Molarity, Molality — Revision Notes

⚡ 30-Second Revision

Molarity ($M$): — Moles of solute per liter of solution. $M = \frac{n_{solute}}{V_{solution}(\text{L})}$. Unit: mol/L or M. Temperature-dependent.
Molality ($m$): — Moles of solute per kilogram of solvent. $m = \frac{n_{solute}}{W_{solvent}(\text{kg})}$. Unit: mol/kg or m. Temperature-independent.
Molar Mass: — $\text{g/mol}$. Used to convert mass to moles.
Density ($\rho$): — $\text{Mass/Volume}$. Crucial for interconversion.
Interconversion Formula (M to m): — $m = \frac{1000 M}{1000 \rho - M \times M_{solute}}$ (where $\rho$ in g/mL, $M_{solute}$ in g/mol).
Interconversion Formula (m to M): — $M = \frac{1000 m \rho}{1000 + m \times M_{solute}}$ (where $\rho$ in g/mL, $M_{solute}$ in g/mol).

2-Minute Revision

Molarity ($M$) and molality ($m$) are key concentration terms. Molarity is defined as moles of solute per liter of *solution*. Its formula is $M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}$.

A critical point is that molarity is temperature-dependent because the volume of the solution changes with temperature. This means if you heat a solution, its molarity will decrease. Molality, on the other hand, is defined as moles of solute per kilogram of *solvent*.

Its formula is $m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}$. Molality is temperature-independent since both moles and mass do not change with temperature. This makes molality particularly useful for colligative property calculations.

For NEET, you must be able to calculate both, convert between them using the solution's density, and understand their temperature dependence. Remember to always check units: volume in liters, mass in kilograms, and molar mass in g/mol.

5-Minute Revision

Let's consolidate Molarity and Molality, which are fundamental for NEET. Molarity (M) quantifies the concentration as the number of moles of solute per liter of the *entire solution*. The formula is $M = \frac{n_{solute}}{V_{solution}(\text{L})}$.

For example, if $9.8,\text{g}$ of H$_2$SO$_4$ (molar mass $98,\text{g/mol}$) is in $500,\text{mL}$ of solution, moles of H$_2$SO$_4 = 9.8/98 = 0.1,\text{mol}$, and volume $= 0.5,\text{L}$. So, $M = 0.1/0.5 = 0.

2, ext{M}$. Molarity is temperature-dependent because the volume of the solution changes with temperature. An increase in temperature leads to an increase in volume and thus a decrease in molarity.

Molality (m), conversely, is defined as the number of moles of solute per kilogram of the *solvent*. The formula is $m = \frac{n_{solute}}{W_{solvent}(\text{kg})}$. For instance, if $18,\text{g}$ of glucose (molar mass $180,\text{g/mol}$) is dissolved in $200,\text{g}$ of water, moles of glucose $= 18/180 = 0.

1, ext{mol}$, and mass of water$= 0.2, ext{kg}$. So,$m = 0.1/0.2 = 0.5, ext{m}$. Molality is temperature-independent because both moles of solute and mass of solvent are unaffected by temperature changes.

This makes it ideal for studies like colligative properties.

Interconversion between Molarity and Molality is a common NEET problem type and requires the **density of the solution ($\rho$)**. The key formulas are:

1
To convert Molarity ($M$) to Molality ($m$): $m = \frac{1000 M}{1000 \rho - M \times M_{solute}}$
2
To convert Molality ($m$) to Molarity ($M$): $M = \frac{1000 m \rho}{1000 + m \times M_{solute}}$

(Here, $\rho$ is in g/mL, $M_{solute}$ is molar mass in g/mol). Always ensure consistent units throughout your calculations. For example, if a $1,\text{M}$ solution of urea (molar mass $60,\text{g/mol}$) has a density of $1.02,\text{g/mL}$, its molality would be $m = \frac{1000 \times 1}{1000 \times 1.02 - 1 \times 60} = \frac{1000}{1020 - 60} = \frac{1000}{960} \approx 1.04,\text{m}$.

Prelims Revision Notes

Molarity (M)

Definition: — Moles of solute per liter of solution.
Formula: — $M = \frac{\text{moles of solute}}{\text{volume of solution (L)}}$
Units: — mol/L or M.
Temperature Dependence: — Temperature-dependent. Volume changes with temperature, so Molarity changes. $\uparrow$ Temp $\implies \uparrow$ Volume $\implies \downarrow$ Molarity.
Key for Calculations: — Ensure volume is in liters. Convert mass of solute to moles using molar mass.
Dilution: — $M_1V_1 = M_2V_2$ (moles of solute remain constant).

Molality (m)

Definition: — Moles of solute per kilogram of solvent.
Formula: — $m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}}$
Units: — mol/kg or m.
Temperature Dependence: — Temperature-independent. Moles and mass do not change with temperature.
Key for Calculations: — Ensure mass of *solvent* is in kilograms. Convert mass of solute to moles.
Applications: — Preferred for colligative properties (e.g., freezing point depression, boiling point elevation) due to temperature independence.

Interconversion between Molarity and Molality

Requires: — Density of the solution ($\rho$) and molar mass of the solute ($M_{solute}$).
From M to m: — $m = \frac{1000 M}{1000 \rho - M \times M_{solute}}$
From m to M: — $M = \frac{1000 m \rho}{1000 + m \times M_{solute}}$
Units Check: — $\rho$ in g/mL, $M_{solute}$ in g/mol.

Common Pitfalls for NEET

Volume vs. Mass: — Molarity uses volume of *solution*; Molality uses mass of *solvent*.
Unit Conversions: — Always convert mL to L, g to kg, and g to moles correctly.
Density: — Remember density is for the *solution*, not just the solvent.
Percentage Concentration: — Be able to convert mass % (w/w) or mass/volume % (w/v) into moles and then to Molarity/Molality, often involving density.

Vyyuha Quick Recall

To remember the temperature dependence: Molarity has Volume, Volume Varies with Temperature (MVT). Molality has Mass, Mass Maintains with Temperature (MMT).

Or, for the denominator: Molarity: Liters of soLution (M-L-L) Molality: Kilograms of soKvent (M-K-K)