At $27^{\circ} C$, a solution containing $25 \,g$ of solute in $2500 \,mL$ of solution exerts an osmotic pressure of $400 \,Pa$. The molar mass of the solute is ____ $g\,mol ^{-1}$. (Nearest integer)
(Given : $R =0.083 \,L\,bar\, K ^{-1} \,mol ^{-1}$ )
At $27^{\circ} C$, a solution containing $25 \,g$ of solute in $2500 \,mL$ of solution exerts an osmotic pressure of $400 \,Pa$. The molar mass of the solute is ____ $g\,mol ^{-1}$. (Nearest integer)
(Given : $R =0.083 \,L\,bar\, K ^{-1} \,mol ^{-1}$ )
Show Hint
Correct Answer: 62250
Approach Solution - 1
\(\pi=CRT \)
\(\frac{400Pa}{10^5}=\frac{\frac{2.5g}{M_o}}{\frac{250}{1000L}}\times0.83\frac{L−bar}{K⋅mol}\times300K \)
\(M_o=62250\)
So, the answer is 62250.
Approach Solution -2
The osmotic pressure (\(\pi\)) of a solution is given by the formula:
\(\pi = MRT\)
where M is the molarity of the solution, R is the gas constant, and T is the temperature in Kelvin.
To find the molar mass of the solute, we need to first find the molarity of the solution:
\(\text{Molarity }(M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\)
We are given that the solution contains 2.5g of solute in 250.0mL of solution. To convert mL to L, we divide by 1000:
\(\text{Volume of solution} = \frac{250.0 mL}{1000} = 0.250 L\)
To find the moles of solute, we need to use the formula:
\(\text{moles of solute} = \frac{\text{mass of solute}}{\text{molar mass}}\)
Let's assume that the molar mass of the solute is x g/mol. Then we have:
\(\text{moles of solute} = \frac{2.5 g}{x} g/mol\)
Now we can calculate the molarity of the solution:
\(\text{Molarity }(M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\)
\(M = \frac{\frac{2.5 g}{x g/mol}}{0.250 L}\)
\(M = \frac{10}{x} mol/L\)
Next, we can use the given osmotic pressure and temperature to find the molarity of the solution:
\(\pi = MRT\)
\(400 Pa = \frac{10}{x} mol/L \times 0.083 L bar K^{-1} mol^{-1} \times (27°C + 273.15) K\)
Simplifying and solving for x, we get:
\(x = 165\ gmol^{-1}\) (nearest integer)
Therefore, the molar mass of the solute is \(165 \ gmol^{-1}\), i.e., 62250.
Top Questions on Colligative Properties
- CrCl\(_3\).xNH\(_3\) can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558°C. Assuming 100\% ionization of this complex and coordination number of Cr is 6, the complex will be:
- JEE Main - 2025
- Chemistry
- Colligative Properties
- Given below are two statements:
Statement (I): NaCl is added to the ice at \( 0^\circ C \), present in the ice cream box to prevent the melting of ice cream.
Statement (II): On addition of NaCl to ice at \( 0^\circ C \), there is a depression in freezing point.
In the light of the above statements, choose the correct answer from the options given below:- JEE Main - 2025
- Chemistry
- Colligative Properties
- Consider the given plots of vapor pressure (VP) vs temperature (T/K). Which amongst the following options is the correct graphical representation showing \( \Delta T_f \) depression in the freezing point of solvent in a solution?
- JEE Main - 2025
- Chemistry
- Colligative Properties
If \(A_2B \;\text{is} \;30\%\) ionised in an aqueous solution, then the value of van’t Hoff factor \( i \) is:
- JEE Main - 2025
- Chemistry
- Colligative Properties
1.24 g of \(AX_2\) (molar mass 124 g mol\(^{-1}\)) is dissolved in 1 kg of water to form a solution with boiling point of 100.105°C, while 2.54 g of AY_2 (molar mass 250 g mol\(^{-1}\)) in 2 kg of water constitutes a solution with a boiling point of 100.026°C. \(Kb(H)_2\)\(\text(O)\) = 0.52 K kg mol\(^{-1}\). Which of the following is correct?
- JEE Main - 2025
- Chemistry
- Colligative Properties
Questions Asked in JEE Main exam
- The sum of the squares of all the roots of the equation \( x^2 + [2x - 3] - 4 = 0 \) is:
- JEE Main - 2025
- Quadratic Equations
- Let ABCD be a trapezium whose vertices lie on the parabola \( y^2 = 4x \). Let the sides AD and BC of the trapezium be parallel to the y-axis. If the diagonal AC is of length \( \frac{25}{4} \) and it passes through the point \( (1, 0) \), then the area of ABCD is:
- JEE Main - 2025
- Coordinate Geometry
- A molecule (P) on treatment with acid undergoes rearrangement and gives (Q). (Q) on ozonolysis followed by reflux under alkaline condition gives (R). The structure of (R) is given below. The structure of (P) is:
- JEE Main - 2025
- Organic Chemistry
- The product B formed in the following reaction sequence is: \[ {C}_6{H}_5{CN} \xrightarrow{{HCl}} (A) \xrightarrow{{AgCN}} (B) \]
- JEE Main - 2025
- Organic Chemistry
- Let integers \( a, b \in [-3, 3] \) be such that \( a + b \neq 0 \). \(\text{Then the number of all possible ordered pairs}\) \( (a, b) \), \(\text{for which}\) \[ \left| \frac{z - a}{z + b} \right| = 1 \quad \text{and} \quad \left| \begin{matrix} z + 1 & \omega & \omega^2 \\ \omega^2 & 1 & z + \omega \\ \omega^2 & 1 & z + \omega \end{matrix} \right| = 1, \] \(\text{is equal to:}\)
- JEE Main - 2025
- complex numbers
Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.