See also Mixtures, Solutions and Suspensions , Solubility product constants and Solubility guidelines for ionic compounds in water
Molarity expresses the molar concentration of a compound in a solution, how many moles of the solute in a given volume of the solution:
M = n / V 
n: number of moles of solute [mol]
M: Molarity of the solution [mol/L] or [M]
V: volume of the solution [L]
The unit for molarity is molar, with the symbol M: 1 M = 1 mol/L, where L refers to the volume of the whole solution. A solution with a concentration of 1 mol/L is equivalent to 1 molar (1 M).
From the definition, we can calculate the number of moles of the solute, n,:
n = M * V 
Dilution is the prosess where a solution is added more of the solvent to decrease the concentration of the solute.
In dilution, the amount of solute does not change, the number of moles are the same before and after dilution.
If subscript "i" represents initial and "f" represents the final values of the quantities involved, we have:
n i = M i * V i and n f = M f * V f
n i = n f and thus,
M i * V i = M f * V f 
From this we can calculate the final molarity after dilution :
M f = M i * V i / V f 
or we can calculate the needed final volume to reach a wanted final molarity:
V f = M i * V i / M f 
What is the strenght (in wt%) of a solution where 56 gram salt is dissolved in 0.8 kg water?
First, we need to have the same unit for salt and water, and convert kg to g: 0.8 kg water = 800 g water
Then, we can calculate the persentage of salt in the water solution: g salt /g total solution *100%
56 [g]/(800+56) [g]* 100% = 6.54 wt% salt in the water solution.
Sodium chloride, NaCl, is the salt used for cooking. This salt has a solubility of 36 g in 100 g of water at 25°C.
1. A saturated solution contains the maximum amount of solute in the solvent, which for NaCl is 36 grams in water at 25°C. Then, the concentration of the saturated solution is:
NaCl concentration = 36 [g]/(100 + 36)[g] * 100% = 26.5 wt%
2. 34 g NaCl is less than the solubility, which means that all the salt will be solved in water at 25°C.
NaCl concentration = 34 [g]/(100+34) [g] * 100% = 25.4 wt%
3. 38 g NaCl is more than the solubility of NaCl in water. This means that the solution will be saturated and some of the salt will remain undissolved. The concentration of the saturated solution is the same as in case 1:
NaCl concentration = 36 [g]/(100 + 36)[g] * 100% = 26.5 wt%
The 2 grams excess of salt will be present as a solid phase.
You add 200 gram of salt (NaCl) into enough water to make exactly 5 L of a salt water solution. What is the molarity of the solution?
Molweight of Na is 22,99 g/mol and molweight of Cl is 35,45 g/mol.
Molar weight of NaCl: 22.99 [g/mol] + 35.45 [g/mol] = 58.44 [g/mol]
Number of moles of NaCl: 200 [g] /58.44 [g/mol] = 3.42 [mol NaCl]
Molarity of solution: 3,42 mol NaCl / 5 L solution = 0.684 mol/L = 0.684 M
You want 2 liter of a 1M solution of acetic acid (CH 3 COOH) in water. How much 100% acetic acid do you need to add (in mol, in gram and in liter)?
1M solution means 1 mol acetic acid per liter of solution.
Moles needed to 2 liter solution: 2 [L] * 1 [mol/L] = 2 mol acetic acid
Molweight of C : 12.01 g/mol, molweight of H : 1.01 g/mol, molweight of O : 16.00 g/mol.
Molweight of acetic acid: 2*12.01 [g/mol]+ 4*1.01 [g/mol] + 2*16.00 [g/mol] = 60.06 [g/mol]
Gram needed to 2 liter solution: 2 [mol] * 60.06 [g/mol] = 120.12 g acetic acid
Density of 100% acetic acid at 20°C is 1.048 g/cm 3
Volume needed to 2 liter solution: 120.12[g] / 1.048 [g/cm 3 ] = 114.62 cm 3 = 114.62 ml = 0.115 L acetic acid
NB! Never start with adding water to undiluted acid!
Practical tip :Use a container with a precise definition of 2 L. Add 1 liter water and then 0.115 L acetic acid (measured at 20°C) and rotate the container to blend the liquids. Add carefully more water untill you reach 2 liter total volume.
You have 500 mL left of the solution with 1M acetic acid. Now you need 100 mL of a 0.3M solution. How can you make that without using more of the 100% acetic acid?
The simplest way is to dilute the 1M solution, which we do by adding more water to it.
From equation  above:
V f = 100 mL=0.100 L and M f = 0.3M = 0.3 mol/L
M i = 1M = 1 mol/L, while V i = unknown (we dont know how much we need of the starting solution)
V i = V f * M f /M i = 0.100 [L] * 0.3 [mol/L] / 1[mol/L] = 0.03 [L] = 30 mL of the 1M solution .
So, start with 30 ml of the 1 M solution and add water until you have exactly 100 ml of the diluted solution.
Number of moles acetic acid wanted in final solution: 0.100[L] * 0.3[mol/L] = 0.03 mol acetic acid
Number of moles from the 1 M solution: 0.03[L] * 1[mol/L] = 0.03 mol acetic acid
n i = n f (we have useed the correct amount of 1M solution
The SI-system, unit converters, physical constants, drawing scales and more.
Material properties of gases, fluids and solids - densities, specific heats, viscosities and more.
Calculator and formulas for conversion between different units of concentration: Molarity, molality, mole fraction, weight percent of solute and grams of solute per liter of solution - descriptive terms for solubility.
Changes in density of aqueous solutions with changes in concentration at 20°C. Density of inorganic chlorides in water is plotted as function of wt%, mol/kg water and mol/l solution.
Changes in density of aqueous solutions with changes in concentration at 20°C. Density of potassium salts in water is plotted as function of wt%, mol/kg water and mol/l solution.
Changes in density of aqueous solutions with changes in concentration at 20°C. Density of inorganic sodium salts in water is plotted as function of wt%, mol/kg water and mol/l solution.
Changes in density of aqueous solutions with changes in concentration at 20°C. Density of acetic acid, citric acid, formic acid, D-lactic acid, oxalic acid and trichloroacetic acid in water is plotted as function of wt%, mol/kg water and mol/l solution.
Changes in density of aqueous solutions with changes in concentration at 20°C. Density of some sugars, alcohols and other organic substances in water is plotted as function of wt%, mol/kg water and mol/l solution.
Changes in density of aqueous solutions with changes in concentration at 20°C. Density of inorganic substances in water is plotted as function of wt%, mol/kg water and mol/l solution.
The elements of the periodic system with names, symbols, atomic numbers and weights, melting and boiling points, density, electronegativity and electron affinity, and electron configuration.
Density of hydrocarbons like alcohols and acids as function of carbon number at 20°C / 68°.
Guidelines or solubility rules to predict whether or not a given ionic compound is soluble in water at room temperature.
Mixtures vs. solutions vs. suspensions.
The mole is the SI base unit for an amount of a substance.
ppm - or parts per million - is commonly used as a unit of concentration.
The equilibrium constant, Ksp, for aqueous solutions of ionic compounds at 25°C.
Solubility of sugar in water.
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