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Before Chemistry

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After Chemistry

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CHEMISTRY

The study of matter and its properties, the changes matter undergoes, and the energy associated with those changes.

Let’s first review some concepts you learned a couple of years ago in Regents chem.:

Substance

Matter that has definite, fixed composition and distinct properties.

Element

A substance that cannot be separated into simpler substances by physical or chemical means

Compound

A substance composed of two or more elements which are chemically united in fixed proportions. Compounds can be separated by chemical means but not by physical means.

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Mixture

Matter composed a physical intermingling of two or more substances and whose composition is variable. Mixtures can be separated by physical means.

Mixtures can be considered to be of two types:

Heterogeneous mixtures do not possess a uniform composition.In a heterogeneous mixture some regions are richer in one component substance than are other regions

Example:

Homogeneous mixtures have composition that is uniform right down to the submicroscopic level.

Example:

It is often difficult to distinguish between heterogeneous and homogeneous mixtures (e.g. milk “looks” uniform, but it’s not). Another term that means homogeneous mixture is solution. If the major component of a solution is water, we call it an aqueous solution. Many chemical reactions occur in aqueous solution.

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Property

A characteristic that can be observed

There are several kinds of properties we will study:

Physical property is one that can be measured/observed without changing the composition or identity of a substance.

Physical change is a change in (physical) properties without any change in the composition or identity of a substance.

Example:

Chemical property is one that can be observed only during a chemical change.

Chemical change is a change in the composition or identity of a substance (which is, naturally, accompanied by changes in physical and chemical properties.

Example:

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Every substance has a unique set of chemical and physical properties.

Macroscopic properties can be measured directly.

Submicroscopic properties cannot be measured directly (they are determined indirectly)

We make macroscopic measurements to determine macroscopic properties. Starting from our macroscopic data, we deduce submicroscopic properties. We use our understanding of the submicroscopic level to account for and explain macroscopic behavior.

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According to the Standard Model, elementary particles are classified into three families which are made up of particles such as the electron, muon, up quark, down quark, electron neutrino, charm quark, strange quark, tau­neutrino and several others. What about dark matter and dark energy?

A new theory model has emerged called String Theory. This theory attempts to create a universal theory of gravity by linking together two theories that are incompatible: quantum mechanics, which describes how matter behaves at the scale of individual atoms or smaller, and Albert Einstein’s General Relativity, which describes how gravity behaves at scales that are larger than individual atoms. String theory says that all of the fundamental particles and forces that make up the universe consist of tiny, vibrating “strings.” The particular vibrational mode of the string determines how it expresses itself: as an electron or an up quark, or a tau­neutrino, etc. These string are so small they are far beyond human ability to detect them, and so far, there is no evidence from any experiments to confirm them. What’s more, there are several varieties of string theory. Some say the strings form loops, like wobbly rubber bands, while others say the strings are open ended. And they require different numbers of dimensions beyond height, width, depth, and time. If confirmed, string theory would give physicists a new basis for modeling the birth of the universe, the formation of matter and energy, the mysterious dark matter and dark energy, and other grand questions about matter, time, and space. In other words, the theory of everything

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Separation of Mixtures

Distillation ­ based on differences in the e(i.e. difference in boiling points)

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Filtration – method of separating the components of a mixture containing a solid and a liquid; based on difference in particle size

Chromatography ­ The fundamental basis for all chromatography concerns the distribution of the individual components of a mixture between two phases: the stationary phase and the mobile phase. As the name implies, the stationary phase is a nonmoving substance which may exist in a variety of forms (usually solid). Commonly it is contained in a column or spread in a thin layer over a glass backing. The mobile phase percolates over the stationary phase and may be either a gas, as with gas chromatography, or a liquid, as with column chromatography. As the mobile phase flows over the stationary phase it carries with it the sample mixture with all of its components. The components are separated as a result of the sorption­desorption which occurs as they are carried through the stationary phase. When an individual component favors (is more strongly attracted to) the stationary phase, it tends to be held longer and, as a result, moves more slowly through the stationary phase column than another component which favors the mobile phase. It is these differences in equilibrium which allow for the separation of compounds in multi­component systems.

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Extraction – separation based on difference in solubility

Centrifugation – separation based on difference in density

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Energy

The ability to do work

We will study energy and energy transfer in chapter 6 (thermochemistry). Understanding energy is crucial if we wish to understand chemistry, because chemical reactions always involve energy changes. In fact, we will learn in the chapter on thermodynamics knowledge of the energy change that would accompany a reaction should it happen to occur is an important part of being able to predict whether or not that reaction is possible. Most processes lead to a lowering of energy. Energy comes in two general forms:

Kinetic energy – energy due to motion

Potential energy – energy due to position

Energy can be converted from one form to another, but it cannot be created nor destroyed (Law of Energy Conservation – the First Law!)

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Measurements in Scientific Study

Almost all our calculations will be done in SI (Systeme Internationale) unit. Below is a summary of SI base units

Base quantity unit name symbol

Mass _______________ _____

Length _______________ _____

Time _______________ _____

Temperature _______________ _____

Electrical current _______________ _____

Amount of substance _______________ _____

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Amount of substance _______________ _____

The base units are not always the most conveniently sized units for expressing some measurements. Therefore, we can use multiple of base units (some of which are “fractional multiples”) to express our measurements. We use a set of prefixes to designate which multiple we are using and these are summarized below:

Prefix symbol meaning example

kilo _____ _____ ____________________

centi _____ _____ ____________________

milli _____ _____ ____________________

micro _____ _____ ____________________

nano _____ _____ ____________________

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There are a few quantities that often confuse people. For example, mass and weight.

Mass – a measure of the quantity of matter in an object, measured with a ____________,

versus

Weight – the force that gravity exerts on an object, measured with a _______________.

Another example involves heat and temperature.

Heat – involves the transfer of thermal energy from a warm object to a cooler object. Thermal energy is the kinetic energy possessed by the submicroscopic particles that make up each object.

versus

Temperature – a measure of the amount of thermal energy that an object contains (or a measure of the average kinetic energies of its particles).

There are three common temperature scales, summarized below:

Scale freezing point H2O boiling point H2O symbol

Kelvin ________ ________ _____

Celsius ________ ________ _____

Fahrenheit ________ ________ _____

Forget Fahrenheit as it is used only by weatherman in the US and Great Britain.

How do we convert between Celsius and Kelvin temperatures?

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Some quantities that we will measure do not correspond to any SI base units but to combinations of these units. These combinations of base units are called “derived” SI units.

Derived unit base unit combinations symbol

Volume product of three lengthsm3*

Density mass/volume kg/m3***the m3 for volume is large and we often use cm3 in chemistry. As far as volume measurements are concerned (for fluids, which refer to liquids and gases),

1 L = 1 dm3 and 1 ml = 1 cm3

**The kg/m3 for density is small and the more commonly used unit in chemistry is g/cm3 (for solids and liquids) and g/L (for gases).

The units we have seen can be separated into two classes:

• Some apply to quantities that depend upon the amount of substance and are called extensive properties.

example:

• Other units apply to quantities that do not depend of the amount of substance and are called intensive properties.

example:

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Experimental Error

Precision and Accuracy

Precision refers to the degree of how close repeated determinations done the same way are to each other. Precision is determined by the scale of the measuring instrument. The more precise the scale (i.e, the greater the number of decimal places it can record), the closer repeated measurements will be to each other. A balance measuring mass to the ten­thousandth place will be more precise compared to one measuring mass to the hundredth place. We like to be as precise as possible, but this does not always insure accuracy. Recall that accuracy is how close our measurement is to some “accepted” value.

We assume that the error between repeated measurements is due to random errors. Random error (or indeterminate error) means that a measurement has an equal probability of being low or high. This error occurs when estimating the value of the last digit of a measurement. This is the recorded uncertainty of the scale of an instrument – the plus/minus or + in a measurement.

As a specific example, consider some actual results of an experiment performed by AT chemistry students at Scarsdale High School on determining the molar mass of a volatile liquid by the Dumas method. Listed below are the data they obtained:

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trial Molar mass (g/mol)

1 83.21

2 84.55

3 82.88

4 83.68

5 82.43

6 81.79

7 80.66

8 81.85

9 82.30

10 84.69

11 82.24

12 81.36

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What do we choose to report for the best estimate of the molar mass? The proper procedure is first to examine the data to see whether any of the results are especially far from the rest (a value of 76.45 might be such an example). Such values are likely to result from some mistake in carrying out or reporting that particular measurement, and therefore are excluded from further consideration (although there have been cases in science where just such exceptional results have led to significant breakthroughs). In our data no such points should be excluded. To obtain our best estimate for the molar mass, we calculate the mean or average value, by adding up the values found and dividing by the number of measurements.

Average = ___________ g/mol

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The average by itself does not convey any estimate of uncertainty. If all the measurements had given results falling between 81.00 and 82.00 g/mol, the uncertainty would be less than if the results had ranged from 80 to 86 g/mol. Furthermore, an average of 100 measurements should have less uncertainty than an average of 5. Therefore, a measure of uncertainty should take into account both the spread of the data and the number of determinations. How these ideas are made quantitative? A statistical measure of the spread of data, called standard deviation, s, is useful in this regard. It is given by the formula

s = (sum of the squares of the deviations from the mean/number of observations ­ 1)1/2

where s = standard deviation from the mean, xi = members of the set, x = mean, and n = number of members in the set of data. The symbol ∑ means to sum over the members.

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Standard

For practical purposes, standard deviation cannot really valid skew the mean. As a rule of measurement (Xi) that differs from the mean byor more (2s) must be discarded and a new mean of data on the molar mass twice the standard dsubtracting 2.46 from the average gives a high80.18. All are measured data fall within this

Random error is only one source of error. Thcalled systematic (or determinate) error. Systhe true value and reduces the accuracy of themeasurements we can reduce the random error anresults, but if systematic errors exist the extrue (or accepted) value. Systematic errors cinstruments or some error in the experimental measured by determining the percent error:

X 100

Problem: If the accepted value for the molar g/mol, calculate the percent error:

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Uncertainty in Measurements

A measurement always has some degree of uncertainty. In recording a measurement, we always use significant figures ­ these indicate the uncertainty of a measurement and are related to precision.In recording a measurement, we record only a limited number of digits (i.e. the ones we got from the instrument, always regarding the last one as “less certain” or estimated). We refer to these recorded digits as significant digits or significant numbers.

The more precisely a measurement is made, the more significant figures that can be recorded.

When we are given a measured value (say, one measured by someone else) we assume that the number of digits shown reflects the precision of the measurement (and that the last digit is less “certain” i.e. estimated, than the other)s.

e.g. 27.13 + 0.01g

the 2, 7 and 1 are certain, the 3 is estimated

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Given a measured value, we count the number of significant figures as follows:

1. All non­zero digits are significant.2. All zeroes that are between non­zero digits are significant.3. Leading zeroes are not significant.4. Trailing zeroes to the right of a decimal point are significant.5. Measured values that have trailing zeroes only to the left of the decimal point (or which do not have a decimal point) are ambiguous and should be expressed in scientific notation

For example, the quantity “one hundred” must be written as

1 X 102 if it has one sig fig1.0 X 102 if it has two sig figs1.00X 103 if it has three sig figs (though 100.0 is perfectly fine to represent four sig figs)

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Problem: How many sig figs are there in each of the following measurements?

a) 8.45 cmb) 1.234 kgc) 606 md) 40, 501 Je) 0.08 Lf) 0.0000349 gg) 2.0 mgh) 0.004200 si) 400 cm

There are numerical values which are not subject to experimental error. These are the “defined quantities” (e.g. 1 m = 100 cm exactly) and numerical values which represent a counted number of objects (e.g. there are 5 boroughs in New York City). For such values, there is no error and so we need not worry about significant figure restrictions for such quantities. These quantities are called “exact numbers”. The important point is that exact numbers are not used in determining the final number of significant figures in any mathematical calculation of measured quantities (data).

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Calculations involving Significant Figures

1) The number of significant figures in the result depends upon the lweast precise piece of data.

2) If only addition and/or subtraction is performed, round the result to the same decimal place as the least precise piece of data. For example, suppose that you weigh a beaker on a crude balance and find that the weight is 52 g. Reporting this result to two sig figs implies that there is some uncertainty in the second digit. The weight could be 51 or 53. (It may actually be less precise than this. If no uncertainty is explicitly stated, you should assume that the uncertainty is 1 in the last sig fig). If you weigh a sample of KHP (potassium hydrogen pthalate) on an analytical balance and obtain 1.2345 g as the weight, what is the combined weight of the beaker plus the salt? If you report a combined weight of 53.2345 g, you will be wrong. Think of the addition as written below:

52. + 1.2345

53.?????

You should report 53 g as the combined weight of the beaker plus salt.

3) If any multiplication and/or division is performed (even if there was addition/subtraction too!), round the result to the same number of significant figures as the least precise piece of data.

For example, 2.8 X 4.5039 = 13

4) We will follow Dr Halpin’s convention at NYU and never round off during a multistep calculation!!! Only round off when reporting an answer!!!

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Uncertainty Analysis

This is a tool for analyzing uncertainties introduced into experiments by the process of measuring. Such an analysis might be useful for several reasons.

You might need to know how much you can trust your resultsIt is important to figure out where the weakest link in an experiment is so that it can be improved.If there is a previously measured or theoretical number, one might wish to know whether there is agreement or not with experiment. Is the difference “real” or is it an experimental quirk?If you have measured something in two different ways, you will wish to know whether the numbers are in agreement within experimental uncertainty or are significantly different.

Rather than rely on blind prejudice, a formal system for calculating the maximum probable uncertainty has been developed. This system computes the largest reasonable uncertainty in a measurement derived from data whose uncertainty is known.

The process of uncertainty analysis is a three step process:

Make estimates of uncertainty in each measurementDerive uncertainty in calculated resultUse uncertainty of result to bolster the argument

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Definitions

Absolute Uncertainty: expressed in some abso

Relative Uncertainty: the quantity reported,uncertainty/measuremen

uncertainty is X

The process of calculauncertainty of measure

readable value.

Once you have an estimate of the uncertainty in the data, you may easily calculate an uncertainty in a result using the rules below:

If the result is determined by addition or subtraction, add absolute uncertainties of measured quantities.

Final answer = _____ + _____ unit

If the result is determined by multiplication and division, add relative uncertainties of measured quantities.

Final answer = _____ + _____ %

The final step is to use your calculated uncertainty to bolster your argument. If, for example, you have calculated that a given value is 2.0 + 0.2 (a 10% error) and the accepted value is 2.1, your number agrees within experimental uncertainty. But if the accepted value is 2.5 + 0.1, then there is a problem with either your number or the accepted value.

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This problem usually turns out to be that you did not measure what you thought you measured: “systematic error.” Either you made an outright blunder (such as dropping some of the compound you just weighed) or there is a systematic error somewhere. All that you ever look at is scale readings and those scale readings may not reflect the quantity they are supposed to. If, for example, you are measuring length, and your meter stick expands, this will produce a systematic error that will make the length seem too short.

It is important to distinguish between systematic errors and the experimental uncertainty. They are totally different concepts. Repeated measurements will reduce experimental uncertainties, but the systematic errors will remain. (If, in the above example, you measure the same length ten times with an expanded meter stick, your average length will still be wrong). Systematic error can be reduced by careful experimental design and the use of control experiments.

One of the real purposes in teaching you the technique of propagation of uncertainty is so that you will know how much variation in results is to be expected from the act of measurement itself. Scrutinize measurements that look off for systematic errors or student blunders.

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Examples of Basic Types of Uncertainty Analysis Calculations

Uncertainty in a concentration. A solution is made up in a 100.0 ml volumetric flask (volume is a measured quantity). The substance has a MW of 120.0 (the MW is defined quantity) and 2.6754 g are weighed out (the mass is a measured quantity). What is the error in the concentration?

Conc = X = 0.2230 M

Weighing is done by weighing a vial containing the solid, then transferring the solid quantitatively to the flask, then reweighing the vial. The absolute uncertainty in each weighing is + 0.0001 g.

Mass vial and solid 15.1254 g + 0.0001 gMass empty vial 12.450 g + 0.0001 g

Mass solid 2.6754 g + ?

Since two weighings are needed, the total absolute uncertainty is + 0.0002 g.

This is X 100 = 0.0075% in relative uncertainty.

The volumetric flask has an uncertainty of + 0.2%. The relative uncertainty in the concentration is the sum of the relative uncertainties of the volume and weight measurements. Total uncertainty in concentrations = 0.2% + 0.0075% = 0.2%

In absolute terms the uncertainty is (0.2230 X 0.002) = 0.0005M and the concentration should be reported as 0.2230 M + 0.0005M.

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Uncertainty in a burette reading. If the liquid level in the burette was initially at 1.05 mL and at 26.74 mL after the solution ran out, what is the uncertainty in volume?

26.75+ 0.05mL here we are adding measured quantities, se we add 1.05 + 0.05mL the absolute uncertainties to get the uncertainty25.70 + 0.10 mL in the final volume.

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Correctly reading and recording a scale measurement:

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A measurement is

precise accurate

if it is in agreement withrepeated measurements the true valuemade by the same procedure

in other words, it is

reproducible correct

The extent of agreement can be expressed as the

range or standard absolute error ordeviation of repeated percent error ofmeasurements the measurement

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Big Idea 1. The chemical elements are fundamental building blocks of matter, and all matter can be understood in terms of arrangements of atoms. These atoms retain their identity in chemical reactions.

Big Idea 2. Chemical and physical properties of materials can be explained by the structure and the arrangement of atoms, ions, or molecules and the forces between them.

Big Idea 3. Changes in matter involve the rearrangement and/or reorganization of atoms and/or the transfer of electrons.

Big Idea 4. Rates of chemical reactions are determined by details of molecular collisions.

Big Idea 5. The laws of thermodynamics describe the essential role of energy and explain and predict the direction of changes in matter.

Big Idea 6. Any bond or intermolecular attraction that can be formed can be broken. These two processes are in dynamic competition, sensitive to initial conditions and external perturbations.

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