Molality: Videos & Practice Problems

Molality is a measure of solution concentration, defined as the number of moles of solute per kilogram of solvent, making it temperature-independent since it does not involve volume. The formula for molality (m) is:

$m=\frac{\mathrm{moles}\mathrm{of}\mathrm{solute}}{\mathrm{kilograms}\mathrm{of}\mathrm{solvent}}$

Osmolality, also known as ionic molality, considers the number of dissolved particles in a solution. For covalent compounds, this value is typically one, as they do not dissociate into ions. However, for ionic compounds, osmolality is calculated by multiplying the number of ions by the molality of the solution. For example, sodium chloride dissociates into two ions, sodium and chloride, resulting in an osmolality that is double the molality of the solution. Understanding these concepts is crucial for accurately determining solution concentrations, particularly in scenarios where temperature changes are a factor.

Molality

Molality, denoted by the lowercase m, is a crucial concept in chemistry for expressing the concentration of a solution. Unlike other concentration measures, molality is temperature independent, which is primarily due to its units not involving volume. This characteristic means that changes in temperature do not affect the measurement of molality.

Molality is defined as the number of moles of solute per kilogram of solvent. The formula for calculating molality is:

m = \frac{n_{solute}}{m_{solvent}}

where n_solute represents the moles of solute and m_solvent is the mass of the solvent in kilograms. Understanding this formula is essential for accurately determining the concentration of solutions in various chemical contexts.

Molality Calculation Example

To calculate the molality of a solution containing 24.8 grams of sucrose (C₁₂H₂₂O₁₁) dissolved in 550 grams of water, we start by understanding the definition of molality. Molality (m) is defined as the number of moles of solute per kilogram of solvent.

First, we convert the mass of the solvent (water) from grams to kilograms. Since 1 kilogram equals 1000 grams, we have:

550 grams of water = 0.550 kilograms.

Next, we need to determine the number of moles of sucrose. The molar mass of sucrose can be calculated by summing the atomic masses of its constituent elements:

• Carbon (C): 12 atoms × 12.01 g/mol = 144.12 g/mol
• Hydrogen (H): 22 atoms × 1.008 g/mol = 22.176 g/mol
• Oxygen (O): 11 atoms × 16.00 g/mol = 176.00 g/mol

Adding these together gives:

Molar mass of sucrose = 144.12 g/mol + 22.176 g/mol + 176.00 g/mol = 342.296 g/mol.

Now, we can calculate the moles of sucrose using the formula:

Number of moles = mass (g) / molar mass (g/mol).

Thus, the moles of sucrose are:

Number of moles = 24.8 g / 342.296 g/mol ≈ 0.07245 moles.

Now, we can calculate the molality of the solution:

Molality (m) = moles of solute / kilograms of solvent = 0.07245 moles / 0.550 kg ≈ 0.1318 mol/kg.

Considering significant figures, the final answer should be reported with three significant figures, resulting in:

Molality ≈ 0.132 mol/kg.

A solution is prepared by dissolving 43.0 g potassium chlorate, KClO₃, in enough water to make 100.0 mL of solution. If the density of the solution is 1.760 g/mL, what is the molality of KClO₃ in the solution?

• A. 1.99 m
• B. 3.51 m
• C. 2.64 m
• D. 4.70 m

Answer: (C)

The density of a 15.7 M methanol (CH₃OH) solution is 0.858 g/mL. If H₂O is the solvent, what is the molality of the solution?

• A. 44.2 m
• B. 18.3 m
• C. 31.2 m
• D. 23.7 m

Answer: (A)

Osmolality in Solutions

Osmolality, often referred to as ionic molality, quantifies the concentration of dissolved particles in a solution. For covalent compounds, the number of ions is considered to be one, as they do not dissociate into multiple particles. Therefore, the osmolality for covalent compounds is simply equal to one molecule.

The formula for calculating osmolality is expressed as:

\[ \text{Osmolality} = \text{Number of Ions} \times \text{Molality} \]

When dealing with ionic compounds, it is essential to break them down into their constituent ions. For instance, sodium chloride (NaCl) dissociates into two ions: sodium ions (Na⁺) and chloride ions (Cl^-). If we have a solution containing 2.5 moles of sodium chloride, we recognize that it produces a total of 2 ions. Thus, the calculation for osmolality becomes:

\[ \text{Osmolality} = 2 \times 2.5 \, \text{mol} = 5 \, \text{mol} \]

This approach highlights the importance of understanding the dissociation of ionic compounds when calculating osmolality, ensuring accurate representation of the total number of dissolved particles in a solution.

Osmolality Calculation Example

To determine the osmolality of total ions in an aqueous solution prepared by dissolving 0.400 moles of lead(IV) nitrate in 750 grams of water, we first need to understand the dissociation of lead(IV) nitrate in solution. Lead(IV) nitrate, represented as Pb(NO₃)₄, dissociates into 5 ions: 1 lead(IV) ion (Pb⁴⁺) and 4 nitrate ions (NO₃^-).

The total number of ions produced from the dissociation is 5. To find the osmolality, we use the formula:

Osmolality = Number of ions × Molality of the solution

Next, we calculate the molality of the solution. Molality (m) is defined as the number of moles of solute per kilogram of solvent. In this case, we have:

Molality = Moles of solute / Kilograms of solvent

Here, the moles of solute (lead(IV) nitrate) is 0.400 moles, and the mass of the solvent (water) is 750 grams, which is equivalent to 0.750 kilograms. Thus, we can calculate the molality:

Molality = 0.400 moles / 0.750 kg = 0.5333 m

Now, substituting the values into the osmolality equation:

Osmolality = 5 ions × 0.5333 m = 2.6665 m

Considering significant figures, we round the final result to three significant figures, yielding an osmolality of:

Osmolality = 2.67 m

This value represents the osmolality of the total ions in the solution.

What is the ionic molality of sodium ions in a solution of 25.7 g NaNO₃ dissolved in enough water to make a 150.0 mL of solution? Density of the solution is 1.02 g/mL.

• A. 1.98 m
• B. 2.57 m
• C. 4.74 m
• D. 2.37 m

Answer: (D)

Here’s what students ask on this topic:

What is molality?

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. It's expressed in units of moles per kilogram (mol/kg). Unlike molarity, which is the number of moles of solute per liter of solution, molality is not affected by changes in temperature or pressure because it's based on the mass of the solvent, not the volume of the solution.

To calculate molality, you use the formula:

$\mathrm{molality}\left(m\right)=\frac{\mathrm{moles}of\mathrm{solute}}{\mathrm{kilograms}of\mathrm{solvent}}$

For example, if you dissolve 2 moles of sodium chloride (NaCl) in 1 kilogram of water, the molality of the resulting solution would be 2 mol/kg. Molality is particularly useful in scenarios involving colligative properties, such as boiling point elevation and freezing point depression, because these properties depend on the number of solute particles in a solvent and not on the volume of the solution.

How do you calculate molality?

Molality is a measure of the concentration of a solute in a solution, defined as the number of moles of solute per kilogram of solvent. To calculate molality, you can follow these steps:

1. Determine the number of moles of the solute. You can do this by dividing the mass of the solute (in grams) by its molar mass (the mass of one mole of the substance, usually given in grams per mole).

$\text{Moles of solute =}\frac{\text{Mass of solute (g)}}{\text{Molar mass of solute (g/mol)}}$

2. Measure the mass of the solvent in kilograms. Make sure you're using the mass of the solvent, not the total mass of the solution.
3. Divide the number of moles of solute by the mass of the solvent in kilograms to get the molality.

$\text{Molality (m) =}\frac{\text{Moles of solute}}{\text{Mass of solvent (kg)}}$

Remember, molality is different from molarity, which is the number of moles of solute per liter of solution. Molality is often used in situations where temperature changes are involved, as it is independent of temperature, unlike molarity.

What is the difference between molarity and molality?

Molarity and molality are both measures of concentration in chemistry, but they are calculated differently and used in various contexts.

Molarity (M) is defined as the number of moles of solute (the substance being dissolved) per liter of solution. It's an expression of concentration that takes into account the volume of the entire solution, which includes both the solute and the solvent. The formula for molarity is:

$M=\frac{\text{moles of solute}}{\text{liters of solution}}$

Molality (m), on the other hand, is the number of moles of solute per kilogram of solvent. Unlike molarity, molality is not affected by changes in temperature or pressure because it's based on the mass of the solvent, not the volume of the solution. The formula for molality is:

$m=\frac{\text{moles of solute}}{\text{kilograms of solvent}}$

In summary, molarity is concentration based on the volume of solution, while molality is based on the mass of the solvent. Molarity is commonly used in reactions that occur in solutions, especially in aqueous solutions, while molality is often used in scenarios where temperature and pressure vary, such as in boiling point elevation and freezing point depression studies.