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Relationship between Molarity and molality

Molarity (M) refers to the number of moles of solute per liter of solution. It is commonly used in the laboratory to express the concentration of a solution. For example, if a solution contains 2 moles of sodium chloride in 1 liter of water, its molarity is 2 M.

Molality (m) refers to the number of moles of solute per kilogram of solvent. Unlike molarity, molality does not depend on temperature or pressure. It is often used in thermodynamic calculations and is particularly useful in determining the freezing point depression and boiling point elevation of a solution.

Relationship Between Molarity and Molality

The relationship between molarity and molality is based on the density of the solution. Density is defined as the mass of a substance per unit volume. In the case of a solution, the mass includes both the solute and solvent.

Density (ρ) can be calculated using the formula:

ρ = mass/volume

For a solution, the mass of the solute (m) can be expressed as:

m = nM

where n is the number of moles of solute and M is the molarity. The mass of the solvent (Msolvent) can be expressed as:

Msolvent = Vsolution x ρsolvent

where Vsolution is the volume of the solution and ρsolvent is the density of the solvent.

The total mass of the solution can be expressed as:

Msolution = m + Msolvent

Substituting the equations for m and Msolvent, we get:

Msolution = nM + Vsolution x ρsolvent

Dividing both sides by the mass of the solvent, we get:

Msolution/Msolvent = nM/Msolvent + Vsolution x ρsolvent/Msolvent

The left side of the equation is the molality (m), while the first term on the right side is the molarity (M). The second term on the right side represents the volume fraction of the solution, which can be expressed as the ratio of the volume of the solute to the volume of the solution.

Therefore, the relationship between molarity and molality is:

m = M x (ρsolvent/1000) / (1 - M x (ρsolvent/1000))

where ρsolvent is the density of the solvent in g/mL.

Calculating Molarity and Molality


To calculate molarity, you need to know the number of moles of solute and the volume of the solution. For example, if you dissolve 0.5 moles of glucose in 1 liter of water, the molarity of the solution is 0.5 M.

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