Colligative properties Questions in English

(C) The elevation in the boiling point $(\Delta T_b = K_b \times m)$ and the depression in the freezing point $(\Delta T_f = K_f \times m)$ are colligative properties.
These properties depend on the molality $(m)$ of the solute particles.
Since the solutions are equimolar (same $m$) and in the same solvent (same $K_b$ and $K_f$),the change in boiling point and freezing point will be identical.
Therefore,equimolar solutions of non-electrolytes in the same solvent exhibit the same boiling point and the same freezing point.

(A) Colligative properties are those properties of solutions that depend only on the number of solute particles and not on their nature. The four main colligative properties are:
$1$. Relative lowering of vapour pressure
$2$. Elevation in boiling point
$3$. Depression in freezing point
$4$. Osmotic pressure
Therefore,$(A)$ Osmotic pressure is a colligative property.

(C) Colligative properties are those physical properties of a solution that depend solely on the number of solute particles in a given volume of the solution,rather than their chemical nature.
The four main colligative properties are:
$(i)$ Relative lowering of vapour pressure.
$(ii)$ Elevation in boiling point.
$(iii)$ Depression in freezing point.
$(iv)$ Osmotic pressure.

(C) Colligative properties are those properties of solutions that depend only on the number of solute particles and not on their nature.
$A$,$B$,and $D$ are colligative properties.
$C$ Vapour pressure is not a colligative property; however,the relative lowering of vapour pressure is a colligative property.

(A) Colligative properties are properties that depend solely on the number of solute particles present in the solution,rather than their nature.
The four main colligative properties are:
$1$. Relative lowering of vapour pressure
$2$. Elevation in boiling point
$3$. Depression in freezing point
$4$. Osmotic pressure
Optical activity is a property related to the interaction of chiral molecules with plane-polarized light and does not depend on the number of particles. Therefore,it is not a colligative property.

(B) Colligative properties are those properties of solutions that depend on the ratio of the number of solute particles to the number of solvent molecules in a solution,and not on the nature of the chemical species present.

(A) Colligative properties are those properties of solutions that depend only on the number of solute particles relative to the total number of particles present in the solution,and not on the nature of the solute particles.
The four main colligative properties are:
$1$. Relative lowering of vapour pressure
$2$. Elevation of boiling point
$3$. Depression of freezing point
$4$. Osmotic pressure
Refractive index is a physical property that depends on the nature of the material,not on the number of solute particles.
Therefore,Refractive index is not a colligative property.

(A) Colligative properties are properties of solutions that depend only on the number of solute particles in a given amount of solvent,not on their chemical identity.
These properties include relative lowering of vapor pressure,elevation in boiling point,depression in freezing point,and osmotic pressure.
By measuring these properties experimentally,the molar mass of the solute can be calculated using the respective formulas.

(B) The osmotic pressure $(\pi)$ is a colligative property given by the formula $\pi = iCRT$,where $i$ is the van't Hoff factor,$C$ is the molar concentration,$R$ is the gas constant,and $T$ is the temperature.
For equimolal solutions,$C$ is the same.
However,for the osmotic pressure to be equal,the van't Hoff factor $(i)$ must also be the same.
Non-electrolytes have $i = 1$,whereas electrolytes dissociate into ions,resulting in $i > 1$.
Therefore,the statement is true only for non-electrolyte solutions.

(C) When a non-volatile solute is dissolved in water,the vapour pressure of the solvent decreases due to the presence of solute particles at the surface.
As a result of the decrease in vapour pressure,the boiling point of the solution increases (elevation in boiling point) and the freezing point of the solution decreases (depression in freezing point).

(C) The addition of a non-volatile solute like sugar to a solvent like water is a classic example of colligative properties.
According to the principles of colligative properties,the addition of a non-volatile solute leads to an elevation in the boiling point and a depression in the freezing point of the solvent.
Therefore,the boiling point of water increases and the freezing point of water decreases upon the addition of sugar.

(C) The elevation in boiling point $(\Delta T_b)$ is a colligative property,which is directly proportional to the van't Hoff factor $(i)$ and the molarity $(M)$ of the solution: $\Delta T_b = i \times K_b \times M$.
For non-electrolytes like urea and glucose,$i = 1$.
For $KNO_3$,$i = 2$ $(K^{+} + NO_3^{-})$.
For $Na_2SO_4$,$i = 3$ $(2Na^{+} + SO_4^{2-})$.
Calculating the effective concentration $(i \times M)$:
$A: 1 \times 0.015 = 0.015 \ M$
$B: 2 \times 0.01 = 0.02 \ M$
$C: 3 \times 0.01 = 0.03 \ M$
$D: 1 \times 0.015 = 0.015 \ M$
Since $0.01 \ M \ Na_2SO_4$ has the highest effective concentration of solute particles,it will exhibit the highest boiling point.

(C) $BaCl_2$ dissociates into $3$ ions $(Ba^{2+} + 2Cl^{-})$,whereas $NaCl$ dissociates into $2$ ions $(Na^{+} + Cl^{-})$.
Glucose and Urea are non-electrolytes $(i = 1)$.
Since boiling point elevation is given by $\Delta T_b = i \cdot K_b \cdot m$,the solution with the highest van't Hoff factor $(i)$ will have the highest boiling point.
Comparing the values of $i$:
For $BaCl_2$,$i = 3$.
For $NaCl$,$i = 2$.
For glucose and urea,$i = 1$.
Therefore,$0.1 \ M$ $BaCl_2$ has the highest boiling point.

(C) The elevation in boiling point is given by $\Delta T_b = i \times K_b \times m$.
Since $K_b$ is constant,$\Delta T_b$ depends on the product of the van't Hoff factor $(i)$ and the molarity $(M)$.
For $0.1 \, N \, Na_2SO_4$,$M = 0.1 / 2 = 0.05 \, M$,so $i \times M = 3 \times 0.05 = 0.15$.
For $0.1 \, N \, MgSO_4$,$M = 0.1 / 2 = 0.05 \, M$,so $i \times M = 2 \times 0.05 = 0.10$.
For $0.1 \, M \, Al_2(SO_4)_3$,$i = 5$,so $i \times M = 5 \times 0.1 = 0.50$.
For $0.1 \, M \, BaSO_4$,$i = 2$ (assuming complete dissociation),so $i \times M = 2 \times 0.1 = 0.20$.
Since $Al_2(SO_4)_3$ has the highest value of $i \times M$,it has the highest boiling point.

(C) When a non-volatile solute is added to a solvent,it leads to colligative properties.
$1$. Vapor pressure of the solution decreases because solute particles occupy surface area.
$2$. Boiling point of the solution increases (elevation in boiling point).
$3$. Freezing point of the solution decreases (depression in freezing point).
Therefore,only option $C$ is correct.

(C) When a non-volatile solute like sugar is added to a solvent like water,it leads to colligative properties.
$1$. Elevation in boiling point: The presence of solute particles decreases the vapor pressure of the solution,requiring a higher temperature to reach the atmospheric pressure,thus the boiling point increases.
$2$. Depression in freezing point: The presence of solute particles interferes with the formation of the solid crystal lattice of the solvent,requiring a lower temperature to freeze,thus the freezing point decreases.

(D) Colligative properties like elevation in boiling point $(\Delta T_b)$ and depression in freezing point $(\Delta T_f)$ depend only on the number of solute particles in the solution.
For equimolar solutions (same concentration) in the same solvent,the number of solute particles is the same.
Therefore,the elevation in boiling point and the depression in freezing point will be the same for all such solutions.
Since $\Delta T_b = T_b - T_b^0$ and $\Delta T_f = T_f^0 - T_f$,if $\Delta T_b$ and $\Delta T_f$ are constant,then the boiling point $(T_b)$ and freezing point $(T_f)$ of the solutions will also be the same.

(C) Colligative properties are those properties of solutions that depend only on the number of solute particles present in a given amount of solvent,regardless of their chemical nature. Therefore,the correct option is $C$.

(D) Colligative properties depend only on the number of solute particles in a solution, not on their nature.
$Osmotic \ pressure$, $lowering \ of \ vapour \ pressure$, and $depression \ in \ freezing \ point$ are colligative properties.
$Refractive \ index$ is an optical property and is not a colligative property.

(D) The depression in freezing point $(\Delta T_f)$ is a colligative property,which depends on the van't Hoff factor $(i)$.
$\Delta T_f = i \times K_f \times m$.
Since the molality $(m)$ is the same for all solutions,the one with the lowest van't Hoff factor $(i)$ will have the smallest depression in freezing point,and thus the highest freezing point.
For $1 \ M \ NaCl$,$i = 2$ $(Na^+ + Cl^-)$.
For $1 \ M \ KCl$,$i = 2$ $(K^+ + Cl^-)$.
For $1 \ M \ CaCl_2$,$i = 3$ $(Ca^{2+} + 2Cl^-)$.
For $1 \ M \ \text{Urea}$,$i = 1$ (non-electrolyte).
Since urea has the lowest $i$ value,it undergoes the least depression in freezing point,resulting in the highest freezing point among the given options.

(B) The boiling point elevation is a colligative property,which depends on the number of particles (van't Hoff factor,$i$) in the solution.
For $1\%$ solutions,the molarity is approximately the same.
Glucose $(C_6H_{12}O_6)$ and urea $(NH_2CONH_2)$ are non-electrolytes,so $i = 1$.
$NaCl$ dissociates as $NaCl \rightarrow Na^+ + Cl^-$ $(i = 2)$.
$ZnSO_4$ dissociates as $ZnSO_4 \rightarrow Zn^{2+} + SO_4^{2-}$ $(i = 2)$.
Since the molar mass of $NaCl$ $(58.44 \ g/mol)$ is lower than that of $ZnSO_4$ $(161.47 \ g/mol)$,a $1\%$ solution of $NaCl$ contains more moles of solute per unit volume than a $1\%$ solution of $ZnSO_4$.
Therefore,the $1\%$ solution of $NaCl$ has the highest number of particles and the highest boiling point.

(A) Colligative properties are those physical properties of a solution that depend solely on the number of solute particles in a given volume of the solution,rather than their chemical nature.
The four main colligative properties are:
$(i)$ Relative lowering of vapour pressure of the solvent.
$(ii)$ Elevation in boiling point of the solvent.
$(iii)$ Depression in freezing point of the solvent.
$(iv)$ Osmotic pressure.

(C) The difference between $P_A^0$ and $P_A$ is the lowering of vapor pressure,which is given by $\Delta P = P_A^0 - P_A = P_A^0 X_B$.
An increase in this difference implies an increase in the mole fraction of the solute $(X_B)$,which means the concentration of the solute increases.
According to the colligative properties:
$1$. Elevation in boiling point: $\Delta T_b = K_b \times m$. As the concentration $(m)$ increases,$\Delta T_b$ increases,so the boiling point increases.
$2$. Depression in freezing point: $\Delta T_f = K_f \times m$. As the concentration $(m)$ increases,$\Delta T_f$ increases,which means the freezing point decreases.

(B) When $CuSO_4$ is added to an aqueous ammonia solution,it forms a complex ion $[Cu(NH_3)_4]^{2+}$.
This reaction reduces the total number of solute particles in the solution.
According to colligative properties,the depression in freezing point $(\Delta T_f = i \times K_f \times m)$ and elevation in boiling point $(\Delta T_b = i \times K_b \times m)$ are directly proportional to the van 't Hoff factor $(i)$.
Since the number of particles decreases,the van 't Hoff factor $(i)$ decreases.
Consequently,the freezing point of the solution increases (less depression) and the boiling point decreases (less elevation).

(C) Colligative properties such as elevation in boiling point $(\Delta T_b)$ and depression in freezing point $(\Delta T_f)$ depend on the molality $(m)$ of the solute particles in the solution.
For non-electrolytes,the van't Hoff factor $(i)$ is $1$.
The formulas are $\Delta T_b = K_b \times m$ and $\Delta T_f = K_f \times m$.
Since the solutions are equimolal (same $m$) and the solvent is the same (same $K_b$ and $K_f$),both $\Delta T_b$ and $\Delta T_f$ will be the same.
Therefore,the boiling point $(T_b = T_b^0 + \Delta T_b)$ and freezing point $(T_f = T_f^0 - \Delta T_f)$ will be the same for both solutions.

(D) Colligative properties are properties of solutions that depend on the number of solute particles in a given amount of solvent,not on the nature of the solute.
$(i)$ $NaBr$ dissociates into $2$ ions $(Na^+, Br^-)$ and $BaCl_2$ dissociates into $3$ ions $(Ba^{2+}, 2Cl^-)$. Since $BaCl_2$ produces more particles,it lowers the vapour pressure more than $NaBr$. Thus,$NaBr$ has a higher vapour pressure. This is a colligative property.
$(ii)$ The freezing point of a pure substance is a characteristic property of that substance,not a colligative property. Comparing two different pure solvents is not a colligative phenomenon.
$(iii)$ The addition of a non-volatile solute $(NaOH)$ to a solvent (water) causes freezing point depression. This is a classic colligative property.
Therefore,$(i)$ and $(iii)$ are correct.

(A) The dissolution of $NH_4NO_3$ in water is an endothermic process,which absorbs heat from the surroundings,thereby lowering the temperature of the pack.
This phenomenon is related to the colligative properties of solutions.
The addition of a non-volatile solute to a solvent leads to a decrease in the vapor pressure,which results in the depression of the freezing point of the solvent.
Since the cooling effect in the cold pack is a practical application of the energy changes associated with dissolving solutes and the principles of colligative properties,both statements are correct and the reason explains the underlying principle.

(N/A) Colligative properties are those properties of solutions that depend only on the number of solute particles present in the solution,regardless of their chemical nature.
These properties include:
$(i)$ Relative lowering of vapour pressure of the solvent
$(ii)$ Depression of freezing point of the solvent
$(iii)$ Elevation of boiling point of the solvent
$(iv)$ Osmotic pressure of the solution.

(B) Colligative properties are those properties of solutions that depend only on the number of solute particles present in the solution,regardless of their chemical nature or identity.
Examples include relative lowering of vapour pressure,elevation of boiling point,depression of freezing point,and osmotic pressure.

(C) The elevation in boiling point is given by the formula: $\Delta T_b = i \cdot K_b \cdot m$.
Since $K_b$ is constant for the same solvent (water) and assuming molality $m \approx M$,the boiling point depends on the product of the van't Hoff factor $(i)$ and molarity $(M)$.
Calculating $i \times M$ for each:
$A$: Urea is a non-electrolyte,$i = 1$. $1 \times 0.01 = 0.01$.
$B$: $KNO_3 \rightarrow K^+ + NO_3^-$,$i = 2$. $2 \times 0.01 = 0.02$.
$C$: $Na_2SO_4 \rightarrow 2Na^+ + SO_4^{2-}$,$i = 3$. $3 \times 0.01 = 0.03$.
$D$: Glucose $(C_6H_{12}O_6)$ is a non-electrolyte,$i = 1$. $1 \times 0.015 = 0.015$.
Since the product $i \times M$ is highest for $Na_2SO_4$,it will exhibit the highest boiling point.

(A) For solute $X$ (univalent electrolyte),the van't Hoff factor $i_X \approx 2$. Thus,the effective concentration is $0.1 \times 2 = 0.2 \ M$.
For solute $Y$ (dimerises),the van't Hoff factor $i_Y \approx 0.5$. Thus,the effective concentration is $0.1 \times 0.5 = 0.05 \ M$.
Since the effective concentration of $X$ is greater than $Y$,colligative properties like boiling point elevation and osmotic pressure will be higher for $X$,and freezing point depression will be greater for $X$ (meaning a lower freezing point).
Relative lowering of vapour pressure depends on the number of particles,which differs for $X$ and $Y$,so statement $(d)$ is incorrect.
Therefore,statements $(a), (b),$ and $(c)$ are correct.

(B) Colligative properties are those properties of solutions that depend only on the number of solute particles present in the solution,not on their nature.
These include:
$1$. Relative lowering of vapour pressure
$2$. Elevation of boiling point
$3$. Depression of freezing point
$4$. Osmotic pressure
Among the given options,$A$,$C$,and $D$ are colligative properties.
$B$ (Boiling point) is a physical property of the solvent/solution,whereas 'Elevation of boiling point' is the colligative property.
Therefore,the correct answer is $B$.

(C) Colligative properties are properties of solutions that depend on the number of solute particles in a given amount of solvent and not on the nature of the solute particles. The four main colligative properties are:
$1$. Relative lowering of vapour pressure
$2$. Elevation of boiling point
$3$. Depression of freezing point
$4$. Osmotic pressure
Since 'vapour pressure of pure benzene' is a property of the pure solvent and not a property dependent on the number of solute particles,it is $NOT$ a colligative property.

(D) Colligative properties depend on the number of solute particles in a solution. The four main colligative properties are:
$1$. Relative lowering of vapour pressure
$2$. Elevation in boiling point
$3$. Depression in freezing point
$4$. Osmotic pressure
Since 'Freezing point' is a physical property of a substance and not a colligative property (which is the 'Depression in freezing point'),option $D$ is the correct answer.

(A) The elevation in boiling point is a colligative property,which depends on the van't Hoff factor $(i)$ and the concentration of the solute particles. The formula is $\Delta T_b = i \times K_b \times m$.
Since the molality $(m)$ is the same for all solutions $(0.1 \ M)$,the solution with the minimum van't Hoff factor $(i)$ will have the minimum boiling point elevation,and thus the minimum boiling point.
For Urea (non-electrolyte),$i = 1$.
For $K_2SO_4$ $(2K^+ + SO_4^{2-})$,$i = 3$.
For $NaCl$ $(Na^+ + Cl^-)$,$i = 2$.
For $FeCl_3$ $(Fe^{3+} + 3Cl^-)$,$i = 4$.
Comparing the values,Urea has the lowest $i$ value $(1)$,therefore $0.1 \ M$ Urea has the minimum boiling point.

(B) Colligative properties are properties of solutions that depend only on the number of solute particles present in a given amount of solvent,not on their identity.
Common colligative properties include:
$1$. Relative lowering of vapour pressure
$2$. Elevation in boiling point
$3$. Depression in freezing point
$4$. Osmotic pressure
Optical activity is a property related to the interaction of a substance with plane-polarized light and is not dependent on the number of solute particles.
Therefore,optical activity is not a colligative property.

(B) Colligative properties are those properties of solutions that depend only on the number of solute particles present in the solution,regardless of their chemical nature.
Osmotic pressure $(\Pi)$ is a colligative property because it is directly proportional to the molar concentration of the solute particles,as given by the equation $\Pi = CRT$.

(D) The correct matching of the methods with their respective colligative properties is:
$A$. Beckmann method $\rightarrow$ $3$. Depression in $F$.$P$.
$B$. Ostwald-Walker method $\rightarrow$ $4$. Relative lowering of vapour pressure
$C$. Berkeley-Hartley method $\rightarrow$ $1$. Osmotic pressure
$D$. Landsberger method $\rightarrow$ $2$. Elevation in $B$.$P$.
Therefore,the correct order is $A-3, B-4, C-1, D-2$.