Question:
Calculate the mole fraction of ethylene glycol $(C_2H_6O_2)$ in a solution containing 20% of $C_2H_6O_2$ by mass.
Calculate the mole fraction of ethylene glycol $(C_2H_6O_2)$ in a solution containing 20% of $C_2H_6O_2$ by mass.
Updated On: Jun 23, 2023
- 0.932
- 0.862
- 0.95
- 0.779
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The Correct Option is A
Solution and Explanation
Assuming that we have $100\, g$ of solutions,
Mass of ethylene glycol $= 20 \,g$
and mass of water $= 80\, g$
Molar mass of $C_2H_6O_2 = 12 ? 2 + 1 ? 6 + 16 ? 2 = 62 \,g\, mol^{-1}$.
Moles of $C_2H_6O_2$ $= \frac{20\,g}{62\,g\,mol^{-1}} = 0.322\,mol$
Moles of water $= \frac{80\,g}{18\,g\,mol^{-1}} = 4.444\,mol$
$x_{glycol} = \frac{mole\, of\, C_{2}H_{6}O_{2}}{mole\, of \,C_{2}H_{6}O_{2} + mole \,of\, H_{2}O}$
$= \frac{0.322\,mol}{0.322\,mol+4.444\,mol} = 0.068$
Similarly, $x_{water}= \frac{4.444\,mol}{0.322\,mol+4.444\,mol} = 0.932$
Mole fraction of water can also be calculated as : $1 - 0.068 = 0.932$
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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.