Determine the amount of urea (NH2CONH2) to be added in 1000 g of water to decrease its vapour pressure by 25%.
Determine the amount of urea (NH2CONH2) to be added in 1000 g of water to decrease its vapour pressure by 25%.
Correct Answer: 1111
Approach Solution - 1
Given :
Mole concept is used here, and the relationship is:
\( P_o - P_s = \frac{n}{N+n} \)
- \( P_o \): Initial vapor pressure
- \( P_s \): Vapor pressure of the solution
- \( N \): Number of moles of solvent
- \( n \): Number of moles of solute
Step-by-Step Calculation:
- The equation simplifies to: \[ 4n = N + n \]
- Rearranging, we get: \[ n = \frac{N}{3} \]
- \( N \), the number of moles of solvent (water), is calculated as: \[ N = \frac{1000}{18} \] \[ N = 55.56 \]
- Now, substituting \( N \) into the formula for \( n \): \[ n = \frac{55.56}{3} = 18.52 \]
- The weight of urea is calculated as: \[ \text{Weight of urea} = n \times \text{Molar mass of urea (60 g/mol)} \] \[ \text{Weight of urea} = 18.52 \times 60 = 1111.1 \, \text{g} \]
Conclusion:
The amount of urea is approximately 1111.1 g.
Approach Solution -2
\(\frac{P^0-P_s}{P_s}=\frac{n_{solute}}{n_{solvent}}\)
= \(\frac{\frac{x}{60}}{\frac{1000}{18}}=\frac{P^0-0.75P^0}{0.75P^0}\)
\(⇒x=\frac{10000}{9}=1111\ gm\)
So , the correct answer is 1111 gm
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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.