Define concentration. Use the terms concentrated and dilute to define the relative concentration of a solution. Calculate the molarity of a solution. Calculate percentage concentration (m/m, v/v, m/v). Describe a solution whose concentration is in ( extppm) or ( extppb). Use concentration systems in calculations. Determine equivalents for an ion. Complete calculations relating equivalents to moles, volumes, or mass. Complete dilution calculations.

You are watching: Which of the following solutions is the most dilute?

There are several means to express the amount of solute present in a solution. The concentration of a solution is a meacertain of the amount of solute that has been dissolved in a offered amount of solvent or solution. A concentrated solution is one that has actually a fairly huge amount of dissolved solute. A dilute solution is one that has a relatively little amount of dissolved solute. However, these terms are loved one, and also we must be able to expush concentration in a more exact, quantitative manner. Still, concentrated and dilute are valuable as terms to compare one solution to one more (check out number below). Also, be mindful that the terms "concentrate" and "dilute" can be used as verbs. If you were to warm a solution, leading to the solvent to evapoprice, you would be concentrating it, because the ratio of solute to solvent would certainly be increasing. If you were to add even more water to an aqueous solution, you would certainly be diluting it because the proportion of solute to solvent would be decreasing.

Figure (PageIndex1): Solutions of a red dye in water from the a lot of dilute (on the left) to the most concentrated (on the right).

Percent Concentration

One method to explain the concentration of a solution is by the percent of the solution that is created of the solute. This percent can be determined in among three ways: (1) the mass of the solute divided by the mass of solution, (2) the volume of the solute divided by the volume of the solution, or (3) the mass of the solute separated by the volume of the solution. Due to the fact that these techniques mostly lead to slightly different vales, it is necessary to always show how a provided percentage was calculated.

Volume Percent

The portion of solute in a solution deserve to more conveniently be identified by volume once the solute and solvent are both liquids. The volume of the solute separated by the volume of the solution expressed as a percent, returns the percent by volume (volume/volume) of the solution. If a solution is made by taking (40. : extmL) of ethanol and also adding enough water to make (240. : extmL) of solution, the percent by volume is:

<eginalign extPercent by volume &= frac extvolume of solute extvolume of solution imes 100\% \ &= frac40 : extmL ethanol240 : extmL solution imes 100\% \ &= 16.7\% : extethanol endalign>

Frequently, ingredient labels on food products and drugs have actually quantities listed as percentages (check out figure below).

Figure (PageIndex2): Hydrogen peroxide is frequently offered as a (3\%) by volume solution for usage as a disinfectant.

It should be noted that, unprefer in the case of mass, you cannot ssuggest add together the volumes of solute and solvent to acquire the last solution volume. When including a solute and also solvent together, mass is conserved, however volume is not. In the instance above, a solution was made by founding through (40 : extmL) of ethanol and adding enough water to make (240 : extmL) of solution. Simply mixing (40 : extmL) of ethanol and also (200 : extmL) of water would not give you the very same result, as the last volume would probably not be precisely (240 : extmL).

The mass-volume percent is also supplied in some instances and is calculated in a comparable means to the previous two percentperiods. The mass/volume percent is calculated by dividing the mass of the solute by the volume of the solution and expushing the outcome as a percent.

For instance, if a solution is all set from (10 : ceNaCl) in sufficient water to make a (150 : extmL) solution, the mass-volume concentration is

<eginalign extMass-volume concentration & frac extmass solute extvolume solution imes 100\% \ &= frac10 : extg : ceNaCl150 : extmL solution imes 100\% \ &= 6.7\% endalign>


muzic-ivan.infoists mainly need the concentration of services to be expressed in a means that accounts for the number of pwrite-ups present that could react according to a particular muzic-ivan.infoical equation. Since portion measurements are based upon either mass or volume, they are mostly not beneficial for muzic-ivan.infoical reactions. A concentration unit based on moles is preferable. The molarity (left( extM ight)) of a solution is the variety of moles of solute liquified in one liter of solution. To calculate the molarity of a solution, you divide the moles of solute by the volume of the solution expressed in liters.

< extMolarity : left( extM ight) = frac extmoles of solute extliters of solution = frac extmol extL>

Keep in mind that the volume is in liters of solution and not liters of solvent. When a molarity is reported, the unit is the symbol ( extM), which is check out as "molar". For example, a solution labeled as (1.5 : extM : ceNH_3) is a "1.5 molar solution of ammonia".

Example (PageIndex1)

A solution is prepared by disaddressing (42.23 : extg) of (ceNH_4Cl) right into enough water to make (500.0 : extmL) of solution. Calculate its molarity.


Tip 1: List the known quantities and also plan the difficulty.


Mass of (ceNH_4Cl = 42.23 : extg) Molar mass of (ceNH_4Cl = 53.50 : extg/mol) Volume of solution (= 500.0 : extmL = 0.5000 : extL)


Molarity (= ? : extM)

The mass of the ammonium chloride is initially converted to moles. Then, the molarity is calculated by dividing by liters. Note that the given volume has been converted to liters.

Tip 2: Solve.

<42.23 : extg : ceNH_4Cl imes frac1 : extmol : ceNH_4Cl53.50 : extg : ceNH_4Cl = 0.7893 : extmol : ceNH_4Cl>

Tip 3: Think around your result.

The molarity is (1.579 : extM), meaning that a liter of the solution would contain 1.579 moles of (ceNH_4Cl). Having four considerable figures is correct.

Figure (PageIndex3): Volumetric flasks come in many kind of sizes, each designed to prepare a different volume of solution.


When additional water is included to an aqueous solution, the concentration of that solution decreases. This is bereason the number of moles of the solute does not adjust, but the total volume of the solution increases. We have the right to erected an ehigh quality in between the moles of the solute before the dilution (1) and the moles of the solute after the dilution (2).

< extmol_1 = extmol_2>

Because the moles of solute in a solution is equal to the molarity multiplied by the volume in liters, we deserve to set those equal.

Finally, because the two sides of the equation are set equal to one another, the volume deserve to be in any kind of units we pick, as lengthy as that unit is the exact same on both sides. Our equation for calculating the molarity of a diluted solution becomes:

In addition, the concentration can be in any various other unit as long as (M_1) and (M_2) are in the same unit.

Suppose that you have (100. : extmL) of a (2.0 : extM) solution of (ceHCl). You dilute the solution by adding sufficient water to make the solution volume (500. : extmL). The new molarity have the right to conveniently be calculated by utilizing the above equation and fixing for (M_2).

The solution has been diluted by a variable of 5, considering that the new volume is five times as good as the original volume. Consequently, the molarity is one-fifth of its original value. Anvarious other widespread dilution trouble entails deciding exactly how a lot a extremely concentrated solution is compelled to make a desired amount of solution through a lower concentration. The highly concentrated solution is commonly described as the stock solution.


Concentration is vital in healthtreatment because it is provided in so many kind of means. It"s additionally important to usage systems with any type of worths to ensure the correct dosage of medications or report levels of substances in blood, to name just 2.

Another way of looking at concentration such as in IV solutions and also blood is in terms of equivalents. One equivalent is equal to one mole of charge in an ion. The value of the equivalents is always positive regardless of the charge. For example, (ceNa^+) and also (ceCl^-) both have actually 1 indistinguishable per mole.

<eginarrayll extbfIon & extbfEquivalents \ ceNa^+ & 1 \ ceMg^2+ & 2 \ ceAl^3+ & 3 \ ceCl^- & 1 \ ceNO_3^- & 1 \ ceSO_4^2- & 2 endarray>

Equivalents are supplied bereason the concentration of the charges is necessary than the identification of the solutes. For instance, a conventional IV solution does not contain the exact same solutes as blood but the concentration of charges is the very same.

See more: Fleet Foxes He Doesn T Know Why Lyrics, Fleet Foxes

Sometimes, the concentration is reduced in which case milliequivalents (left( extmEq ight)) is an extra correct unit. Similar to metric prefixes supplied through base devices, milli is provided to modify equivalents so (1 : extEq = 1000 : extmEq).