Molality: Definition & Formula

In chemistry, knowing the concentration of a solution is very important. There are different ways to express the amount of concentration, and one of these is by calculating the molality. In this lesson, we discuss molality.
What Is Molality?
The concentration of a substance is very important in our daily lives. Household items, like rubbing alcohol, mouthwash, bleach and various cleaning products, can have various concentrations of their active ingredients. When we buy products, we sometimes take the concentration of the active ingredient into consideration, such as when buying a skin-treating astringent; it is either one percent or two percent salicylic acid, so we make our choice based on how sensitive our skin is.
Chemists also have to be aware of the concentration of solutions they use during laboratory procedures. One of the ways concentration is expressed is through molality. Molality, symbolized by a small ‘m,’ is the number of moles of solute per kilograms of solvent.
Formulas Needed for Problem Solving
The unit of molality is, therefore, expressed in moles per kilogram. The formula for molality is m = moles of solute / kilograms of solvent.
In problem solving involving molality, we sometimes need to use additional formulas to get to the final answer. One formula we need to be aware of is the formula for density, which is d = m / v, where d is density, m is mass and v is volume. Let’s use the density triangle as another way to remember.
You can use the placement of the letters in the triangle to know how to find the value for any of the variables:
Density = mass / volume
Mass = density * volume
Volume = mass / density
In molality, the unit is in moles of solute per kilogram of solvent. There are times when we are given the mass of the solvent in grams. Since we know that one kilogram equals 1,000 grams, we can convert the number of grams into kilograms. Just multiply the number of grams, x, by 1 kilogram over 1,000 grams.
Sometimes, we are given the number of grams of solute. Molality is the moles of solute per kilogram of solvent. To convert the number of grams of solute to moles of solute, we follow the equation: moles of solute = mass of solute / molar mass solute.
To find the molar mass, we need to count the number of atoms for each element and get the sum of all the atomic masses of the atoms in the chemical compound. We can get these from the periodic table. The molar mass equals the sum of the number of atoms times the atomic mass of atoms.
Let us go over a few examples of common problems encountered when we want to find the molality of a substance.
Problem Solving: Example 1
Example 1: What is the molality of a solution containing 0.75 moles of sodium hydroxide in 500 milliliters of water? The density of water is 1 gram per milliliter.
We can find the solution by plugging into the equation of mass = density * volume = 1 gram per milliliter * 500 milliliters. Therefore, mass = 500 grams. Convert the grams to kilograms by multiplying 500 grams * 1 kilogram / 1000 grams. This equals 0.5 kilograms of water.
Molality equals moles per kilogram, so the molality is 0.75 moles sodium hydroxide / 0.5 kilograms water, which equals 1.5 m or moles per kilogram. The molality of the solution has 1.5 moles of sodium hydroxide per kilogram of water.
Problem Solving: Example 2
Let’s try a second example: What is the molality of a solution containing 85 grams of sodium hydroxide in 1 kilogram of water?
Well, to determine the number of moles of solute, we need to first find the molar mass of our solute, sodium hydroxide.
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Additional Activities
Molality is one of the ways to express the concentration of a solution. The equation for molality is moles of solute divided by the mass of solvent in kilograms. Let’s practice working through some word problems involving molality.
Practice Problems
1. A student dissolves 5 grams of magnesium chloride in 500 grams of water. What is the molality of the solution?
2. You need to make a 0.1 molal solution of silver sulfate. You are told to use all of the silver sulfate powder in the bottle, which is 14.3 grams. How much water do you need to add to make this solution?
1. First we need the chemical formula for magnesium chloride, which is MgCl2. Now we need the molar mass of this compound:
1(Mg) + 2(Cl) = 1(24.31 g/mol) + 2(35.45 g/mol) = 95.21 g/mol
Next we need to convert the given mass to moles:
5 g x (1 mol) / (95.21 g) = 0.0525 mol
The solvent (water) mass has to be in kilograms, so we have 0.5 kg of water. Now we can calculate the molality:
m = moles solute / kg solvent
m = 0.0525 mol / 0.5 kg
m = 0.105 molal
2. The formula for silver sulfate is Ag2 SO4. Now we need to calculate the molar mass of silver sulfate:
2(Ag) + 1(S) + 4(O) = 2(107.87 g/mol) + 32.06 g/mol + 4(16 g/mol) = 311.8 g/mol
Converting the given mass to moles is next:
14.3 g x (1 mole) / (311.8 g) = 0.0459 mole
Solving for the mass of water is next:
m = moles solute / kg solvent
0.1 = 0.0459 / x
x = 0.459 kg water needed
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