Chapter 11: Measurements and data processing Flashcards
What are random uncertainties causes by?
Random uncertainties are caused by the limitations of the measuring apparatus and other uncontrollable variables that are inevitable in any experiment.
What are several sources of random uncertainties?
Variations due to air currents in the room, the heating effects of the current in the circuits, friction between various mechanical parts etc
How can the effect of random uncertainties be reduced?
Repeating the measurements more often
They can never be completely eliminated
How to calculate the uncertainty of a measurement?
It is half the smallest division to which you take a reading.
for example,
on the 100cm3 measuring cylinder, it is divided apart by 1cm3 and so the uncertainty is + or - 0.5cm3
On an electronic balance, it reads to two decimal places, the smallest division is 0.01g, what is the uncertainty?
±0.005 g
What does precision relate to?
Precision relates to the reproducibility of results. If a series of readings is taken with high precision, it indicates that the repeated values are all very close together and close to the mean (average) value.
What does accuracy refer to?
Accuracy refers to how close a measurement is to the actual value of a particular quantity.
What causes systematic errors and can it be reduced?
A systematic error is an error introduced into an experiment by the apparatus or the procedure.
It cannot be reduced by repeating the readings?
What are some example of systematic errors?
- the beaker is not that well insulated so heat will escape – the measured temperature rise will be less than the actual value
- the reaction does not occur instantaneously and the thermometer does not respond instantaneously and so the measured temperature rise will be less than the actual value
- the concentration of the sodium hydroxide is less than 0.10moldm−3 and so the measured temperature rise will be less than the actual value
How to calculate percentage error?
What is the difference between accuracy and precision?
Precision: the reproducibility of results
Accuracy: how close a value is to the true value of the measurement
What does it mean when the percentage error is greater than the percentage random uncertainty?
this suggests that the experiment involves some systematic errors
How can systematic errors be reduced?
By changing the way the experiment is carried out
See this example, how do we find out the uncertainty of the temperature change?
Add 0.02 +0.02 together
Wen quantities with uncertainties are added or subtracted, what is done to the absolute uncertainty?
They are added
When multiplying or dividing quantities with uncertainties, what is done to the uncertainties?
The percentage uncertainties should be added
What is done to the percentage uncertainty when multiplying or dividing a quantity with a pure number?
The absolute uncertainty is multiplied/divided by that number so that the percentage uncertainty stays the same
How should the uncertainty be quoted?
The uncertainty is usually quoted to one sig fig and your measurement should be stated so that the uncertainty is in the last sig dig - no figures should be quoted after the uncertainty
What does the gradient represent in a graph?
The rate of the reaction
What is an infrared spectroscopy used for?
To determine the structure of an organic compound
Electromagnetic radiation in the range 400-4000cm01 is passed through a sample. The printout of the spectrum then shows which frequencies (wavenumber) are absorbed. Can be used to determine which bonds are present in a molecule because the precise wavenumber at which infrared radiation is absorbed by a particular functional group depends on the adjacent atoms.
What happens to a sample of organic compound is injected into a mass spectrometer?
- Bombarded with high energy electrons to produce positive ions.
- Pass on through the mass spectrometer where they are separated according to mass and detected
What are the other peaks other than the molecular ion peak?
When do fragmentation pattern arise?
When a molecule can break apart into smaller fragments when it is bombarded by high energy electrons
Only what type of ions give peaks in a mass spectrum?
Positive ions
What elements nucleus has a property called spin?
Hydrogen
How many decimal places should the final answer have?
If a calculation involves just adding or subtracting numbers, the final answer should be quoted to the same number of decimal places as the piece of original data that has the fewest decimal places
e. g.
23. 57-8.4=15.17 but the final answer should be quoted as 15.2
If a calculation involves multiplication/division, what is the general rule for the final answer compared to a calculation with addition/subtraction?
The final answer should be quoted to the number of significant figures of the piece of data with the fewest significant figures.
for addition and subtraction, it is the same number of decimal places rather than significant figures
When should rounding values in calculations take place?
Only when an answer to a particular part of a question is required
When should rounding values in calculations take place?
Only when an answer to a particular part of a question is required
When should rounding values in calculations take place?
Only when an answer to a particular part of a question is required
How to calculate percentage uncertainty?
What values do you put in the formula to calculate percentage uncertainty?
What unit is used for a percentage uncertainty?
A percentage uncertainty has no units
What unit is used for a percentage uncertainty?
A percentage uncertainty has no units
What unit is used for a percentage uncertainty?
A percentage uncertainty has no units
How are uncertainties propagated in multiplication/division calculations?
The percentage uncertainties should be added
for addition and subtraction the absolute uncertainties are added
What to do about the uncertainty when multiplying or dividing a quantity with uncertainty by a pure number?
the absolute uncertainty is multiplied/divided by that number so that the percentage uncertainty stays the same
Does proportional and directly proportional mean the same thing?
Yes
What is a proportional and inversely proportional relationship?
How to draw a line of best-fit?
- Do not join the dots
- may be a straight line or a curve
- should represent the trend in the data
- points should be evenly distributed about the line
- is very much a matter of judgement and no two lines of best fit drawn by different people will be identical
When should the line of best fit not be drawn?
When discrete data are plotted
- points may be joined or the data could be plotted as a bar chart
What does the gradient tell us?
Gives us an idea how much one quantity (the dependent variable) is affected by another quantity (the independent variable)
What does it mean when the gradient is big?
A small change in the IV has a large effect on the DV
How to calculate the gradient?
Change in y or change in x
How are the units of the gradient obtained?
by dividing the units of y by the units of x
How to find the gradient of a curve?
- Draw a tangent
Gradient = (70-0)/(32-0) = 2.2cm3s-1
How should a tangent be drawn?
As large as possible to minimise uncertainties caused by reading values off the graph
How do we know if there is one double bond or a ring present?
for every two hydrogen atoms fewer than in the alkane with the same number of carbon atoms
How many H will an alkane have with 4 carbons? (C₄H?)
C₄H₁₀
CnH2n+2 - alkane formula
If the parent alkane is C₄H₁₀, what would the molecule that contain one double bond or one ring look like?
C₄H₈
How many rings or double bonds or triple bonds would there be present in C₄H₆?
Has four hydrogens fewer than in the alkane and therefore has two double bond equivalents
* 2 double bonds
* one triple bond
* two rings (not possible with 4 carbon atoms)
* one right and one double bond
What is IHD (degree of unsaturation or the index of hydrogen deficiency)?
The number of double bond equivalents
How many double bond is a ring equivalent to?
1
How many double bond is a triple bond equivalent to?
2
WHat is the IHD of C₂H₆O?
Has the same number of hydrogen as ethene (C₂H₆) and contains no double bonds
IHD = 0
What is the IHD of C₄H₈O?
Has two hydrogens fewer than butane and contains either one double bond or one ring
IHD = 1
How to calculate the IHD of a compound with a halogen atom?
we count this as a hydrogen atom and work out the number of double bond equivalents
What is the IHD of C₄H₈Cl₂?
We replce the Cl atoms with hydrogen atoms which has the same number of hydrogen atoms to make C₄H₁₀ = same number of hydrogen atoms as butane and therefore there are no double bond equivalents
IHD = 0
How to calculate the IHD when a compound contains nitrogen atoms?
subtract one hydrogen for every nitrogen atom and then calculate as usual
What is benzene’s formula?
C₆H₆
What is benzenes IHD?
C₆H₆
4 because it contains one ring and the equivalent of three double bonds
What is infrared spectroscopy used for?
when determining the structure of an organic compound
What does an infrared spectroscopy printout?
printout of the spectrum then shows which frequencies (wavenumbers) are absorbed
What does the baseline at the top in an infrared spectra show?
100% transmittance/zero absorbance of infrared radiation
What do the trouphs represent?
usually called bands or peaks
represents wavenumbers at which radiation is absorbed
What can an infrared spectrum be used to determine?
which bonds are present in a molecule
What is the ginerprint region?
the segment of the spectrum below 1500cm-¹
is characteristic of the molecule as a whole
can be used to distubguish compounds with similar bands in the region above 1500cm-¹ (i.e. butanone and propanone, both have the same functional group C=O and can be distinguished using their fingerprint regions
What does the precise wavenumber at which infrared radiatio is absorbed by a particular functional group depend on?
on the adjacent atoms
so a C=O bond in a ketone absorbs at a slightly different frequency to a C=O bond in an ester
What can be not always distinguish using infrared spectra?
can identify the bonds present
but not always distinguish between funcitonal groups
i.e. we could identify the presence of C=O in a molecule but would not be able to distinguish between an aldehyde and a ketone
What is the boradness of the O-H band due to?
due to hydrogen bonding between molecules
If the infrared spectrum of a carboxylic acid is in gas phase, what would the O-H absorption band look like?
much narrower
Where do we look at the infrared spectrum to identify the bonds present?
the region above 1500cm-¹
not the fingerprint region
What is a characteristic of carboxylic acids in the 2400 and 3400cm-¹ region?
of carboxylic acid due to the O-H bond
How do we make sure that our hypothesis that this is showing a carboxylic acid?
- we have to check the fingerprint region to look for the functional group of a carboxylic acid which has a C-O bond
- there is no band in this region (1000-1300cm-¹) so this may not be a carboxylic acid
Why dos the region below 1500cm-¹ contain many absorptions?
due to C-C bonds and C-H bonds and is difficult to interpret
When doe we usually only look at the fingerprint region?
to confirm the presence of a particular vibration once we have a good idea of the structure of the molecule
i.e. a band in the 1000-1300cm-¹ region does not confirm th presence of a C-O bond in a molecule - but the absence of a band in this region means that a C-O bond is not present
What does a mass spectrometer do to a sample of organic compound?
sorts molecules according to their mass;charge (m/z or m/e) ratio
we assume here that only 1+ ions are formed so that the mass:charge ratio is equal to the mass
How does a mass spectrometer work?
- a sample of the organic compound is injected into the mass spectrometer
- it is bombarded with high-energy electeons to produce positive ions
- these pass on through the mass spectrometer where they are separated according to mass (actually the mass:charge ratio) and detected
What happens when a sample of propane is introduced into a mass spectrometer? (C₃H₈)
C₃H₈+ positive ions are produced
What is molecular ion, M+?
the ion produced when just one electron is removed from a molecule
the molecular ion peak is not necessarily the biggest peak in terms of abundance, but it has the highest m/z value
What does the peak in the spectrum at the highest mass (m/z value correspond to?
corresponds to the molecular ion and indicates the relative molecular mass of the molecule
so the relative molecular mass of the compound being investigated is 44
What are the other peaks besides the molecular ion peak called?
fragmentation pattern
Why does the fragmentation pattern arise?
because a molecule can break apart into smaller fragments when it is bombarded by high-energy electrons
Only which ions resulting from fragmentation will produce a peak inthe mass spectrum?
only the positive ions because only they can pass thorugh a mass spectrometer
Which would show as a peak on the mass spectrum
only positive ions can pass through a mass spectrometer, so the CH₃ radical produced in this proces does not give rise to a peak
however there is a peak due to CH₃+ at m/z 15, which is produced in a different fragmentation process
Why may a mass spectrum also show a peak with a mass one unit higher than the molecular ion - an (M+1)+ peak?
because this is caused by the presence of an artom of ¹³C in some molecules. It is an isotope of carbon - its natrual abundance is low at 1.1%
What is ¹³C and its natural abundance?
it is an isotope of carbon
its natrual abundance is low at 1.1%
What are 2 ways in which we can look at fragmentation patterns?
- the ion formed when a molecular ion breaks apart
- the group lost from a molecular ion
Where does the molecular ion peak at?
m/z 74
What is the relative molecular mass of this?
74
where the molecular ion peaks
How do we know that at m/z 57, it correspond to the loss of OH?
because the difference from the relative molecular mass is -17 and according to this table, it suggests that it is an OH
What is lost from C₂H₅COOH+ and what is formed at the peak at m/z 45?
the peak at m/z 45 corresponds to the loss of 29 mass units from the molecular ions. C₂H₅ is a group with mass 29 and so we can deduce that C₂H₅ is lost from C₂H₅COOH+ to form the COOH+ ion
What is the relative molecular mass of chloroethane? Why?
64.5 because because chlorine has two isotopes ³⁵Cl and ³⁷Cl with an abundance ratio of 3:1
so some chloroethane molecules contain a ³⁵Cl atom and other have a ³⁷Cl atom - therefore we get molecular ion peaks at m/z 64 (C₂H₅³⁵Cl+) and m/z 66 (C₂H₅³⁷Cl+)
What property does a hydrogen nucleus have?
a property called spin
What does a spinning nucleus acts as?
like a tiny bar magnet
What can the bar magnet (spinning nucleus) either align itself with?
align itself with (lower energy) or against (higher energy) an externally applied magnetic field
What are the requirements of the nuclei so that they have the property of spin?
only nuclei with an odd value for the mass number and/or atomic number have the property of spin
What can be used to cause a hydrogen nucleus to change its orientation relative to the applied magnetic field?
Energy in the radio frequency range of the electromagnetic spectrum can be used to cause a hydrogen nucleus to change its orientation relative to the applied magnetic field
it is these changes in energy state that occur in nuclear magnetic rosonance (NMR) spectra
What are we looking at in an NMR spectra?
absorptions due to ¹H nuclei (usually just called protons)
What information does NMR spectra provide?
information about the environments of protons in molecules
What do the peaks in an NMR spectrum corespond to?
groups of protons (hydrogen atoms) in different chemical environments
How do you determine the ratio between the number of hydrogen atoms (protons) in each environment?
measure the vertical height of each step in the intergration trace using a rule and find the ratio between the heights
this is the same as the ratio between the numbers of protons in each environment
What do the 3 peaks in the spectrum correspond to?
to three difference chemical environments for the protons (hydrogen atoms) in one molecule of the aldehyde
What is said about the hydrogen atoms joined to the same carbon atom?
said to be chemically equivalent
What is the area underneath a peak proportional to?
to the number of hydrogen atoms in that envioronment
so the area under the red peak is twice (2H in this environment) the area under the blue peak (1H in this environment); and the area under the green peak (3H in this environment) is 3 times that under the blue peak
What can the NMR spectrometer work out the area under each peak to produce?
an integration trace
What are the vertical heights of the steps in the integration trace proprotional to?
to the number of hydrogen atoms in each environment
What is the horizontal scale on an NMR spectrum?
the chemical shift
given by the symbol δ and has units of parts per million (ppm)
this quantity gives information about the environments that the protons (hydrogen atoms) are in - protons in difference chemical environments have diference chemical shifts
What is the first step to working out the number of hydrogen environments?
decide whether or not the molecule is symmetrical
If the molecule is not symmetrical, what cad be said about hydrogen atoms on the different atoms in the carbon chain?
they will be in different chemical environments
Why is there only 2 different chemical environments for. thehydrogen atoms?
because the molecule is symmetrical
What is the ratio of the numbers of hydrogens in each environment?
The heights of the steps in the integration trace are in the ratio 2:3 because there are 4 hydrogen atoms in one environment and 6 hydrogen atoms in the other
How many chemical environments does butanone have? ratio?
3
ratio is 3:2:3
How many peaks will there be in the NMR spectrum of propan-2-ol?
3 because the molecule is symmetrical
the CH₃ groups are equivalent
the ratio of the numbers of protons in each environment is 6:1:1
Why is there only 2 environments in 2-methylpropan-2-ol?
because the CH₃ groups that are attached to the same carbon atom will be equivalent
Proton environments more exmples
