# Solution Dilution Calculator

Created by Gabriela Diaz
Last updated: Jul 04, 2022

You'll see that the solution dilution calculator is a versatile tool. You can use the calculate how to dilute a solution or to find the concentration of a dilute solution.

You may also use this tool to calculate the stock solution required to obtain a desired molarity of a dilute solution or to find the concentration of the stock solution.

## Concentration of a solution

A solution is a homogeneous mixture of two or more components that cannot be identified by sight. This is because the components are of molecular dimensions.

Solutions are composed of solute and solvent:

$\small \text{Solution = Solute + Solvent}$

The solvent is always in greater amounts than the solvent, meaning that the solute is the dissolved substance. The processes for which dilution is possible are chemical dilution, solvation, and hydration. There are no chemical reactions in the latter two.

A solution's concentration is a measure of how much solute has been dissolved in a given quantity of solvent or solution:

$\small \text{Concentration = } \cfrac{\text{Solute}}{\text{Solution}}$

Depending on the amount of solute, we can distinguish between concentrated and dilute solutions. The former refers to a solution with a large amount of solute, whereas the latter refers to a solution with a lower amount of solvent.

Nevertheless, these are relative terms; for example, a concentrated sulfuric acid H2SO4 solution normally has a concentration of 98%, yet a solution of hydrochloric acid HCl at 38% can be considered a concentrated solution as well.

That is why quantitative expressions for the concentrations of solutions are used. Since the amounts of solute and solvent can be measured in weight, volume, or moles, there are a few methods for describing concentration, some of which are as follows:

• Percent — This composition indicates the percentage of the solution that corresponds to the solute. It can be expressed in weight or volume as m/m, v/v, m/v, with weight composition (m/m) being the most common.
• Molality — Expresses the number of moles per 1000 g of solvent.
• Molarity — Indicates the number of moles of solute $n$ per liters or m3 of solution $v$$M = n / v$. The unit is the molar (M).
• Formality — Similar to molarity, formality is calculated as moles of solute per liter of solution, with the difference that formality does not consider what happens to the solute once dissolved. It's expressed in formals (F).
• Mole fraction — Gives the ratio between the number of molecules of a particular component in a solution, either the solute or the solvent, and the total number of moles of solution ($n_{\text{solute}} + n_{\text{solvent}}$).
• Parts per million or parts per billion (ppm or ppb) — This expresses the concentration in mass, as the ratios of grams of solute per one million or one billion grams of sample, respectively.

In this calculator, the concentrations of the solutions are expressed in molar (M).

## How to calculate dilution — Solution dilution formula

A dilute solution is obtained by adding more solvent to a solution of a given initial volume and concentration.

With this in mind, let's see how to dilute a concentrated solution? Imagine that we'd like to obtain 9 liters of 2 M dilute solution of sulfuric acid from a stock solution of 18 M. How can we calculate the stock solution that we need to achieve the specified molarity of the dilute solution? The solution dilution formula can provide an answer to this question.

By employing the solution dilution formula, you may determine the volume or concentration of the dilute or the stock solution by solving for the desired variable. The formula is as follows:

$\small m_1 \cdot V_1 = m_2 \cdot V_2$

where:

• $m_1$ — Initial concentration of stock solution;
• $m_2$ — Concentration of diluted solution;
• $V_1$ — Volume of the stock solution; and
• $V_2$ — Volume of diluted solution.

Returning to our example. By solving the volume $V_1$, which will correspond to the volume of the stock solution, we obtain that its value is 1 liter, which means that the final volume of the dilute solution (9 liters) is composed of the 1 liter of the solute and the remaining 8 liters area of solvent.

Do you need to express these volumes in other units? take a look at our volume converter.

## How to use the solution dilution calculator

To illustrate how to use the solution dilution calculator, suppose we want to determine the final volume of a dilute solution of 0.05 M obtained from 0.01 liters of stock solution of hydrochloric acid (HCl) of concentration 12 M:

1. In the first row of the calculator, Concentration (initial), input the concentration of the stock solution of HCl, 12 M.
2. In the Volume (initial) field, proceed to enter the volume of the stock solution. In our example, this is 0.01 liters.
3. Next, enter the desired concentration of the dilute solution. This corresponds to 0.05 M.
4. In the final row, Concentration (final), the calculator will show you the final volume of the dilute solution. In this case, 2.4 liters.

This is not the only use you can give to the solution dilution calculator. By providing three of the four variables involved in the tool, the calculator will determine the remaining one. This means that you could also use this tool to determine the volume of a stock solution of a given concentration, or find the volume of a stock solution given the parameters of the dilute solution, or find the molarity of a dilute solution.

Gabriela Diaz
Concentration (initial)
M
Volume (initial)
liters
Concentration (final)
M
Volume (final)
liters
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