# Molarity to molality and vice versa

This online calculator converts the molar concentration of a solution to molar concentration and vice versa if the density of the solution is known.

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#### Timur

Created: 2024-04-12 06:28:00, Last updated: 2024-04-17 07:14:29

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The translation requires the formula of the substance to be dissolved (you need the formula to determine molar mass), the density of the solution, and a known value, that is, either the molarity (molar concentration of the solution) or the molality (molar concentration of the solution). The calculator will find the unknown value. The calculation formulas are listed below the calculator.

#### Molarity to molality and vice versa

Molarity, M (mol/L)

Molality, mol/kg

Digits after the decimal point: 2

### Converting molar concentration to molar concentration and vice versa

Molar concentration is the amount of dissolved substance (mole number) in a unit volume of solution. It is denoted as C, the most common unit of measurement in practice is mol/L.
$C=\frac{n}{V}$
where n is the number of moles of the substance and V is the volume of the solution

Molar concentration is the amount of dissolved substance (number of moles) in 1000 g of solvent. It is denoted as m and the units are mol/kg.
$m=\frac{n}{m_s}$
where n is the number of moles of the substance and mₛ is the mass of the solvent, kg

Let us introduce the notations
mₐ - mass of the solution
ρ - density of the solution
mᵦ - mass of dissolved substance
M - molar mass of the dissolved substance

Then
$m_s=m_a-m_{\beta}$

and we can make the following transformations
$m=\frac{n}{m_s}=\frac{n}{m_a-m_{\beta}}=\frac{n}{\rho V - nM}=\frac{CV}{\rho V - CVM}=\frac{C}{\rho - CM}$.

From the resulting formula for calculating molality by molarity
$m=\frac{C}{\rho - CM}$

we can derive the inverse formula for calculating molarity by molality as well
$C=\frac{m\rho}{1 + mM}$

These formulas are what the calculator above uses.

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