# Dilution calculator and problems solver

This online calculator can calculate the molar concentration (molarity) of a solute or volume of a solution before or after the dilution.

These online calculators can help with dilution problems. Generally, in dilution problems, you either dilute a solution or mix two solutions with different concentrations. So, the first calculator below can solve dilution problems, and the second calculator below can solve mix problems. Theory and formulas can be found below the calculators.

### Dilute a solution problems solver

This calculator can solve the following types of problems:

1. Find the final molarity of a solution
2. Find the final volume of a solution
3. Find the initial molarity of a solution
4. Find the initial volume of a solution

To see examples for each type of problem, change the problem type in the calculator below.

#### Dilution calculator and problems solver

Example problem

Molarity of initial solution, mol/L

Volume of initial solution, liters

Molarity of final solution, mol/L

Volume of final solution, liters

Digits after the decimal point: 2

### Mix solutions problems solver

This calculator can solve the following types of problems:

1. Find the molarity of the final solution
2. Find the volume of the final solution
3. Find the molarity of one of the starting solutions

To see examples for each type of problem, change the problem type in the calculator below.

Example problem

#### Final solution

Molarity of final solution, mol/L

Volume of final solution

Molarity of second starting solution, mol/L

Digits after the decimal point: 2

### Dilution and molarity

Dilution is the process of decreasing the concentration of a solute in a solution, usually simply by mixing with more solvent, like adding more water to a solution. To dilute a solution means to add more solvent without the addition of more solute. The resulting solution is thoroughly mixed to ensure that all parts of the solution are identical.

Solution concentration is described with molarity (or molar concentration), which is the number of moles of solute per liter of solution, measured in mol/liter, denoted as M, and calculated as follows:

$M=\frac{\text{mol solute}}{\text{L of solution}}$

which can be rearranged like this

$M \cdot \text{L of solution}=\text{mol solute}$

The key to problem solving is the understanding that after dilution we still have the same amount of solute in moles. If we denote starting molarity as $M_s$, starting volume as $V_s$, final molarity as $M_f$ and final volume as $V_f$, we can write

$M_s \cdot V_s=\text{mol solute}=M_f \cdot V_f$,

which gives us the following proportion

$M_s \cdot V_s=M_f \cdot V_f$,

This equation is used in the first calculator. For example, to find final molarity, you use

$M_f =\frac{M_s \cdot V_s}{V_f}$

The same logic can be applied to the mix problems. Of course, we assume that the problems are about mixing the same solute, and there is no volume contraction upon mixing.

Thus, the equation look like follows:

$M_{s_1} \cdot V_{s_1} + M_{s_2} \cdot V_{s_2}=M_f \cdot V_f$, and

$V_{s_1} + V_{s_2}= V_f$

where $s_1$ and $s_2$ denotes two different starting solutions.

From these equations, it is easy to find the final values or unknown concentration of one of the starting solutions.

Sometimes dilution problem gives amounts of solute in grams. In this case, you need to know the solute's chemical formula and then convert the mass of the solute to the number of moles or find molarity. You can use Molar mass of the substance and Molarity calculator for this.

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PLANETCALC, Dilution calculator and problems solver