Measurement, Problem Solving, and the Mole. Measurement - Units Common English-Metric Conversion Factors 2.54 cm = 1 inch 1 lb = 453.6 g 1 qt = 943 mL

Measurement, Measurement, Problem Problem

Solving, and the Solving, and the MoleMole

Measurement - UnitsMeasurement - Units

Common English-Metric Conversion Common English-Metric Conversion FactorsFactors

2.54 cm = 1 inch2.54 cm = 1 inch

1 lb = 453.6 g1 lb = 453.6 g

1 qt = 943 mL1 qt = 943 mL

MeasurementsMeasurements

Prefixes Commonly used in Chemistry:Prefixes Commonly used in Chemistry:prefix nameprefix namesymbolsymbol value value

exponential notationexponential notation

kilo kilo k k 1,000 1,000 101033

centicenti c c 1/100 or .01 1/100 or .01 1010-2-2

millimilli m m 1/1,000 or .001 101/1,000 or .001 10-3-3

micromicro µ µ .000001 .000001 1010-6-6

nanonano n n 1010-9-9

picopico p p 1010-12-12

Measurement - Measurement - TemperatureTemperature

In the chemistry lab, In the chemistry lab, temperature is temperature is measured in degrees measured in degrees Celsius or Celsius or Centigrade. The Centigrade. The temperature in temperature in Kelvins is found by Kelvins is found by adding 273.15 adding 273.15

The Fahrenheit scale The Fahrenheit scale has 180 has 180 ooF/100 F/100 ooC. C. This is reason for the This is reason for the 5/9 or 9/5 in the 5/9 or 9/5 in the conversion formulas.conversion formulas.

Significant FiguresSignificant Figures

When writing a number, the When writing a number, the certainty with which the number is certainty with which the number is known should be reflected in the way known should be reflected in the way it is written.it is written.

Digits which are the result of Digits which are the result of measurement or are known with a measurement or are known with a degree of certainty are called degree of certainty are called significant digits or significant figuressignificant digits or significant figures..


The goal of paying attention to The goal of paying attention to significant figures is to make sure that significant figures is to make sure that every number accurately reflects the every number accurately reflects the degree of certainty or precision to degree of certainty or precision to which it is known.which it is known.

Likewise, when calculations are Likewise, when calculations are performed, the final result should performed, the final result should reflect the same degree of certainty as reflect the same degree of certainty as the the least certainleast certain quantity in the quantity in the calculation. calculation.


If someone says If someone says ““There are There are roughly a hundred students enrolled roughly a hundred students enrolled in the freshman chemistry course,in the freshman chemistry course,”” the enrollment should be written as the enrollment should be written as 100100 or or 1 x 101 x 1022. .

Either notation indicates that Either notation indicates that the number is approximate, with the number is approximate, with only one significant figure.only one significant figure.


If the enrollment is exactly one If the enrollment is exactly one hundred students, the number hundred students, the number should be written with a decimal should be written with a decimal point, as point, as 100.100. , or , or

1.00 x 101.00 x 1022..

Note that in either form, the Note that in either form, the number has three significant figures.number has three significant figures.


The rules for counting significant The rules for counting significant figures:figures:

1. Any non-zero integer is a 1. Any non-zero integer is a significant figure.significant figure.


2. Zeros 2. Zeros maymay be significant, depending be significant, depending upon where they appear in a number.upon where they appear in a number.

a) Leading zeros (one that precede any a) Leading zeros (one that precede any non-zero digits) are non-zero digits) are not significant.not significant.

For example, in 0.02080, the first For example, in 0.02080, the first two zeros are not significant. They only two zeros are not significant. They only serve to place the decimal point.serve to place the decimal point.

Significant Figures – Zeros Significant Figures – Zeros (cont(cont’’d)d)

b) Zeros between non-zero integers are b) Zeros between non-zero integers are always significant.always significant. In the number In the number 0.02080, the zero between the 2 and the 0.02080, the zero between the 2 and the 8 is a significant digit.8 is a significant digit.

c) Zeros at the right end of a number are c) Zeros at the right end of a number are significant only if the number contains a significant only if the number contains a decimal point. In the number 0.02080, decimal point. In the number 0.02080, the last zero is the result of a the last zero is the result of a measurement, and measurement, and is significant.is significant.


Thus, the number 0.02080 has Thus, the number 0.02080 has four significant figures. four significant figures.

If written in scientific notation, If written in scientific notation, all significant digits must appear. all significant digits must appear. So 0.02080 becomes So 0.02080 becomes

2.080 x 102.080 x 10-2-2..


3. Exact numbers have an unlimited 3. Exact numbers have an unlimited number of significant figures. number of significant figures. Examples are 100cm = 1m, the Examples are 100cm = 1m, the ““22”” in in the formula 2the formula 2ππr, or the number of r, or the number of atoms of a given element in the formula atoms of a given element in the formula of a compound, such as the of a compound, such as the ““22”” in H in H22O.O.

Using an exact number in a calculation Using an exact number in a calculation will not limit the number of significant will not limit the number of significant figures in the final result.figures in the final result.

Significant Figures - Significant Figures - CalculationsCalculations

When calculations are performed, When calculations are performed, the final result should reflect the same the final result should reflect the same degree of certainty as the degree of certainty as the least certainleast certain quantity in the calculation.quantity in the calculation.

That is, the least certain quantity That is, the least certain quantity will influence the degree of certainty in will influence the degree of certainty in the final result of the calculation. the final result of the calculation.


There are two sets of rules when There are two sets of rules when performing calculations. One for addition performing calculations. One for addition and subtraction, and the other for and subtraction, and the other for multiplication and division.multiplication and division.

For Multiplication and DivisionFor Multiplication and Division::The result of the calculation should The result of the calculation should

have the same number of significant have the same number of significant figures as the figures as the least preciseleast precise measurement measurement used in the calculation.used in the calculation.


Multiplication & DivisionMultiplication & Division::

Example: Determine the density of Example: Determine the density of an object with a volume of 5.70 cman object with a volume of 5.70 cm33 and a mass of 8.9076 grams.and a mass of 8.9076 grams.


Multiplication & DivisionMultiplication & Division::

Example: Determine the density of Example: Determine the density of an object with a volume of 5.70 cman object with a volume of 5.70 cm33 and a mass of 8.9076 grams.and a mass of 8.9076 grams.

δδ = mass/volume = 8.9076 g/5.70 cm = mass/volume = 8.9076 g/5.70 cm33

δδ = 1.5627368 = 1.56 g/cm = 1.5627368 = 1.56 g/cm33


Addition and SubtractionAddition and Subtraction::

The result has the same number The result has the same number of places after the decimal as the of places after the decimal as the least least preciseprecise measurement in the measurement in the calculation.calculation.

For example, calculate the sum of:For example, calculate the sum of:

10.011g + 5.30g + 9.7093g = 10.011g + 5.30g + 9.7093g = 25.0203 = 25.02g25.0203 = 25.02g

Significant Figures - Significant Figures - MeasurementMeasurement

All measurements involve some degree All measurements involve some degree of uncertainty. When reading a mass of uncertainty. When reading a mass from a digital analytical balance, the from a digital analytical balance, the last digit (usually one-ten thousandth of last digit (usually one-ten thousandth of a gram) is understood to be uncertain.a gram) is understood to be uncertain.

When using other devices in the When using other devices in the laboratory, such as a ruler, graduated laboratory, such as a ruler, graduated cylinder, buret, etc., you should cylinder, buret, etc., you should estimate one place beyondestimate one place beyond the smallest the smallest divisions on the device.divisions on the device.

Significant Figures - Significant Figures - MeasurementsMeasurements

The volume should be The volume should be estimated to the estimated to the nearest hundredth of a nearest hundredth of a milliliter, since the milliliter, since the buret is marked in buret is marked in tenths of a milliliter.tenths of a milliliter.

The correct reading is The correct reading is 20.15 (or 20.14 or 20.15 (or 20.14 or 20.16) mL. It is 20.16) mL. It is understood that the understood that the last number is last number is uncertain.uncertain.

Significant Figures - Significant Figures - MeasurementsMeasurements

The value of 20.15 The value of 20.15 mL indicates a mL indicates a volume in between volume in between 20.1 mL and 20.2 20.1 mL and 20.2 mL. mL.

If the liquid level If the liquid level were resting right on were resting right on one of the divisions, one of the divisions, the reading should the reading should reflect this by ending reflect this by ending in a zero. in a zero.

Conversion of UnitsConversion of Units

Many chemical calculations involve Many chemical calculations involve the conversion of units. An example is the conversion of units. An example is calculating how many grams of a calculating how many grams of a product can be obtained from a given product can be obtained from a given mass of a reactant. The calculation mass of a reactant. The calculation involves going from mass of reactant to involves going from mass of reactant to moles of reactant to moles of product to moles of reactant to moles of product to grams of product. You should write in grams of product. You should write in your units for all calculations, and make your units for all calculations, and make sure they cancel properly.sure they cancel properly.

Metric Conversion Metric Conversion FactorsFactors

These conversion factors are These conversion factors are useful and worth learning.useful and worth learning.

1 inch = 2.54 cm1 inch = 2.54 cm

1 lb = 453.6 g1 lb = 453.6 g

1 L = 1.0567 qt1 L = 1.0567 qt

ProblemProblem

The density of mercury is 13.6 The density of mercury is 13.6 g/mL. What is the weight, in lbs, of g/mL. What is the weight, in lbs, of a quart of mercury?a quart of mercury?

Accuracy & PrecisionAccuracy & Precision

Most experiments are Most experiments are performed several times to help performed several times to help ensure that the results are ensure that the results are meaningful. A single experiment meaningful. A single experiment might provide an erroneous result if might provide an erroneous result if there is an equipment failure or if a there is an equipment failure or if a sample is contaminated. By sample is contaminated. By performing several trials, the results performing several trials, the results may be more reliable.may be more reliable.


If the experimental values are If the experimental values are close to the actual value (if it is known), close to the actual value (if it is known), the data is said to be the data is said to be accurate. accurate.

If the experimental values are all If the experimental values are all very similar and reproducible, the data very similar and reproducible, the data is said to be is said to be preciseprecise..

The goal in making scientific The goal in making scientific measurements is to that the data be measurements is to that the data be both accurate and precise.both accurate and precise.


Data can be precise, but Data can be precise, but inaccurate. If a faulty piece of inaccurate. If a faulty piece of equipment or a contaminated sample is equipment or a contaminated sample is used for all trials, the data may be in used for all trials, the data may be in agreement (precise), but inaccurate. agreement (precise), but inaccurate. Such an error is called a Such an error is called a systematic systematic errorerror. If the scientist has good . If the scientist has good technique, the results will be similar, technique, the results will be similar, but too high or too low due to the but too high or too low due to the systematic error.systematic error.

Random ErrorRandom Error

In many experiments, data varies a bit In many experiments, data varies a bit with each trial. The variation in the with each trial. The variation in the results is due to results is due to random errorrandom error. . Examples might be estimating the last Examples might be estimating the last digit for the volume in a buret. digit for the volume in a buret. Random errors have an equal Random errors have an equal probability of being too high or too low. probability of being too high or too low. As a result, if enough trials are As a result, if enough trials are performed, the random error will performed, the random error will average itself out.average itself out.

MolesMoles Many chemical reactions are carried out Many chemical reactions are carried out

using a few grams of each reactant. using a few grams of each reactant. Such quantities contain huge numbers Such quantities contain huge numbers (on the order of 10(on the order of 102323) of atoms or ) of atoms or molecules.molecules.

A unit of quantity of matter, the A unit of quantity of matter, the molemole, , was established. A mole is defined as was established. A mole is defined as the number of carbon atoms in exactly the number of carbon atoms in exactly 12 grams of 12 grams of 1212C.C.

Avogadro determined the number of Avogadro determined the number of particles (atoms or molecules) in a mole.particles (atoms or molecules) in a mole.

MolesMoles AvogadroAvogadro’’s number = 6.022 x 10s number = 6.022 x 102323 particles/mole particles/mole

Atoms are so small, that a mole of most Atoms are so small, that a mole of most substances can be easily held in ones hand.substances can be easily held in ones hand.

CuAl

Hg Fe

I2

S

MolesMoles

If we consider objects we can see, a If we consider objects we can see, a mole of pennies would cover the mole of pennies would cover the entire planet and be 300 meters entire planet and be 300 meters deep! However, the collection of deep! However, the collection of atoms, called a mole, is very atoms, called a mole, is very convenient in the laboratory (just convenient in the laboratory (just like dozens are useful in buying eggs like dozens are useful in buying eggs or pencils).or pencils).

MolesMoles

A mole of any atom has a mass equal A mole of any atom has a mass equal to the elementto the element’’s atomic mass s atomic mass expressed expressed in gramsin grams..

A mole of iron atoms has a mass of A mole of iron atoms has a mass of 55.85 grams; a mole of iodine 55.85 grams; a mole of iodine moleculesmolecules (I (I22) has a mass of (126.9) ) has a mass of (126.9) (2) = 253.8 grams.(2) = 253.8 grams.

MolesMoles The masses of each molar sample are The masses of each molar sample are

provided below.provided below.Cu = 63.55g Al=26.9

8g

Hg = 200.6 g

Fe=55.85 g

I2=253.8 g

S=32.07g

Molar MassMolar Mass For compounds, once the formula is For compounds, once the formula is

known, the mass of a mole of the known, the mass of a mole of the substance can be calculated by summing substance can be calculated by summing up the masses of all the atoms in the up the masses of all the atoms in the compound. compound. For example, hydrogen peroxide has the For example, hydrogen peroxide has the formula Hformula H22OO22::2H +2O = 2(1.008g) + 2(16.00g) = 34.02 2H +2O = 2(1.008g) + 2(16.00g) = 34.02 g/molg/mol A mole of hydrogen peroxide has a mass A mole of hydrogen peroxide has a mass of 34.02 grams.of 34.02 grams.

ProblemProblem

Determine the number of silver Determine the number of silver atoms in a 10.0 gram sample of atoms in a 10.0 gram sample of silver.silver.

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Measurement, Problem Solving, and the Mole. Measurement - Units Common English-Metric Conversion Factors 2.54 cm = 1 inch 1 lb = 453.6 g 1 qt = 943 mL