# Definition of Molality and Formula – Clear Examples

Molality of a solution can be tested by adding a few solvents. When we are making a syrup, we surely dissolve syrup into the water. The more syrup that is poured, the sweeter the drinks get. Syrup is called as the solute and water is called the solvent. In a chemical calculation, the number of solute inside a solvent is called a concentrate. Solution concentrate needs to be calculated precisely by determining the mass of the solute and solvent. Here’s we will discuss about definition of molality and formula.

Molality Definition

When we are measuring the physical parameter of a solution, what should we do? For certain purpose, the usage of molality indeed is the most conventional choice. But, when we want to know the solute concentration in a situation where there’s a changing in temperature, molality won’t work. This is because the solution’s volume will change slightly along with the temperature, that changes turns out to have a slight effect to give an inaccuracy that’s supposed to be accurate. There’s another parameter that’s needed, something that is not affected by the temperature.

Another way that we can use to express a solution’s concentrate is by its molality. Molality (m) from a solution is the solute’s mole divided by the kilogram of its solvent. E.g. when a solution contains 1,0 mole of NaCl dissolved in a kilogram of water, then it will be called “one molal” solution of Sodium chloride. The symbol of molality is written in a lower case “m”.

Molality is different to molarity, not only by its expression, but also by its use. Molarity is based by solution’s liter while molality is based on solvent’s kilogram. Concentration usage in molality is when we are learning solution’s properties that correlates with vapor pressure and temperature changes. On the other hand, molarity is used effectively because its number did not change with temperature changes. While volume of a solution, on the other side, slightly depends on temperature.

Molality and molarity is closely related with the number for diluted water solution because the solidity of a diluted solution is relatively close to 1,0g/ml. This thing indicates that 1,0L of solution has a mass almost equal to 1,0kg. When a solution in a concentrated state, its density will change so that it will slowly stay away from 1,0g/ml and causes a difference in its molality and molarity. But, for solution other than water, the molality is very different from its molarity. You are suggested to pay attention to the quantity that’s currently used to every given problem.

Molality is a concentrate of a solution that states the number of molecule (n) of solute inside a kilogram or 1000 gram of solute. Mole is the base international unit that measure the number of a substance. The term “mole” is first introduced by Wilhelm Ostwald in 1893, even though there’s a concept of mass equivalent that had been used a century before.

The formula of a molality can be expressed as below.

Molality (m) = total solvent mole / 1 kg solvent.

m = g/Mm x 1000/p

Where:

m = molality (mole/kg)

g = solute mass (g)

Mm = substance’s molar mass (g/mole)

P = solute mass (g)

Concentration of Solution

Solution is a homogenous mixture made of two substances, those are solute and solvent. When we are making a solution, we will have a solute, a substance that will be dissolved, and a solvent. The most common solvents are water and distilled water. The total solute that is dissolved in a solvent is expressed as the concentration of solution. There are several ways to express the difference of solute inside a solvent quantitatively, it is molality (molarity (M), molality (m), also normality(N), but normality will be discussed in another post).

Concentration of solution can be in the form of molality, molarity, or even the difference of both, mole fraction, and mass percentage. The sub discussion of molality and mole fraction that will be discussed are definition of molality, relation between molality and mass percentage, relation between molality and molarity, difference of molality and molarity, definition of mole fraction, formula of solvent mole fraction (Xp) and formula of solute mole fraction (Xt).

Here are the explanations.

1. #### Relation Between Molality and Mass Percentage

Mass percentage is a concentration unit that is usually used in a chemical solution. E.g. a solution that we usually see every day, 75% alcohol and 24% vinegar. Mass percentage that is meant is the total mass of solute inside a 100gram of solution’s mass.

To make it simpler, mass percentage is mass of the solute divided by the mass of solution (solute’s mass + solvent’s mass) multiplied with 100. The formula is expressed as below.

Mass% = solute’s mass/solution’s mass x 100%

1. #### Relation Between Molality and Molarity

Molarity states the total mole of a solute inside a liter of solution. Molarity can be converted into molality, by changing its solution’s volume into mass of solution. The changing of volume into mass needed the density of solution (p), from above explanation we can expressed the formula as below

Density (p) = mass of solution/volume of solution

Density is a measurement of mass for every volume unit of an object. The higher the density of an object, the bigger its mass per volume is. Density unit in “CGS (centi – gram – second)” is: gram per centimeter cubic (g/cm3).

1. #### Difference of Molality and Molarity

If we discussed the relation of molality and molarity earlier, now we will discuss the difference of molality and molarity. Molality expressed the number of solute’s mole inside a 1000gram of solvent while molarity expressed the number of solute’s mole inside a liter of solution. Molarity is notated as M and its unit is mole/liter.

### Mole Fraction

Mole fraction is a measurement of solution’s concentration that expressed the ratio of mole of a partial substance to the total mole of a solution. Mole fraction is divided into two, solute mole fraction and solvent mole fraction.

1. #### Solute Mole Fraction (Xt)

Solute mole fraction is expressed as below.

Xt = Nt/(Nt+Np)

Where:

Xt = Solute mole fraction

Nt = Total mole of solute

Np = Total mole of solvent

1. #### Solvent Mole Fraction (Xp)

Solvent mole fraction is expressed as below.

Xp = Np/(Nt+Np)

Where:

Xp = solvent mole fraction

Nt = total mole of solute

Np = total mole of solvent

The total of solute mole fraction and solvent mole fraction is 1

Xt + Xp = 1

More Chemistry Hacks:

### Molality Exercises

1. What is the molality of a solution with 4 gr NaOH (Ar Na = 23 gr/mole, Ar O = 16 g/mole, and Ar H = 1 gr/mole) dissolved in 250 gr water?

Known:

• Mass of NaOH = 4 gr
• Ar Na = 23 gr/mole
• Ar O = 16 g/mole
• Ar H = 1 gr/mole
• mass of water = 250 gr = 0,25 kg

Solution:

Mr NaOH = 40 gr/mole

Total mole of NaOH = mass/Mr

Total mole of NaOH = 4 gr/(40 gr/mole)

Total mole of NaOH = 0,1 mole

m = Total mole/p

m = 0,1 mole/0,25 kg

m = 0,4 m

1. Determine the molality of a solution that is made by dissolving 12 gram urea CO(NH2)2 in 250 gram of water.

Known:

• mass of urea = 12 gr
• Mr Urea= 60 g/mole
• Mass of solvent = 250 gr = 0,25 kg

Solution:

Total mole of Urea = mass/Mr

Total mole of Urea = 12 gr /(60 g/mole)

Total mole of Urea = 0,2 mole

m = Total mole/mass of solvent

m = 0,2 mole /0,25 kg

m = 0,8 m

1. What is the molality of HCl 37% solution (w/w)? (Ar H = 1 g/mole, Ar Cl = 35,5 g/mole)

Known:

• Masss of HCl = 37%
• Ar H = 1 g/mole
• Ar Cl = 35,5 g/mole

Solution:

Mr HCl = 36,5 gr/mole

If the solution mass is 100 gr, then the mass of HCl:

Mass of HCl = 37% x 100 gr

Mass of HCl = 37 gr

Mass of solvent = mass of solution – mass of HCl

Mass of solvent = 100 gr – 37 gr

Mass of solvent = 63 gr = 0,063 kg

Total mole of HCl = mass/Mr

Total mole of HCl = 37 gr /(36,5 gr/mole)

Total mole of HCl = 1,01 mole

m = total mole/mass of solvent

m = 1,01 mole /0,063 kg

m = 16,03 m

More Chemistry Hacks:

1. Determine the total (gram) of NaOH that has to be dissolved in 1 liter of water (air = 1,00 g/mL) so that 0,25 m of NaOH is acquired.

Explanation:

1 L water = 1.000 mL = 1.000 g (ρ water = 1,00 g/mL)

NaOH = gr / Mr x 1.000 / P

0,25 =gr / 40 x 1.000 / 1.000

0,25 = g/40

g = 0,25 x 40 = 10 gram

So, the total of NaOH needed is 10gram.

1. Determine how many mL volumes of water is needed to dissolve 4,9gram H2SO4that has 0,25 M concentration (ArH = 1; S = 32; O =16)

Explanation:

m =gr / Mr x 1.000 / P

0,25 =4,9 / 98 x 1.000 / p

p = 20 gram (20 mL)

So, volume of water needed = 20 ml.

So, that’s all about definition of molality and formula. Molality itself is considered as colligative property of a solution. This can also be applied in everyday life like when we are pouring a milk and then we add it with water so the solute is less than the solvent. Hopefully it’s helpful.