Stoichiometry Introduction: Matter and Measurement

Stoichiometry

Introduction:Matter and Measurement

Stoichiometry

Units of Measurement

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SI Units

• Système International d’Unités• Uses a different base unit for each quantity

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Metric System

Prefixes convert the base units into units that are appropriate for the item being measured.

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THE METRIC SYSTEM

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WHY DO WE USE THE METRIC SYSTEM?

• Almost all other countries are using the metric system

• Other countries’ companies are refusing to buy products from the U.S. if not labeled in metric units

• Scientists need a universal way to communicate data (SI Units)

Stoichiometry

APPROXIMATE CONVERSIONS BETWEEN METRIC & US LENGTH UNITS

• A meter is about the same length as a yard

• A meter is about three feet long• A decimeter is about four inches long• An inch is about 25 millimeters• A foot contains about 30 centimeters• A foot contains about 3 decimeters

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WHAT DOES THE METRIC SYSTEM MEASURE?

• The gram measures mass or how much something weighs

• The liter measures volume which is used when measuring liquids

• The meter measures the length of an object or the distance from place to place

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THE METRIC CONVERSION CHART (STAIRCASE METHOD)

Kilo1000units

Hecto100units

Deka10

unitsBasic Unit Deci

0.1units

Centi0.01units

Milli0.001units

To convert to a smaller unit, movedecimal point to the right or

multiply.

To convert to a larger unit, movedecimal point to the left or divide

Stoichiometry

TRY THIS USING THE STAIRCASE METHOD

1000 mg = ______ g

Step 1: Determine if you are going to go up or down the ladder.Step 2: Determine how many steps there are from milligrams to grams.Step 3: Move the decimal point the amount of places that was determined in steps 1 & 2.

Stoichiometry

TRY THIS USING THE STAIRCASE METHOD

1000 mg = ______ g

Step 1: Determine if you are going to go up or down the ladder.Step 2: Determine how many steps there are from milligrams to grams.Step 3: Move the decimal point the amount of places that was determined in steps 1 & 2.

1

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TRY THIS USING THE STAIRCASE METHOD

.15 L = __________ ml

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TRY THIS USING THE STAIRCASE METHOD

.15 L = __________ ml150

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Volume

• The most commonly used metric units for volume are the liter (L) and the milliliter (mL).□ A liter is a cube 1 dm

long on each side.□ A milliliter is a cube 1 cm

long on each side.

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Uncertainty in Measurements

Different measuring devices have different uses and different degrees of accuracy.

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Temperature:

A measure of the average kinetic energy of the particles in a sample.

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Temperature

• In scientific measurements, the Celsius and Kelvin scales are most often used.

• The Celsius scale is based on the properties of water.□ 0C is the freezing point

of water.□ 100C is the boiling

point of water.

Stoichiometry

Temperature

• The Kelvin is the SI unit of temperature.

• It is based on the properties of gases.

• There are no negative Kelvin temperatures.

• K = C + 273.15

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Temperature

• The Fahrenheit scale is not used in scientific measurements.

• F = 9/5(C) + 32• C = 5/9(F − 32)

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A Standard Measurement System

The Metric System

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When and why was the metric system invented?

• The metric system was invented in 1790

• The metric system was invented because countries were using many different systems of measurement causing confusion and lack of consistency

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Who invented the metric system?

• The metric system was invented by a group of French scientists

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Metric System

• A system of measurement used by the majority of countries on Earth based on the number 10

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A Standard Measurement System

The International System of Units (SI)

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Scientists all over the world use the International System of Units to measure:

• Length• Volume• Mass• Density• Temperature• Time

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Figure 1: Calculating - How much larger is a kilo- than a deka-?

• 100 times

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Reading Checkpoint (page 45): SI units are based on multiples of what

number?

• SI units are based on multiples of 10

• Add a zero• Subtract a zero

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Key Concept: Why do scientists use a

standard measurement system?

• Using SI as the standard system of measurement allows scientists to compare data and communicate with each other about their results

• Using SI measurement also allows experiments to be repeated and most importantly achieve a desired result

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Length

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What is length?

• Length is the distance from one point to another

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Length

Units of Length

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The basic unit of length in the SI system is the …

• The basic unit of length in the SI system is the meter

Stoichiometry

The two units that measure the length of smaller objects are, …

• millimeter

• centimeter

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Complete the Table Below

Prefix Meaning Unit of Length

milli

one-hundredth

meter

one-thousand

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Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

one-hundredth

meter

one-thousand

Stoichiometry

Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

millimeter

one-hundredth

meter

one-thousand

Stoichiometry

Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

millimeter

centi one-hundredth

meter

one-thousand

Stoichiometry

Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

millimeter

centi one-hundredth centimeter

meter

one-thousand

Stoichiometry

Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

millimeter

centi one-hundredth centimeter

none meter

one-thousand

Stoichiometry

Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

millimeter

centi one-hundredth centimeter

none one meter

one-thousand

Stoichiometry

Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

millimeter

centi one-hundredth centimeter

none one meter

kilo one-thousand

Stoichiometry

Complete the Table Below

Prefix Meaning Unit of Length

milli One-thousandth

millimeter

centi one-hundredth centimeter

none one meter

kilo one-thousand kilometer

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Length

Measuring Length

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The longer lines on the metric ruler are called…

• centimeters

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The shorter lines on the metric ruler are called…

• millimeters

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Checkpoint One centimeter is divided into how many millimeters?

• 10 millimeters (mm)

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Figure 2: Calculating: Measure the turtle in figure 2 from the rear of its shell to the tip of its nose. Record its length in both centimeters and

millimeters.

• 10.5 cm

• 105 mm

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Density

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Density

• The measure of how much mass is contained in a given volume

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The formula of density is:

Density = Mass / Volume

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Figure 5: Comparing Densities - Inferring: Which item has the greater density?

• The bowling ball• Since the bowling

bowl has a greater mass, it has a greater density, even though both balls have the same volume

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Density

Units of Density

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Why is density expressed as a combination of two different units?

• Because density is actually made up of two other measurements – mass and volume – an objects density is expressed as a combination of two units

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Two Common Units For Density

• Grams per cubic centimeter (g/cm³)

• Grams per milliliter (g/mL)

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Math Practice: What is the density of a wood block with a volume of 125 cm³ and a mass of 57 g?

Density = mass / volume

Density = 57 g / 125 cm³

Density = 0.46 g/ cm³

Stoichiometry

Math Practice: What is the density of a liquid with a mass of 45 g and a volume of 48 mL?

Density = mass / volume

Density = 45 g / 48 mL

Density = 0.94 g/mL

Stoichiometry

Density

Densities of Common Substances

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The density of a substance is the ______for all samples of that substance.

• Same

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An object will float if it is _____ _____ than a surrounding liquid.

• Less dense

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Figure 6: Applying Concepts: How could you use density to determine whether a bar of metal is pure gold?

• If the bar of gold has a density that is greater than or less than 19.3 g/cm³, then the sample is not pure gold.

Densities of Some Common

SubstancesSubstanc

eDensity(g/cm³)

Air 0.001Ice 0.9

Water 1.0Aluminum 2.7

Gold 19.3

Stoichiometry

Checkpoint Will an object with a density of 0.7 g/cm³ float or sink in water?

• An object that has a density of 0.7 g/cm³ will float in water (1 g/cm³) because it is less dense than water

Stoichiometry

Density:

Physical property of a substance

d=mV

Stoichiometry

Time

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Time

Units of Time

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What is the SI unit used to measure time?

• The second(s) is the SI unit to measure time

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Common Conversions for Time

1s =

= 60 s

1h =

Stoichiometry

Common Conversions for Time

1s = 1,000 ms

= 60 s

1h =

Stoichiometry

Common Conversions for Time

1s = 1,000 ms

1 min = 60 s

1h =

Stoichiometry

Common Conversions for Time

1s = 1,000 ms

1 min = 60 s

1h = 60 min

Stoichiometry

Time

Measuring Time

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Why would a stop watch be used to measure time in an important race?

• Because stop watches measure in units smaller than the second

• These measurements include the tenth and hundredth of a second

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Checkpoint

- How many milliseconds are in one second?

• 1,000 milliseconds

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Temperature

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Temperature

Units of Temperature

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A common unit to measure temperature is the ___ ___.

• Celsius scale

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Water freezes at ______ and boils at ______.

• 0 °C• 100 °C

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The normal human body temperature is approximately ________.

• 37 °C

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What is the official SI unit for temperature?

• The Kelvin Scale (°K)

• 0 °K = -273 °C

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Figure 8: Measuring Temperature - Observing: At what temperature on the Kelvin scale does water boil?

• 373 °K

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What is absolute zero?

• Absolute zero is considered by scientists to be the coldest temperature possible

• 0 °K or –273 °C

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Temperature

Measuring Temperature

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What instrument is used to measure temperature?

• Thermometer

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Volume

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Volume

• The amount of space an object takes up

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Volume

Volume of Liquids

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When measuring the volume of a liquid, scientists use a unit known as the…

• Liter (L).

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To measure the volume of smaller liquids, the _________ is used.

• Milliliter (mL)

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The instrument used to measure the volume of liquids is called the…

• Graduated cylinder.

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This instrument has markings that are in increments of…

• 1 milliliter (mL)

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Meniscus

• The curve in the top surface of water in the graduated cylinder

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Figure 4: Observing - What is the proper way to read a meniscus?

• Read the milliliter marking at the bottom of the curve

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Volume

Volume of Rectangular Solids

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Common Conversions For Volume

1 L =

= 1,000 cm³

1 mL =

Stoichiometry

Common Conversions For Volume

1 L = 1,000 mL

= 1,000 cm³

1 mL =

Stoichiometry

Common Conversions For Volume

1 L = 1,000 mL

1 L = 1,000 cm³

1 mL =

Stoichiometry

Common Conversions For Volume

1 L = 1,000 mL

1 L = 1,000 cm³

1 mL = 1 cm³

Stoichiometry

How can the volume of a solid object such as a shoebox be measured?

• To measure a solid objects that are regular shaped, a formula for volume can be applied

• To measure a rectangular object such as a shoebox, multiply the object’s length, width, and height

Stoichiometry

The SI unit known for measuring solids with a larger volume is known as the…

• Cubic meter (m³).

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The formula for calculating the volume of a rectangular object is:

Volume = Length x Width x Height

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Why is the unit cm³ used when calculating the volume of a rectangular object?

• When multiplying the object’s length, width and height, the cm units are also multiplied

cm x cm x cm = cm³

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Suppose a cereal box is 10 centimeters long, 4 centimeters wide, and 20 centimeters high. What would be the volume of the box?

Volume = Length x Width x Height

Volume = 10 cm x 4 cm x 20 cm

Volume = 800 cm³

Stoichiometry

Checkpoint What is a cubic meter?

• The SI unit used to measure solids with a larger volume

• A cubic meter is equal to the volume of a cube that measures 1 meter on each side

Stoichiometry

Volume

Volume of Irregular Solids

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How is the volume of an irregular solid such as a rock measured?

• To measure the volume of an irregular solid, immerse the object in water, and measure how much the water level rises

• Water displacement method

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How does the water displacement method work?

• Record the volume of water in the graduated cylinder

• Carefully place the irregular solid into the water. Record the volume of the water plus the object

• Subtract the volume of the water alone from the volume of the water plus the object

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Uncertainty in Measurement

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Significant Figures

• The term significant figures refers to digits that were measured.

• When rounding calculated numbers, we pay attention to significant figures so we do not overstate the accuracy of our answers.

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Significant Figures

1. All nonzero digits are significant.

2. Zeroes between two significant figures are themselves significant.

3. Zeroes at the beginning of a number are never significant.

4. Zeroes at the end of a number are significant if a decimal point is written in the number.

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Significant Figures

• When addition or subtraction is performed, answers are rounded to the least significant decimal place.

• When multiplication or division is performed, answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.

Stoichiometry

Relating Significant Figures to the Uncertainty of aMeasurement

What difference exists between the measured values 4.0 g and 4.00 g?

Solution Many people would say there is no difference, but a scientist would note the difference in the number of significant figures in the two measurements. The value 4.0 has two significant figures, while 4.00 has three. This difference implies that the first measurement has more uncertainty. A mass of 4.0 g indicates that the uncertainty is in the first decimal place of the measurement. Thus, the mass might be anything between 3.9 and 4.1 g, which we can represent as 4.0 ± 0.1 g. A measurement of 4.00 g implies that the uncertainty is in the second decimal place. Thus, the mass might be anything between 3.99 and 4.01 g, which we can represent as 4.00 ± 0.01 g. Without further information, we cannot be sure whether the difference in uncertainties of the two measurements reflects the precision or accuracy of the measurement.

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Answer: five, as in the measurement 24.995 g

PRACTICE EXERCISE

A balance has a precision of ± 0.001 g. A sample that has a mass of about 25 g is placed on this balance. How many significant figures should be reported for this measurement?

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SAMPLE EXERCISE 1.6 Determining the Number of Significant Figures in a Measurement

How many significant figures are in each of the following numbers (assume that each number is a measured quantity):

(a) 4.003,

(b) 6.023 1023,

(c) 5000?

Four; the zeros are significant figures

Four; the exponential term does not add to the number of significant figures.

One. We assume that the zeros are not significant when there is no decimal point shown. If the number has more significant figures, a decimal point should be employed or the number written in exponential notation. Thus, 5000. has four significant figures, whereas 5.00 103 has three.

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PRACTICE EXERCISEHow many significant figures are in each of the following measurements:

(a) 3.549 g, (b) 23 104 cm, (c) 0.00134 m3?

Answers: 

(c) three

(b) two,

(a) four,

Stoichiometry

Determining the Number of Significant Figures in a Calculated Quantity

The width, length, and height of a small box are 15.5 cm, 27.3 cm, and 5.4 cm, respectively. Calculate the volume of the box, using the correct number of significant figures in your answer.

Solution The volume of a box is determined by the product of its width, length, and height. In reporting the product, we can show only as many significant figures as given in the dimension with the fewest significant figures, that for the height (two significant figures):

When we use a calculator to do this calculation, the display shows 2285.01, which we must round off to two significant figures. Because the resulting number is 2300, it is best reported in exponential notation, 2.3 103, to clearly indicate two significant figures.

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PRACTICE EXERCISEIt takes 10.5 s for a sprinter to run 100.00 m. Calculate the average speed of the sprinter in meters per second, and express the result to the correct number of significant figures.

Answer: 9.52 m/s (3 significant figures)

Stoichiometry

Determining the Number of Significant Figures in a Calculated QuantityA gas at 25°C fills a container whose volume is 1.05 103 cm3. The container plus gas have a mass of 837.6 g. The container, when emptied of all gas, has a mass of 836.2 g. What is the density of the gas at 25°C?

Solution  

To calculate the density, we must know both the mass and the volume of the gas. The mass of the gas is just the difference in the masses of the full and empty container:

(837.6 – 836.2) g = 1.4 g

In subtracting numbers, we determine the number of significant figures in our result by counting decimal places in each quantity. In this case each quantity has one decimal place. Thus, the mass of the gas, 1.4 g, has one decimal place.Using the volume given in the question, 1.05 103 cm3, and the definition of density, we have

In dividing numbers, we determine the number of significant figures in our result by counting the number of significant figures in each quantity. There are two significant figures in our answer, corresponding to the smaller number of significant figures in the two numbers that form the ratio.

Stoichiometry

To how many significant figures should the mass of the container be measured (with and without the gas) in Sample Exercise 1.8 in order for the density to be calculated to three significant figures?

Answer: five (In order for the difference in the two masses to have three significant figures, there must be two decimal places in the masses of the filled and empty containers.)

Stoichiometry

Accuracy versus Precision

• Accuracy refers to the proximity of a measurement to the true value of a quantity.

• Precision refers to the proximity of several measurements to each other.