Numbers and Concentration (2023)

GeneralIssues
Numbers and Concentration (1)When we look at vacancies or carbonatoms inside an iron crystals, we can describe that qualitatively like: a lot of vacancies, a fewvacancies, a substantial amount of carbon atoms, and so on. It's an easydescription, giving you a general idea of what is at stake, but it is simplynot good enough.
We need a quantitative way for looking atthese things, and that means we need numbers.
Numbers and Concentration (2)Giving the number of vacancies orcarbon atoms in some piece of iron is an easy thing to do - provided you knowthe number. You may have, for example, about 2 000 000 000 000 000 000000 000 carbon atoms in your steel blade, and that is obviously not alot compared to the number of iron atoms inthere, rouhly around 100 000 000 000 000 000 000 000 000.
Allright, you get the point: those numbers are a bit unwieldy—so we usethe exponential notation.Now you have, for example, about 2 · 1024 carbon atoms insidethe 1 · 1026 iron atoms of your steel blade.
Numbers and Concentration (3)Is that a lot or rather not so many?How does this number compare to the number of carbon atoms in the steel wheelof a high-speed ICE train? That wheel weighs at least 100 times more then yoursword blade. If it is made from the same steel, it must have at least 100 timesmore carbon atoms than your sword blade.
Numbers and Concentration (4)You get my point once more: Precisenumbers for the amount of carbon atoms or whatever in your iron arenice—but concentrations are nicer!Concentrations are always relative in the sense that you compare two numberswith one number as a reference.
Numbers and Concentration (5)Concentrations are often given inpercent (%) or asdensity. We only must be clear onone thing now: percent or density relative to what? Here are the options:
  • You go for "weight percent"(wt %). That's the standard way, rather common and comfortable, since it iseasy to weight things. 1 wt % carbon in iron means that 1 % of the total weight—iron plus carbon— is due tothe carbon.
  • You go for "atom percent" (at%). How many percent of all atoms (ormolecules, particles, ...) of the material are carbon atoms?
  • You go for volume percent. How muchvolume, in percent of the total volume, would be occupied by the carbon atoms?Not a very useful way to measure the carbon concentration in iron but not badfor giving the amount of oxygen in air, for example.
  • You go for atoms / molecules / particles per volume unit, i.e. adensity. The unit then is cm–3,i.e. number (no unit) per cubic centimeter.
  • You go for atoms / molecules / particles per weight unit. The unit then iskg–3
Numbers and Concentration (6)There is no "best" kind ofconcentration measure. What is best depends on your needs; what you want to dowith the number.
Numbers and Concentration (7)If you want to bake a cake, it mightbe best to give the concentration of sugar relative to the flour in weightpercent. Actually, it is mostly done by volume, even omitting the percent: onecup of flour, two teaspoons of sugar. It certainly would be pointless to usemolecule percent.
Numbers and Concentration (8)But if you want to assess possiblereactions between ingredients, it is far better to do atom percent. If you wantto make water from scratch by reacting one atom of oxygen (O) with two atoms ofhydrogen (H), i.e 2H + 1O = H2O, you should mix theoxygen atoms : hydrogen atoms = 1 : 2. Hydrogen atoms then accountfor 66,66 at % of the mix, the oxygen atoms supply the remaining 33,33 at %.Weight-wise that would be, for example, about 70 g of H to 533 g of oxygen,i.e. a relation of 1 : 7.6. The 70 g of H then would be 11.6 wt %.
Numbers and Concentration (9)If you want to make iron carbide(Fe3C, also known as cementite) from scratch, you need one atom ofcarbon (C) and three iron (Fe) atoms, i.e 3Fe + 1C =Fe3C. You should mix carbon to iron 1 : 3, i.e. 25 at % C and75 at % Fe.
Since a carbon atoms weighs 12 u = atomic units (or "Daltons"; with 1u = 1,66·10–27 kg), and an iron atom weighs about 56 u,weight-wise that would be about 24 · 12 = 300 g of C to 75 · 56 =4.200 g of iron, i.e. a relation of 1 : 14.
The 300 g of carbon are thus about 6,6 wt % - but 25 at %
Carbon inIron
Numbers and Concentration (10)There is no simple relation between atom percent (at %) and weightpercent (wt %), i.e. you can't just multiply one number with some constant toget the other. But there are simple equations. Here they are, together with graphs forthe full range and for small carbon wt %.
[A]Bat %= AA + B·100 %
[A]Bwt %=a · A a · A + b · B·100 %
[A]B is theconcentration of A inB.
A, B are the numbers of A and Batoms, resp., contained in the material.
a, b are the atomicweights of A and B atoms,respectively
Numbers and Concentration (11)Of course, you could rewrite thefirst equation for B, and insert that in the second one to get somerelation between [A]Bat % and[A]Bwt %. Do it! It's a good exercise in doingfractions. Hereistheresult:
[A]Bat %= 100 %
[B]wt % ·a [A]wt % ·b+ 1
Numbers and Concentration (12)If we look at carbon (A =C) in iron (B = Fe), we have a / b = 12 : 56 = 0.21and get
[C]at %= 100 %
[Fe]wt % ·0.21 [C]wt % + 1
Numbers and Concentration (13)Let's see how it works and assume welook at one weight percent (1 wt %) or two weight percent(2 wt %= carbon in iron. How much will that be in atom percent (at %)?Well, we have [C]wt % = 1 or 2, which leaves[Fe]wt % = 99 or 98. Multiplied by 0,21 it is20.79 or 20.58. Dividing by 1 or2 leaves 20.79 or 10.29. Adding 1 you get 21.79 or 11.29. Finally, 100 divided by 21.79 or11.29 gives 4.81 at% and 8.86 at%
Numbers and Concentration (14)For very small carbonconcentrations, let's say below 1 wt %, we obviously get in a goodapproximation:

[C]at % » 4.67 [C]wt %

Numbers and Concentration (15)To save you a lot of calculations, Igive you some graphs below that are more practical as far as carbon in iron isconcerned.
Numbers and Concentration (16)Here is the relation between carbonin weight percent (wt %) and carbon atom percent (at %). It is valid for allcarbon atomically dissolved in theiron.
Numbers and Concentration (17)
Carbon in iron; weight and atom percentconversion
Numbers and Concentration (18)However! We know that iron at room temperature canhardly dissolve any carbon. Instead an ironcarbide is formed, It carries the name "cementite" and the chemicalshorthand Fe3C. Upon carbide formation any carbon atom takes3 iron atoms out of the "iron".
The curve below shows how much iron and carbon atoms are found in the cementitein at % for a carbon concentration given inwt %
Numbers and Concentration (19)
How much cementite in at % forms for a carbonconcentration given in wt %
Numbers and Concentration (20)Let's see how one should"read" this curve.
Let's assume that we have 2 wt % carbon in the iron. That corresponds to 8.86at % (upper graph). Imagine that you have 10.000 atoms altogether; then we have886 carbon atoms and 9.114 iron atoms. Now form cementite or Fe3C.That "eats up" 3 × 886 = 2.658 iron atoms that become part ofthe cementite, leaving only 9.114 - 2.658 = 6.456 iron atoms that still belongto the iron proper. The iron concentration is now only 65.56 at%,the cementite concentration accordingly 100 - 65.56 = 34.44 at%
The curve shows that for 2 wt%: The carbon and iron atoms in the cementiteaccount for about 3 at %; leaving about 66 at% for the iron
Add 6.7 wt % carbon and it will eat up allthe iron left. You would end up with pure iron carbide!
Densities
Numbers and Concentration (21)It is very common and useful not togive concentrations in relative values or percent, but as volume density and(less frequently) as mass density. That means that instead of the concentrationwe now refer to the density rA; B of some particleA (atom, molecule, whatever) in some host B asThose densities are often used if the numbers are very small or very large orif the "particles" are a bit more complex than simple atoms ormolecules. Here are a few examples:
Numbers and Concentration (22)Small concentrations: Forexample, the always very small impurity concentrations in silicon are mostly referred to like this
riron = 5 ·1013 cm–3
rP = 2.38 ·1018 cm–3
Numbers and Concentration (23)Large concentrations: Thecapacity of a battery, for example a lithium (Li) ion battery, is always givenby how much Li you can "store" in the electrodes. A fully chargedbattery has all its Li in the anode; during discharge it moves to the cathode.When all the Li is in the cathode, the battery is empty and needs to bere-charged by moving the Li back into the anode.
Numbers in percent (atom or weight) would be high and on occasion > 100 %.You can put more than 1 kg Li into a 1 kg Si anode, for example.
There is a big difference between the volume density or mass density. If thebattery is supposed to go into a car, weight matters far more than volume. Ifit is supposed to go into your basement to store you solar energy, it is theother way around.
Numbers and Concentration (24)Complex particles: How do yougive a number for the concentration / density of precipitates? You may care farmore how many there are per volume than howbig they are (needed for wt %). Giving atom % does not make muchsense.
Similar arguments go for other crystal lattice defects.
If your "particle" is something more abstract, like the energy stored in a battery, you need to usedensities. Energy has the unit "Watt hour" (Wh), and it is possibleand easy to give the "specific capacity" in Watt hour per gram(Whg–1) or the energy density in Watt hour per cubic centimeter(Whcm–3). Obviously, percent scales are not useful here.
SmallNumbers
Numbers and Concentration (25)If we don't discuss carbon in ironbut for example vacancies in iron (or most other crystals), the maximumatomic concentration rarely exceeds 0.01 at% but can be far, far smaller.
Numbers and Concentration (26)1 vacancy within 1.000.000 (1 mio)atoms would be a concentration of 0.0001 at %. Try to express that in weightpercent!
Small numbers like that become cumbersome and error prone. So we do it byexponentials or by some frequently used abbreviations. I dealt with thatalready in this earlymodule. Here is the important table from this module, what we need here ishighlighted in pink. Use it but be careful about possible mix-ups with thebillion/ trillion confusion.
Large numbers Small numbers
PotencyNameSymbolPotencyNameSymbolAs "parts per.."
1024YottaY10–1Dezid
1021ZettaZ10–2Zentic%
percent
1018ExaE10–3MillimNumbers and Concentration (27)
promille
1015PetaP10–6Mikroµppm
million
1012TeraT10–9Nanonppb
billion
109GigaG10–12Pikopppt
trillion
106MegaM10–15Femtofppqt
quatrillion
103Kilok10–18Attoa
102Hektoh10–21Zeptoz
101Dekada10–24Yoctoy

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FAQs

What does 2% w/v mean? ›

% (W/V) Percent of weight of solution in the total volume of solution. Percent here is the number of grams of solute in 100 mL of solution. Example: A 4% (W/V) NaCl solution is 4 g of NaCl in 100 mL of solution.

How do you get 5 concentrations? ›

For example: Mix 500 mL of water and 25 g of NaCl to make a 5% solution. Remember, if you're diluting a liquid compound, you must subtract out the volume of liquid being added from the final volume: 500 mL – 25 mL = 475 mL of water.

What are the 3 ways to calculate concentration? ›

The three ways to measure the concentration of a solution are molarity, mole fraction, and molality.
  1. Molarity (M): It is calculated by the number of moles (n) of solute and volume of solution (V). ...
  2. Mole fraction (x): It is the ratio of number of moles of particular element ( ) and total number of moles of substance ( ).

What are the 4 types of concentration? ›

In chemistry, concentration is the abundance of a constituent divided by the total volume of a mixture. Several types of mathematical description can be distinguished: mass concentration, molar concentration, number concentration, and volume concentration.

What is a 10% solution? ›

10 percent solution means the solute is only 10% in the solution, so taking the volume of the solvent 100 ml then the mass of the solute will be either 10 gram or 10 ml. For example, 10% solution of sodium chloride (NaCl) means 10 grams of sodium chloride is mixed in 100 ml of water.

What does 70% V V mean? ›

For example, when you buy isopropanol at the store (rubbing alcohol), you'll notice that it says 70% (vv), which means by volume. This tells you that the solution is 70% isopropanol. The equation for volume percent is pretty straightforward: vv%=volume of solutevolume of solution×100.

What is 5% w/v mean? ›

What does a 5% w/v solution of KCl mean? It means that for every 100 mL of solution you have 5 grams of KCl.

How do you write 10X concentration? ›

This 10X PBS recipe contains 1.37 M NaCl, 27 mM KCl, 100 mM Na2HPO4, and 18 mM KH2PO4. To make 1 L of 10X PBS stock solution, combine 17.8 g of Na2HPO4, 2.4 g of KH2PO4, 80 g of NaCl, 2 g of KCl, and adjust final volume to 1 L.

How do you get 0.05 concentration? ›

You can first prepare 0.5% solution (0.5 g per 100 ml) and for 0.25, 0.1, 0.025 and 0.05%, respectively, dilute to half, one fifth, one twentieth and one tenth. For example, add 9 ml water to 1 ml of the stock solution, to 10 times dilute and obtain a concentration of 0.05%.

What are examples concentration? ›

The concentration of the solution tells you how much solute has been dissolved in the solvent. For example, if you add one teaspoon to two cups of water, the concentration could be reported as 1 t salt per 2 c water.

What are the 3 types of concentration of solution? ›

Concentrations of Solutions
  • Percent Composition (by mass)
  • Molarity.
  • Molality.
  • Mole Fraction.

What is concentration short answer? ›

(a) Concentration of a solution is defined as the amount of solute that is present in a given amount of solution. It can be expressed in terms of: Mass by the mass percentage of a solution =mass of solutemass of solution×100.

What is the rule of concentration? ›

The Law of Concentration: Every action we do contributes to the whole. Therefore, your actions are neither big nor small as all your actions influence the whole, I.e. the butterfly effect.

What are the 2 ways we measure concentration? ›

Concentration of a Solution

There are two basic ways of reporting the concentration of a solute in a solvent, by reporting the mass of solute in a given volume of solution, or the number of moles of solute in a given volume of solution.

Which unit is used for concentration? ›

Quantitative units of concentration include molarity, molality, mass percentage, parts per thousand, parts per million, and parts per billion.

What is concentration strategy with example? ›

For many firms, concentration strategies are very sensible. These strategies involve trying to compete successfully only within a single industry. McDonald's, Starbucks, and Subway are three firms that have relied heavily on concentration strategies to become dominant players.

What are the 5 ways of expressing concentration of solution? ›

It can be expressed in several ways: molarity (moles of solute per liter of solution); mole fraction, the ratio of the number of moles of solute to the total number of moles of substances present; mass percentage, the ratio of the mass of the solute to the mass of the solution times 100; parts per thousand (ppt), grams ...

What are the 5 examples of solution? ›

Here is a brief list:
  • Salt water is formed when we mix salt (generally table salt) in water. ...
  • Sugar water is formed by mixing sugar in water.
  • Mouthwash consists of a number of chemicals dissolved in water.
  • Tincture of iodine is obtained by dissolving crystals of iodine in alcohol.

What is a 9% solution? ›

"Normal saline" is an aqueous solution of 0.9% NaCl. This means that normal saline can be prepared by measuring out 0.9 g of NaCl and diluting this amount of NaCl to a final volume of 100 ml's in water. This would be the same as diluting 9 g of NaCl to a final volume of 1 liter in water.

How do you make a 30% solution? ›

You want to end up with 100ml of liquid, 30% of which is alcohol. 30% of 100ml is 30/100 100 = 30 ml. Thus you need 30 ml of alcohol and 70 ml of water.

What does 80% vv mean? ›

Alcohol (ethanol) (USP or Food Chemical Codex (FCC) grade) (80%, volume/volume (v/v)) in an aqueous solution denatured according to Alcohol and Tobacco Tax and Trade Bureau regulations in 27 CFR part 20. Glycerol (1.45% v/v). Hydrogen peroxide (0.125% v/v).

What does 15% vv mean? ›

Explanation: V/V INDICTING VOLUME BY VOLUME PERCENTAGE OF THE ALCOHOL SOLUTION WHICH MEANS THAT 15% OF THE TOTAL VOLUME OF THE SOLUTION IS OF ALCOHOL AND REMAINING 85% IS OF SOLVENT.

How do you make a 1 VV solution? ›

A 1%(v/v) solution implies that 1 mL of the solute is present in every 100 mL of the solution. To prepare a 100-mL 1 %(v/v) solution, 1 mL of the solute is obtained and added to a 100-mL volumetric flask. The solute is diluted with solvent up to the 100-mL mark of the flask. The solution is mixed and a label is added.

What does 7% w/v mean? ›

By definition, a percent w/v solution is the measure of weight per 100 mL. 7.5 g/100 mL = 7.5%

What is meant by 10% w V? ›

10%w/v solution of sugar in water means 10 g of glucose present in 100g of water.

How many mg is a 0.1 solution? ›

A 1% solution is the same as 1000 milligrams in 100 cc or 10mg/cc. Percent solutions all are 1000mg/100cc.
...
CONCENTRATIONDOSAGE EQUIVALENCEPERCENT
1:1,0001mg/mL0.1%
1:10,0000.1mg/mL0.01%
1:100,0000.01mg/mL0.001%
1:200,0000.005mg/mL0.0005%

How can I study 16 18 hours a day? ›

Here are some of the best science-backed techniques to focus while studying:
  1. Meditate for at least 20 minutes every day.
  2. Create a study schedule.
  3. Use soothing study music.
  4. Turn off all the technology that distracts you.
  5. Prepare a perfect study spot.
  6. Get up for a walk or workout.
  7. Train your mind to focus for a longer time.

Why can't I study for long hours? ›

Take a break every hour or so to stay fresh.

You may be tempted to hunker down and study for several hours straight, but that's a quick way to lose motivation. Your body and brain need breaks, so take 10 minutes or so to refresh yourself every hour. Go for a walk, grab a snack, or stretch, then get back to work.

Why do I lose focus so easily? ›

Such symptoms may be due to an underlying condition, like mild cognitive impairment, or a mood disorder, like depression and anxiety. Declining focus also could result from lifestyle issues that should be addressed, such as stress, fatigue, poor sleep, dehydration, an unhealthy diet, or sedentary behavior.

Is 10% the same as 10x? ›

10x means to maximize and expand your results ten times over, rather than just by 10%.

What does 20X concentration mean? ›

A solution 20 times more concentrated would be denoted as 20x and would require a 1:20 dilution to restore the typical working concentration. Example: A 1x solution of a compound has a molar concentration of 0.05 M for its typical use in a lab procedure.

What does 1000x concentration mean? ›

1000x refers to the stock concentration respect to the concentration in the working solution, ie 1000 times higher concentration. If the final concentration of the chemokines you need is 20ug/mL, 1000x would be 20,000 ug/mL or 20 mg/mL.

What is a 100% concentration? ›

1% m/v solutions are sometimes thought of as being gram/100 mL but this detracts from the fact that % m/v is g/mL; 1 g of water has a volume of approximately 1 mL (at standard temperature and pressure) and the mass concentration is said to be 100%.

What is a 0.5% solution? ›

0.5% means 0.5 grams in 100 ml, so if you only need 50 ml, you need 0.5 g / 2 = 0.25 g agarose for a 50 ml gel solution.

What does a 1% concentration mean? ›

• A 1% (w/v) concentration is obtained by dissolving 1 g of substance in a final. volume of 100 ml solution, e.g. 1 g glucose dissolved in water to a final volume of 100 ml solution gives a 1% (w/v) glucose solution.

What are some concentration skills? ›

There's no one answer for how to improve focus, but the following tips can help.
  • Eliminate distractions. ...
  • Reduce multitasking. ...
  • Practice mindfulness and meditation. ...
  • Get more sleep. ...
  • Choose to focus on the moment. ...
  • Take a short break. ...
  • Connect with nature. ...
  • Train your brain.
3 Feb 2021

What are concentration skills? ›

Concentration has been defined as "the ability to direct one's thinking in whatever direction one would intend”. We all have the ability to concentrate some of the time.

Does concentration mean number? ›

The concentration of a substance is the quantity of solute present in a given quantity of solution. Concentrations are usually expressed in terms of molarity, defined as the number of moles of solute in 1 L of solution.

What are the 4 different ways to measure concentration? ›

Chemists can express concentrations in various ways including: Molarity (M), Parts per million (ppm), % composition, or gram/Liter (g/L).

What are the 3 types of solutions and examples? ›

Types of Solution
S.NoTypes of SolutionExamples
1Solid-solidAlloys like brass, bronze etc.
2Solid-liquidThe solution of sugar, salt etc in water.
3Solid-gasSublimation of substances like iodine, camphor etc into the air.
4Liquid-solidHydrated salts, mercury in amalgamated zinc, etc.
5 more rows
17 Aug 2021

What is your concentration? ›

Your concentration is a specific area of emphasis within your chosen major. Like minors, schools don't usually require you to declare a concentration; instead, they're used as an optional tool to help you customize your college experience.

Why is concentration important? ›

Why is concentration so important? Concentration allows you to better use your resources and approach problems more efficiently. When you are concentrating it is less likely that you will miss important information. Staying focused helps you memorise things more easily.

How do you calculate concentration using Beer's law? ›

The equation for Beer's law is a straight line with the general form of y = mx +b. where the slope, m, is equal to εl. In this case, use the absorbance found for your unknown, along with the slope of your best fit line, to determine c, the concentration of the unknown solution.

Does concentration mean amount? ›

In chemistry, concentration refers to the amount of a substance in a defined space. Another definition is that concentration is the ratio of solute in a solution to either solvent or total solution. Concentration is usually expressed in terms of mass per unit volume.

What is concentration and how do we measure it? ›

Concentration measures the amount of a substance dissolved in a volume of another substance. It can be measured in moles per liter, also called molarity.

How do you calculate concentration and absorbance? ›

Absorbance Measurements – the Quick Way to Determine Sample Concentration
  1. Transmission or transmittance (T) = I/I0 ...
  2. Absorbance (A) = log (I0/I) ...
  3. Absorbance (A) = C x L x Ɛ => Concentration (C) = A/(L x Ɛ)
4 Sept 2019

How do you calculate absorbance from concentration? ›

Absorbance is directly proportional to concentration and length: A = εcl. ε is the wavelength-dependent molar absorbtivity coefficient and it is constant for a particular substance. ε has units of L mol 1 cm 1.

What is the relationship between absorbance and concentration? ›

One factor that influences the absorbance of a sample is the concentration (c). The expectation would be that, as the concentration goes up, more radiation is absorbed and the absorbance goes up. Therefore, the absorbance is directly proportional to the concentration.

What is concentration example? ›

The concentration of the solution tells you how much solute has been dissolved in the solvent. For example, if you add one teaspoon to two cups of water, the concentration could be reported as 1 t salt per 2 c water.

What is your concentration means? ›

Definition of concentration

1a : the act or process of concentrating : the state of being concentrated especially : direction of attention to a single object All that noise is disturbing my concentration. b : an academic major or area of focus within a major The student chose law as his concentration.

What is concentration simple? ›

(KON-sen-TRAY-shun) In science, the amount of a substance, such as a salt, that is in a certain amount of tissue or liquid, such as blood. A substance becomes more concentrated when less water is present.

How do you measure concentration and attention? ›

Scientific Focus Tests

Attention tests such as the Attentional Capacity Test (ACT), Continuous Performance Tests (CPTs), and Tests of Variable Attention (TOVA) are used to measure one's selective attention, sustained attention, and divided attention.

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