Question

The vapour pressure of water at room temperature is 23.8 mm Hg. The vapour pressure of an aqueous solution of sucrose with mole fraction 0.1 is equal to

• A. 2.39 mm Hg
• B. 2.42 mm Hg
• C. 21.42 mm Hg
• D. 21.44 mm Hg

Hint:

The equation can be written as, (P_o−P_s) / P_o=ix_B

Answer 1

The Correct Option is C

The correct answer is Option C) 21.42 mm Hg

Lowering of vapor pressure = ΔP=P_o−P_s

Here, The vapor pressure of water = P_o=23.8mmHg
The vapor pressure of solution = P_s

Now, the equation can be written as, (P_o−P_s) / P_o=ix_B

Here, i = Van't Hoff factor; for sucrose i= 1

x_B= mole fraction of sucrose

⇒ (23.8−P_s) / 23.8 = 1 x 0.1

P_s = 21.42 mm Hg

The vapour pressure of water at room temperature is 23.8 mm Hg. The vapour pressure of an aqueous solution of sucrose with a mole fraction of 0.1 is equal to 21.42 mm of Hg.

Discover More From This Chapter: Colligative Properties

Answer 2

The correct answer is Option C) 21.42 mm Hg

Real Life Applications

• The volume of a material that can dissolve in a certain volume of water at a specified temperature is known as its solubility in water. 
• The vapor pressure of the solution can have an impact on a substance's solubility. 
• The temperature at which a liquid's vapor pressure equals that of the surrounding atmosphere is known as the boiling point of the substance. 
• A sucrose solution's boiling point will be greater than that of pure water because its vapor pressure is lower than that of pure water. 
• For this reason, sugar increases the temperature at which water boils.
• The temperature at which a liquid's vapor pressure equals that of its solid phase is known as the liquid's freezing point.
• A sucrose solution's freezing point will be lower than that of pure water because its vapour pressure is lower than that of pure water. 
• Because of this, water that has been salted will freeze at a lower temperature.

Question can also be asked as

1. What is the vapor pressure of an aqueous solution of sucrose with mole fraction 0.1?
2. How does the vapor pressure of an aqueous solution of sucrose with mole fraction 0.1 compare to the vapor pressure of pure water?
3. What is the relationship between the mole fraction of sucrose in a solution and its vapor pressure?
4. How can the vapor pressure of an aqueous solution of sucrose be calculated?
5. What are the factors that affect the vapor pressure of an aqueous solution of sucrose?

Answer 3

The correct answer is Option C) 21.42 mm Hg

Vapor pressure, sometimes referred to as equilibrium vapor pressure, is the force exerted by a vapor that is in thermodynamic equilibrium with either its solid or liquid condensed phases at a certain temperature in a closed system. 

• The equilibrium vapor pressure controls how quickly a liquid evaporates.
• It has to deal with particles' propensity to elude solid or liquid surfaces.

Van’t Hoff Factor

“The ratio of the concentration of particles formed when a particular substance is dissolved to the concentration of the substance by mass.”

• The value of "i" in most circumstances will be 1 when a non-electrolytic material dissolves in water.
• However, the value of "i" will stay the same as the total number of ions present in one formula unit of the material when a solution is formed in water as a result of an ionic compound.
• For instance, when CaCl2 is split into one Ca2+ ion and two Cl- ions, the Van't Hoff factor will be 3.
• The overall number of particles in the solution will decrease as a result of some of these ions in the solution associating with one another.
• This factor has the name of Jacobus Henricus Van't Hoff, a well-known scientist who received the first Nobel Prize in Chemistry.

Also Read: 

Related Topics
Types of solutions	Mole Fraction	Solvent Examples

Answer 4

To find the vapor pressure of an aqueous solution of sucrose with a mole fraction of 0.1, we use Raoult's Law. Raoult's Law states that the vapor pressure of a solvent in a solution (P₁) is equal to the mole fraction of the solvent (X₁) multiplied by the vapor pressure of the pure solvent (P₁⁰).
Given:
- Vapor pressure of pure water (P₁⁰) = 23.8 mm Hg
- Mole fraction of sucrose (X₂) = 0.1
First, calculate the mole fraction of water (X₁):
\[ X₁ = 1 - X₂ \]
\[ X₁ = 1 - 0.1 \]
\[ X₁ = 0.9 \]
Next, apply Raoult's Law:
\[ P₁ = X₁ \cdot P₁⁰ \]
\[ P₁ = 0.9 \cdot 23.8 \text{ mm Hg} \]
\[ P₁ = 21.42 \text{ mm Hg} \]
Therefore, the vapor pressure of the aqueous solution of sucrose is 21.42 mm Hg.
Hence, the correct option is (C): 21.42 mm of Hg.