Chapter 2: Chemistry and Measurements

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33 Terms

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International System of Units (SI)

Chemists use metric system and the International System of Units (SI), for measurement when they:

  • measure quantities

  • do experiments

  • solve problems

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Volume

The space occupied by a substance

  • is measured using units of m³ in the SI system

  • is commonly measured in liters (L) and milliliters (mL) by chemists

  • is measured using a graduated cylinder in units of milliliters (mL)

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Length

Measured in:

  • units of meters (m) in both the metric and SI systems

  • units of centimeters (cm) by chemists

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Mass

The mass of an object, a measure of the quantity of material it contains,

  • is measured on an electronic balance

  • has the SI unit of kilogram (kg)

  • is often measured by chemists in grams (g)

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Temperature

Temperature, a measure of how hot or cold an object feels,

  • is measured on the Celsius (°C) scale in the metric system

  • is measured on the Kelvin (K) scale in the SI system

  • is 18°Celsius or 64 °Fahrenheit on this thermometer

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Time

Time is based on an atomic clock and is measured in units of seconds (s) in both the metric and SI systems

Useful relationships between units of mass include:

  • 1 day = 24 hour

  • 1 hour = 60 minutes

  • 1 minute = 60 s

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Measuring Tool

Used to determine a quantity such as the length or the mass of an object

  • Provides numbers for a measurement called measured numbers

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Reporting Length

To report the length of an object,

  • observe the numerical values of the marked lines at the end of the object

  • estimate the last digit by visually dividing the space between the smallest marked lines

This estimated # is the final digit that is reported for a measured number

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Reporting Length Example

Reporting Length: 4.55 cm

  • The metric ruler is marked at every 0.1 centimeter

  • You can now estimate that the length is halfway between the 4.5-cm and 4.6-cm marks and report the value as 4.55 cm

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Significant Figures

In a measured number, the significant figures (SFs) are all the digits, including the estimated digit

  • All nonzero numbers are counted as significant figures

  • Zeros may or may not be significant, depending on the position in the number

<p>In a measured number,<strong> the significant figures (SFs) </strong>are all the digits, including the estimated digit</p><ul><li><p>All nonzero numbers are counted as significant figures</p></li><li><p>Zeros may or may not be significant, depending on the position in the number</p></li></ul>
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Exact Numbers

  • Numbers obtained by counting items

  • Definitions that compare two units in the same measuring system

<ul><li><p>Numbers obtained by counting items</p></li><li><p>Definitions that compare two units in the same measuring system </p></li></ul>
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Calculated Answers

In calculations,

  • Answers must have the same number of significant figures as the measured numbers

  • Calculator answers must often be rounded off

  • Rounding rules are used to obtain the correct number of significant figures

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Rules for Rounding Off

1) If the first digit to be dropped is 4 or less, then it and all following digits are simply dropped from the number

2) If the first digit to be dropped is 5 or greater, then the last retained digit is increased by 1

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Rounding Off Calculated Answers

Rounding Off Calculated Answers:

  • When the first digit dropped is 4 or less, The retained numbers remain the same

    • To round 45.832 to 3 significant figures drop the digits 32 = 45.8

  • When the first digit dropped is 5 or greater, the last retained digit is increased by 1

    • To round 2.4884 to 2 significant figures drop the digits 884 = 2.5 (increase by 0.1)

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Calculations with Measured Numbers

In calculations with measured numbers, significant figures or decimal places are counted to determine the number of figures in the final answer

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Multiplication and Division with Measured Numbers

In multiplication and division, the final answer is written to have the same number of significant figures (SFs) as the measurement with the fewest SFs

2.8 (Two SFs) * 67.40 (Four SFs) / 34.8 (Three SFs) = 5.422988506 (Calculator display) = 5.4 (Answer, rounded off to two SFs)

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Addition and Subtraction with Measured Numbers

In addition and subtraction, the final answer is written so that it has the same number of decimal places as the measurement having the fewest decimal places

2.045 (Thousandths place) + 34.1 (Tenths place, fewer decimal places) = 36.745 (Calculator display) = 36.1 (Answer, rounded off to the tenths place)

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Prefixes

In the metric and SI systems of units, a prefix attached to any unit increases or decreases its size by some factor of 10.

  • The relationship of a prefix to a unit can be expressed by replacing the prefix with its numerical value.

    • 1 kilometer (1 km) = 1000 meters

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Metric and SI Prefixes

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Measuring Length: Equalities

An equality shows the relationship between two units that measure the same quantity

For example, 1 meter is the same length as 100 centimeter or 1000 millimeter. The equality is written as:

  • P T G M k h da B d c m u n p f

    • P: Peta-

    • T: Tera-
      G: Giga-

    • M: Mega-

    • k: Kilo-

    • h: Hecto-

    • da: Deca-

    • B: BASE UNITS (meter, liter, gram, second, degree (Celsius)

    • d: Deci-

    • c: Centi-

    • m: Milli-

    • u: Micro-

    • n: Nano-

    • p: Pico-

    • f: Femto-

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Measuring Volume

The cubic centimeter (cm³ or cc) is the volume of a cube with the dimensions:

  • 1cm x 1cm x 1cm

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Measuring Mass: Equalities

Equalities can be written for mass in the metric (SI) system

  • When metric equalities are used, 1 gram is the same mass as 1000 milligram and 0.001 kilogram

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Writing Conversion Factors

Equalities:

  • use different units to describe the same quantity

  • can be between units of the metric system, between U.S. units, or between metric and U.S. units

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Exact and Measured Numbers in Equalities

Equalities between units of:

  • The same system are definitions and use exact numbers

  • Different systems (metric and U.S.) use measured numbers and count as significant figures

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Conversion Factors from a Percent, ppm (parts per million) and ppb (parts per billion)

A percent (%) is written as a conversion factor by choosing a unit and expressing the numerical relationship of the parts of this unit to 100 parts of the whole

  • For example, a person has 18% body fat by mass

  • Equality: 18 mass units of fat per 100 mass units of body mass

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Problem-Solving Process

The problem-solving process begins by analyzing the problem in order to:

  • identify the given unit and needed unit

  • write a plan that converts the given unit to the needed unit

  • identify one or more conversion factors that cancel units and provide the needed unit

  • set up a calculation

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Density

Density:

  • compares the mass of an object to its volume

  • is the mass of a substance divided by its volume

<p><strong>Density:</strong></p><ul><li><p>compares the mass of an object to its volume</p></li><li><p>is the mass of a substance divided by its volume</p></li></ul>
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Sample Problem - Calculating Density: A 0.258-gram sample of high-density lipoprotein (HDL) has a volume of 0.215cm³. What is the density of the HDL sample?

Step 1) State the given and needed quantities

Given:

  • 0.258g of HDL

  • 0.215mL

Need:

  • Density (g/mL) of HDL

Connect:

  • Density expression

2) Write the density expression

D = M/V

3) Express mass in grams and volume in milliliters

  • Mass of HDL sample = 0.258 g

  • Volume of HDL sample = 0.215 mL

4) Substitute mass and volume into the density expression and calculate the density

D = 0.258g/0.215mL = 1.20g/1mL = 1.20g/mL

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Sample Problem - Density of Solids in Water: What is the density (g/cm³) of 48.0 g of a metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?

1) State the given and needed qualities

Given:

  • 48.0g

  • Volume of water = 25.0mL

  • Volume of water + metal = 33.0mL

Need:

  • Density (g/mL)

2) Plan out your calculations

  • Calculate the volume difference. Change to cm³, and place in density expression.

    • 33.0mL - 25.0mL = 8.0mL

    • 8.0mL * 1cm³/1mL = 8.0cm³

3) Set up the problem

Density = 48.0g/8.0cm³ = 6.0g/1cm³ = 6.0g/cm³

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Sink or Float?

In water,

  • Ice floats because the density of ice is less than the density of water

  • Aluminum sinks because its density is greater than the density of water.

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Density as a Conversion Factor

Density can be written as an equality:

  • For a substance with a density of 3.8g/mL, the equality is:

    • 3.8g = 1mL

  • From this equality, two conversion factors can be written for density:

    • Conversion factors: 3.8g/1mL and 1mL/3.8g

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Sample Problem - Using Density as a Conversion Factor: Greg has a blood volume of 5.9 qt. If the density of blood is 1.06 gram/mL, what is the mass, in grams, of Greg’s blood?

Step 1) State the given and needed quantities

Given:

  • 5.9qt of blood

Need:

  • grams of blood

Connect:

  • U.S. - metric conversion factor

  • Density conversion factor

Step 2) Write a plan to calculate the needed quantity

quarts (U.S.-metric factor) milliliters > (Density factor) grams

Step 3) Write the equalities and their conversion factors including density

1qt = 946.4mL

946.4mL/1qt and 1qt/946.4mL

1mL of blood = 1.06g of blood

1.06g blood/1mL blood and 1mL blood/1.06g blood

Step 4) Set up the problem to calculate the needed quantity

5.9qt blood (Two SFs) x 946.4mL (Four SFs)/1qt (Exact) x 1.06g blood (Three SFs)/1mL blood (Exact) = 5900g of blood (Two SFs)

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Specific Gravity (s p g r)

Relationship between the density of a substance and the density of water - compares the density of a substance to the density of water

  • Calculated by dividing the density of a sample by the density of water, which is 1.00 gram/milliLiter at 4 °Celsius

  • Example: A substance with a specific gravity of 1.00 has the same density as water (1.00 gram/milliLiter)