Mass % of any component of the solution = (Mass of the component in the solution / Total mass of the solution) x 100
Other methods are:
Volume percentage:
Volume % of a component = (Volume of the component/Total volume of the solution) x
100
Mass by volume percentage: It is the mass of solute dissolved in 100 mL of the solution.
i.e. Mass by Volume percentage = (Mass of solute in grams/Volume of solution in mL) x 100
Here's a point to be kept in mind : Whenever we say mass or volume of the solution, you need to add the respective masses and volumes of ALL the components of the solution. Do NOT commit the error of taking the mass or volume of
only the solute or solvent in the denominators of the above expressions.
The concentration of a solution is most of the time expressed as the number of moles of solute present in 1 Liter of the solution (also called molarity )
(There are also other ways to express
concentration. Please follow this link. )
EXAMPLE: (a) If 25 moles of NaCl are present in 100 L of a solution wherein H2O is the solvent, then the concentration of the solution is #25/100=0.25 "mol·L"^-1#.
(b) What is the molarity of a solution
prepared by dissolving 15.0 g of sodium hydroxide in enough water to make a total of 225 mL of solution?
Solution
Calculate the number of moles of solute present.
Moles of NaOH = 15.0 g NaOH × #(1"mol NaOH")/(40.00"g NaOH")# = 0.375 mol NaOH
Calculate the number of litres of solution present.
Volume = 225 mL × #(1"L")/(1000"mL")# = 0.225 L soln
Divide the number of moles of
solute by the number of litres of solution.
Molarity = #(0.375"mol")/(0.225"L")# = 1.67 mol/L
Let's address the question for both percent concentration by mass and for percent concentration by volume.
Percent concentration by mass is defined as the mass of solute divided by the total mass of the solution and multiplied by 100%. So,
#c% = m_(solute)/(m_(solution)) * 100%#, where
#m_(solution) = m_(solvent) + m_(solute)#
There are two ways to
change a solution's concentration by mass
Adding more solute - making the solution more concentrated;
Adding more solvent - making the solution more dilute;
Let's take an example to better illustrate this concept. Say we dissolve 10.0g of a substance in 100.0g of water. Our
concentration by mass will be
#c% = (10.0g)/(10.0g + 100.0g) * 100% = 9.09%#
Now let's try doubling the mass of the solute; the new concentration will be
However, if we keep the mass of the solute at 10.0g and doubled the mass of the solvent (in this case, water), the concentration will be
#c% = (10.0g)/(10.0g + 2*100.0g) * 100% = 4.76%#
The same is
true for percent concentration by volume, which is defined as the volume of the solute divided by the total volume of the solution and multiplied by 100%.
It's easy to see that manipulating either the volume of the solute or the volume of the solvent (or both) would change the solution's percent concentration
by volume.
There are two types of percent concentration: percent by mass and percent by volume.
PERCENT BY MASS
Percent by mass (m/m) is the mass of solute divided by the total mass of the solution, multiplied by 100 %.
Percent by mass = #"mass of solute"/"total mass of solution"# × 100 %
Example
What is the percent by mass of a solution that contains 26.5 g of glucose in 500 g of solution?
Solution
Percent by mass =
#"mass of glucose"/"total mass of solution" × 100 % = (26.5"g")/(500"g")# × 100 % = 5.30 %
PERCENT BY VOLUME
Percent by volume (v/v) is the volume of solute divided by the
total volume of the solution, multiplied by 100 %.
Percent by volume = #"volume of solute"/"total volume of solution"# × 100 %
Example
How would you prepare 250 mL of 70 % (v/v) of rubbing alcohol
Solution
70 % = #"volume of rubbing alcohol"/"total volume of solution" × 100 %# × 100 %
So
Volume of rubbing alcohol = volume of solution × #"70 %"/"100 %"# = 250 mL ×
#70/100#
= 175 mL
You would add enough water to 175 mL of rubbing alcohol to make a total of 250 mL of solution.
How do you calculate the percentage of salt in a solution?
Salt is the solute (the dissolving substance), and water is the solvent (the substance that dissolves another to create a solution). To make a salt solution by weight percent (w/v), you apply the formula w/v = (mass of solute ÷ volume of solution) × 100.
When 5 gram of sugar is dissolved in 25 gram of solvent the concentration of the sugar will be W W?
Explanation: The mass by volume percentage of 250 ml of a solution containing 5 g of sugar is 2%.
What is the percentage mass by mass amount of salt in the solution containing 5 grams of a salt dissolved in 25 grams of water?
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Total mass = 0.5+25=25.5%=0.5/25.5+×100=1.9607%. The value can be calculated with the amount of salt in that solution that gives answers percentage with dissolved in 25g of water.
What is the percentage by mass of 50g salt dissolve in a 500g of water?
Mass by vol % = 50 g / 500 ml x 100. Mass by vol % = 0.1 x 100 = 10 %