When we talk about the concentration of a solution, the mind hits on the water and sugar. The addition of sugar in water is the basic hint to understanding the mechanism for the concentration of a solution. This article will be covering on different types of percentage concentrations of solution along with formulas, derivations, and examples.

What is the concentration of a solution?

The concentration of a solution is defined as the ratio of solute to solvent. A concentrated solution is one where the amount of solute is much greater than the amount of solvent. This means that the solute molecules are packed together tightly, making it difficult for solvent molecules to enter the space between the solute molecules. When we add water to sugar, we create a concentrated sugar solution. Sugar molecules are packed together tightly because they are attracted to each other due to their polarity. Water molecules are polar but not as strongly as sugar molecules. Therefore, water molecules cannot penetrate the sugar molecules as quickly as sugar molecules can penetrate the water molecules.

In simple words, the concentration of a solution is the measurement of the amount of a solute dissolved in each amount of solvent.

As per concentration of a solution, there are two types of solution

1. A concentrated solution: If a solution has a large amount of dissolved solute.
2. A dilute solution: If a solution has a small amount of dissolved solute.

There are some common ways to describe the concentrations of a solution as below:

1. Molarity
2. Normality (Less commonly used)
3. Molality (Less commonly used)
4. Weight-by-weight (Less commonly used)
5. Weight-by-volume
6. Volume-by-volume

What is the percentage of a solution?

The percentage of a solution is the simplest way to represent the concentration of a solution in percentage. It is an efficient, convenient, and easy way to describe the solution concentrations. There are three types of percentage solutions commonly used in chemistry and chemical engineering:

1. Percentage weight by weight (w/w)
2. Percentage weight by volume (w/v)
3. Percentage volume by volume (v/v)

What is the percentage weight by weight (w/w)?

Percentage weight by weight (w/w) is the easiest way to describe a solution but is not often used in experiments.

For example,

“We dissolve sugar in water. Take 10-gram sugar and mix in 90 grams (equivalent to 90 ml) of water. Now, it can be said that the solutions simply as 10% sugar in water. The concentration of sugar in water will be on a (w/w) basis. It should be noted that the weight of water strictly depends upon the density of water, and the final weight of the solution is not necessarily equal to the final volume.”

Definition and formula:

A weight by weight (w/w) percent concentration can be defined as the weight (mass) of solute divided by the volume (in gram) of solution and multiplied by 100%. The mathematical expression for weight by weight (w/w) percent concentration is below:

Percent\;of\;mass\;(w/w)\;=\frac{mass\;of\;solute}{mass\;of\;solution}\;\times100

If the solute is solid in a solution, the concentration will be expressed as a weight (w/w) or mass (m/m). To prove the above equation, take an example.

Example 1: Prepare a solution in which 30 grams of salt (NaCl) into 100 grams of water. Now we can calculate the percent by weight or mass as below:

Suppose that a solution was prepared by dissolving 25.0 g of sugar into 100 g of water. The percent by mass would be calculated by:

Percent\;of\;mass\;(w/w)\;=\frac{25\;g\;sugar}{25\;g\;sugar+100\;g\;water\;}\;\times100

\mathrm{Percent}\;\mathrm{of}\;\mathrm{mass}\;(\mathrm w/\mathrm w)\;=\frac{25\;\mathrm g\;\mathrm{sugar}}{125\;\mathrm g\;\mathrm{solution}\;\;}\;\times100\;=\;20\;\%\;\mathrm{sugar}

 

Example 2: If you are going to make 300 g of 10 % solution of sodium chloride (NaCl). How much solute will be needed?

Using the same formula of percent concentration of a solution (w/w) as above:

Percent\;of\;mass\;(w/w)\;=\frac{mass\;of\;solute}{mass\;of\;solution}\;\times100

Put the values:

10\;=\frac{\mathrm{Mass}\;\mathrm{of}\;\mathrm{solute}\;(\mathrm g)}{300\;(\mathrm g)}\;\times100

\mathrm{Mass}\;\mathrm{of}\;\mathrm{solute}=30\;g

The answer will be 30 g, you would need to weigh out 30 g of NaCl and add it to 270 g of water.

 

What is the percentage weight by volume (w/v)?

Percentage weight by volume (w/v) is the general and easy way to describe a concentration of a solution. This method of calculation is often used in experiments because of its easiness. In the weight by volume (w/v) basis concentration the solids are dissolved in liquids solvent. The measurement of liquid solvent is easy than the weight of solvent, that’s why this is easy to use in general experiments.

Definition and formula:

A weight by volume (w/v) percent concentration can be defined as the weight (mass) of solute divided by the volume of solution and multiplied by 100%. The mathematical expression for weight by volume (w/v) percent concentration is below:

Percent\;of\;mass\;(w/v)\;=\frac{mass\;of\;solute}{mass\;of\;solution}\;\times100

 

Example 1: If we dissolve sugar in water. Take 10-gram sugar and mix in 100 ml water of final volume.

\mathrm{Percent}\;\mathrm{concentration}\;(\mathrm w/\mathrm v)\;\%\;=\frac{10\;\mathrm g}{100\;\mathrm{mL}}\times100\;=10\%

Now, it can be said that the solutions simply as 10 % sugar in water. The sugar concentration in water will be on the weight by volume (w/v) basis.

 

Example 2: Dissolve 1 gram of salt (NaCl) into a final volume of 100 ml of water.

\mathrm{Percent}\;\mathrm{concentration}\;(\mathrm w/\mathrm v)\;\%\;=\frac{1\;\mathrm g}{100\;\mathrm{mL}}\times100\;=10\%

This solution will be called a 1% NaCl solution on the weight by volume (% w/v) basis.

What is the percentage volume by volume (v/v)?

Percentage volume by volume (v/v) is the easiest way to describe a solution’s concentration of a solution. On the volume by volume (v/v) basis, the liquid as a solute is mixed in a liquid solution. In this method, the solutes are typically prepared volumetrically. Furthermore, the addition of solutes in the solvent has required a kind of attention to get an exact desired concentration.

Definition and formula:

A volume by volume (v/v) percent concentration can be defined as the volume of the solute divided by the volume of solution and multiplied by 100%. The mathematical expression for volume by volume (v/v) percent concentration is below:

\mathrm{Percent}\;\mathrm{concentration}\;(\mathrm v/\mathrm v)\;\%\;=\frac{\mathrm{volume}\;\mathrm{of}\;\mathrm{solute}}{\mathrm{volume}\;\mathrm{of}\;\mathrm{solution}}\times100

Example 1: If we add 40 mL of ethanol with 60 mL of water. The percentage concentration of the solution (v/v) can be calculated as below:

\mathrm{Percent}\;\mathrm{concentration}\;(\mathrm v/\mathrm v)\;\%\;=\frac{40\;\mathrm{mL}}{(40+60)\;\mathrm{mL}}\times100\;=40\;\%

The solution will be known as 40% ethanol solution on the volume by volume (% v/v) basis.

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