. Here’s a trick . . . • When converting between metric units, the larger unit is 1

  34. Multiple Variables • Dimensional analysis can be used to convert multiple variables. • You will have more than one conversion factor. • Ex. How many seconds are there in an hour? • 60 sec = 1 minute • 60 minutes = 1 hour • So,

  35. Try this one • In Europe gasoline is sold by the liter. Assume that it takes 14 gallons of gasoline to fill the tank of a compact car. How many liters of gasoline will it take? • 1 L = 1.057 quarts • 4 quarts = 1 gallon

  36. Solve These • Convert your distance from school to home from miles to cm. • How many kilometers is it from your house to school?   • A person’s weight is 154 pounds. Convert this to kilograms. (1 lbs. = 454 grams) • An aspirin tablet contains 325 mg of acetaminophen. How many grains is this equivalent to? (1 gram = 15.432 grains)

  37. And now, these • Each liter of air has a mass of 1.80 grams. How many liters of air are contained in 2.5 x103 kg of air? • 16.0 grams of food contain 130 calories. How many grams of food would you need in order to consume 2150 calories? • The cost of 1.00 Liters of gas is 26.9 cents. How many dollars will 12.0 gallons cost? •   Light travels 186 000 miles / second. How long is a light year in meters? (1 light year is the distance light travels in one year)

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