Q.What will be the molality of the solution containing 18.25 g of HCl gas in 500 g of water?

The key idea here is Molality, which quantifies the concentration of a solute in a solution based on the mass of the solvent.

1. First, calculate the moles of HCl (solute). The molar mass of HCl is $1.008 + 35.453 = 36.461$ g/mol. Moles of HCl = $\frac{18.25 \text{ g}}{36.461 \text{ g/mol}} \approx 0.5005 \text{ mol}$. For exam purposes, using $36.5$ g/mol gives exactly $0.5$ mol, which is typical for such problems. Let's proceed with $0.5$ mol. …

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 a particularly useful concentration unit because, unlike molarity, it does not depend on temperature. Volume changes with temperature, but mass does not, making molality a temperature-independent measure of concentration.

Let's apply this concept to the given problem.

1. Identify the given quantities:

   We are given the mass of the solute, HCl gas, and the mass of the solvent, water.

   • Mass of HCl (solute) $= 18.25 \text{ g}$
   • Mass of water (solvent) $= 500 \text{ g}$

2. Calculate the moles of solute (HCl):

   To find the moles of HCl, we need its molar mass.

   • Molar mass of H $= 1.008 \text{ g/mol}$
   • Molar mass of Cl $= 35.45 \text{ g/mol}$
   • Molar mass of HCl $= 1.008 + 35.45 = 36.458 \text{ g/mol}$ For practical calculations in such problems, it's common to use rounded values like $36.5 \text{ g/mol}$ for HCl, which simplifies the calculation significantly and is often implied by the numbers given. Let's proceed with $36.5 \text{ g/mol}$.

   Moles of HCl $= \frac{\text{Mass of HCl}}{\text{Molar mass of HCl}}$

   Moles of HCl $= \frac{18.25 \text{ g}}{36.5 \text{ g/mol}} = 0.5 \text{ mol}$

3. Convert the mass of solvent to kilograms:

   The definition of molality requires the mass of the solvent to be in kilograms.

   Mass of water $= 500 \text{ g}$

   Mass of water in kg $= 500 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 0.5 \text{ kg}$

4. Calculate the molality of the solution:

   Now we have the moles of solute and the mass of solvent in kilograms, so we can directly apply the molality formula. …

Method: Molality Formula Using Moles of Solute and Mass of Solvent (in kg)

Concept-first understanding:

Molality ($m$) measures moles of solute per kilogram of solvent — not solution. Here, the solute is HCl gas and the solvent is water. We are given masses, so we first convert solute mass to moles, then solvent mass to kilograms.

Steps:

1. Find moles of HCl

   Molar mass of HCl = $1 + 35.5 = 36.5 \, \text{g/mol}$

   Moles of HCl = $\frac{\text{mass}}{\text{molar mass}} = \frac{18.25}{36.5}$

   $\Rightarrow$ 0.5 mol

2. Convert solvent mass to kg

   Mass of water = $500 \, \text{g} = 0.5 \, \text{kg}$ …

Here are the common mistakes students make when solving this problem, along with the correct reasoning to avoid them.

Mistake 1: Confusing Molality with Molarity

• The Error: Students see "HCl gas in water" and immediately calculate molarity (M). They take the volume of water (500 mL) as the volume of the solution.

  • They calculate moles of HCl: $18.25 / 36.5 = 0.5$ moles.
  • They then do: $0.5 / 0.5 = 1 \text{ M}$.
  • They pick option (ii) 1 M or mistakenly think $1 \text{ M} = 1 \text{ m}$.

• Why it's wrong: Molality ($m$) uses mass of solvent in kg, not volume of solution. Molarity uses volume of solution. Water's density is ~1 g/mL, but the final solution volume is not exactly 500 mL. The question explicitly asks for molality.

• How to avoid: Read the unit symbol carefully. "m" means molal (mol/kg). "M" means molar (mol/L). Always check if the question asks for molality or molarity before starting.

Mistake 2: Using the Wrong Mass for the Solvent

• The Error: Students include the mass of the solute (HCl) in the mass of the solvent.

  • They calculate: Mass of solution = $18.25 + 500 = 518.25 \text{ g}$.
  • They then use $0.51825 \text{ kg}$ as the solvent mass.

• Why it's wrong: Molality is defined as moles of solute per kilogram of solvent (the substance doing the dissolving). The solute (HCl) is dissolved in the water. The water is the solvent.

• How to avoid: Identify the solvent first. In an aqueous solution, water is almost always the solvent. The mass of the solvent is given directly: 500 g of water. Convert that to kg: $500 \text{ g} = 0.5 \text{ kg}$.

Mistake 3: Incorrect Molar Mass Calculation

• The Error: Students use the wrong molar mass for HCl.

  • They might use $H = 1$, $Cl = 35$ (instead of 35.5), giving $36 \text{ g/mol}$.
  • Or they might use $Cl = 35.5$ but forget to add H, using $35.5 \text{ g/mol}$.

• Why it's wrong: The atomic mass of chlorine is 35.5 u (average of isotopes). Using 35 or 36 changes the mole calculation significantly.

• How to avoid: Memorize common atomic masses. For HCl: $H = 1$, $Cl = 35.5$, so molar mass = $1 + 35.5 = 36.5 \text{ g/mol}$. Always write it down before calculating moles. …