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Name ___KEY______Period ____

CRHS Academic Chemistry

Unit 2 - Measurement and Calculations

Notes

Key Dates

Quiz Date ______Exam Date ______

LAB Dates ______

Notes, Homework,Exam Reviews and Their KEYS located on CRHS Academic Chemistry Website:

2.1 CONVERSION FACTORS, DIMENSIONAL ANALYSIS, AND UNITS OF MEASURE

Conversion Factors – A common practice in chemistry is to utilize conversion factors to convert from one unit to another. Conversion factors are derived from equalities and therefore conversion factors are equal to 1.

Example of common equalities and common conversion factors:

Equality / Conversion Factor (h to days) / Conversion Factor (day to h)
1 day = 24 h / /
Equality / Conversion Factor (min to h) / Conversion Factor (h to min)
1 h = 60 min / /
Equality / Conversion Factor (s to min) / Conversion Factor (min to s)
1 min = 60 s / /

Using conversion factors – The conversion factors are equal to one and you can use these ratios to convert a number from one unit to another by simply multiplying by the appropriate conversion factor. The process of keeping track of the units as you multiply by conversion factors is called Dimensional Analysis.

Example: Convert 2.4 days to hours.

You can also multiply a series of conversion factors together to complete a sequence of conversions. These conversions could be done one at time, but it is much easier to complete the series. Take caution to use Dimensional Analysis to insure correct units are obtained.

Example: Convert 2.4 days to seconds

Practice: How many inches are in 2.5 miles? ( 1 mile = 1760 yards)

UNITS OF MEASURE IN CHEMISTRY

For the most part, the METRIC system will be used in this course.

The Standard International (SI) units for length, mass, and volume are shown below. These units are recognized globally in the scientific community. The metric system is based on the decimal system, i.e. multiples of 10, which makes it easy to carry out math and calculations, compared to the English units for weight (pound & ounces) or length (inches & feet& miles).

Prefixes for Metric System

kilo (k) – 1000 times greater

hector (h) – 100 times greater

deca (da) – 10 times greater

Length  Meter (m)

Mass  Gram (g)

Volume  Liter (L)

deci (d) – 10 time smaller

centi (c) – 100 times smaller

milli (m) – 1000 times smaller

Metric Conversion Factors Used in Chemistry

1 km = 1000 m1 kg = 1000 g1 L = 1000 mL

1 m = 100 cm1 g = 1000 mg

1 m = 1000 mm

Practice:

1. Convert 25.5 g to kg2. Convert 3.56 kg to mg

3. 0.052 km = ______cm4. 38129 mL = ______L

5. If 1.00 lb = 454 g and 1000 g = 1 kg, then how many kg is 2000 lb?

2.2 SIGNIFICANT FIGURES

Significant figures are the digits in a measurement that you can prove are true on a measuring device plus one unknown, or uncertain digit that you estimate.

  • When any measurement falls BETWEEN 2 lines on a measuring device,
  • then you WILL estimate the final digit. This is the doubtful digit.
  • When a measurement falls on a line, your doubtful digit is zero (in the
  • graphic, 43.0 mL).

For example, a ruler:

measurement is 3.7 cm. We are certain of the first digit, the “3”, but we are not certain of the second digit, estimate the “.7”. Therefore the ”.7” is our doubtful digit.

Given a measurement, we can COUNT how many significant figures are present in that number. This is important, because in science, our work is only as good as our measurements.

How to determine number of significant figures in a measurement. (ADD HANDS NMOMINC)

Determine if the decimal is Absent or Present.

Decimal is Absent (Atlantic) - From RIGHT of the number (the Atlantic side), find the first non-zero digit and count Right to Left until you reach the end of the number.

Ex: 6050  __3__ sig figsEx: 6051  __4____ sig figs

Decimal is Absent (Pacific) -From LEFT of the number (the Pacific side), find the first non-zero digit and count Left to Right until you reach the end of the number.

Ex: 700.70  __5__ sig figsEx: 0.0070  __2___ sig figs

Practice – How many significant figures

65000  __2___
0.00005  __1__
1.0040  __5___
0.00341  __3__ / 40300  ___3__
200300  __4___
5.300  __4___
870  ___2___ / 37.76  __4___
0.61  ___2__
600.0  ___4__
0.1707  __4___

Adding/Subtracting – arrange numbers in a ______. Line up the ______. Omit any digits to the right of a column that contains a doubtful digit (think place value). Units must match!

Practice: 2.43 cm

+ 21.1 cm

23.53 - 23.5 cm

27.789 m

+ 6.1 m

33.889  33.9 m

87 mL + 11.87 mL = 98.87 mL  99 mL

Multiplying/Dividing – the number of sigfigs in your product or quotient is the same as the number in the operation with the ___least__ sigfigs. When using a calculator, round to the sigfig needed. Units must stay in the place they are located in the operation!

Practice:5.12 m x 223 m = 1141.76  1140 m2

4.750 g x 2.00 g = 9.5  9.50 g2

2.483 m  0.52 s = 4.775  4.8 m/s

Combining Operations – First, observe the “order of operations” (_PEMDAS______) when considering sigfigs. For each step, you must determine sigfigs, then use that result in the next step of the operation. Keep track of the units.

Practice:(2.3 cm + 4.37 cm) x 38.2 cm = _254.79 cm2  250 cm2____

(2 Sig Fig’s !) Final answer can only be 2 sig figs

62.2 kg  2.0 kg + 47.3 kg = 31.1 + 47.3 = 78.4  78 kg______

Note:

PEMDAS – perform operations in this order.

  1. Parenthesis
  2. Exponent
  3. Multiply
  4. Divide
  5. Add
  6. Subtract

2.3 SCIENTIFIC NOTATION

Scientific notation is used to express very large and very small numbers. Often in science we measure and count extremely small and large numbers. Scientific notation makes our work easier (promise!).

*The number of sig figs does not change when converting to or from scientific notation.

General formula:

  • The coefficient (number in front) is always between 1 and 10.
  • For very large numbers (greater than 10), n is positive.
  • For very small numbers (less than 1), n is negative.

To convert TO scientific notation from ordinary notation:

  1. Move the decimal point one digit at a time so the coefficient is between 1 and 10.
  2. Count how many places you moved the decimal point.
  3. This will be the exponent, or n.
  4. For large numbers, n is positive
  5. For small numbers, n is negative.

Practice:

91.4 m = 9.14 x 101 m0.000 000 000 154 m = 1.54x10-10 m

6,378,000 m = 6.378 x 106 m34,071,000 m = 3.4071 x 10-7 m

To convert FROM scientific notation to ordinary notation, move the decimal point the number of places signified by the exponent n.

  1. For a positive n, move the decimal to the right to make the number large.
  2. For a negative n, move the decimal to the left to make the number smaller.
  3. No decimal present = an implied decimal after the ones place.

Term - Ordinary notation – a method of expressing numerical values in which the entire number is expressed in the notation.

Practice Conversions:

4 x 107 m = 40,000,000 m2 x 10-3 m = 0.002 m

1.8 x 103 m = 1800 m3.499 x 104 m = 34990 m

0.670005 cm = 6.70005 x 10-1 cm31,580,000 s = 3.158 x 107 s

0.0000018 km = 1.8 x 10-6 km7.8 x 10 5 mm = 780,000 mm

Practice Math Problems with Scientific Notation:

(2.43 x 104) x (4.43 x 105) = 1.08 x 1010251 x (6.5 x10-5) = 1.6 x 10-2 or 0.016

0.0023 x (3 x 107) /( 4.3 x 1013) = 1.6 x 10-9(6.02x10-23) /[ (2.3 x 1016) x (4.3 x 1015)] = 6.1 x 10-55

How many lithium (Li) atoms in 25.0 g of Li? (1.00 mol Li = 6.02x1023 Li atoms & 1 mol Li = 6.94 g Li)

2.4 ACCURACY AND PRECISION AND QUALITATIVE VS. QUANTITATIVE DATA

Accuracy describes how close a measurement is to the known or “true” value of the object measured.

Precision is both:

  • the number of significant figures in a measurement, where more digits is more precision, and;
  • the repeatability of the measurement

A measurement system that is both accurate and precise is considered valid.

Example: Jennie massed an object known to have a mass of 100.0 g. She measured the object three times with the same device: 175.6 g, 175.3 g, and 175.8 g. Were her measurements accurate? Precise?

Explain.______Precise because correct number of sig figs and repeatable, but not accurate ______

____________

Practice:

Is this an accurate measurement? _NO_ Why or why not? “4” is the doubtful digit in first measurement, so it wasn’t accurate to 2nd decimal place______

Is this a precise measurement? _NO__ Why or why not? “4” is the doubtful digit in first measurement, so it wasn’t precise to 2nd decimal place______

Is this an accurate measurement? _Yes_ Why or why not? The diiference is within the doubtful digit______

Is this a precise measurement? __No_ Why or why not? ____1st measurement did not have enough significant figures to allow average to be classified as precise______

QUALITATIVE vs. QUANTITATIVE DATA

Qualitative data is descriptive and non-numerical. (Examples: color and phase of matter).

Quantitative data gives results in a definite form, usually in numerical form with units. (Examples: length and mass)

Practice: Describe the following as Qualitative or Quantitative

Mass _____Quantitative______Rough _____ Qualitative ______

Color _____Qualitative______Volume ____ Quantitative ______

Length _____ Quantitative ______Turbulent ____ Qualitative ______

Smooth ____ Qualitative ______Radius ______Quantitative ______

Temperature _ Quantitative _____Hazy ______Qualitative ______

Time ____ Quantitative ______Soft ______Qualitative ______