
Given that the molecular weight of ethyl alcohol (\[C{H_3}C{H_2}OH\]) is 46, and that of water is 18, how many grams of ethyl alcohol must be mixed with 100ml of water for the mole fraction (X) of ethyl alcohol to be 0.2?
(A) 74.4g
(B) 54.4g
(C) 44.4g
(D) 64.4g
Answer
154.2k+ views
Hint: Mole fraction is defined as the number of moles of a particular component in a mixture divided by the total number of moles in that solute-solvent mixture. Ratio of given mass to molar mass gives the value of number of moles.
Complete step-by-step solution:
Mole fraction is the ratio of moles of one substance in a solution mixture to the total number of moles of all substances in the same mixture. For a mixture of two substances, A and B, we can write the mole fractions of each as follows:
\[mole{\text{ }}fraction{\text{ }}of{\text{ }}A = \dfrac{{{n_A}}}{{{n_A} + {n_B}}}\]
We can calculate number of moles of each substance using the below formula:
\[moles = \dfrac{{given{\text{ }}mass}}{{molar{\text{ }}mass}}\]
Number of moles of water are
\[moles = \dfrac{{100}}{{18}} = 5.55moles\]
We are provided that the mole fraction of ethyl alcohol is 0.2 and molecular weight of ethyl alcohol is 46 grams, putting these values in mole fraction formula, we get
\[0.2 = \dfrac{{{m_x}/46}}{{{m_x}/46 + 5.55}}\]
Solving this equation, we get the value of \[{m_x}\]= 64.4 grams.
Therefore, 64.4 grams of ethyl alcohol must be mixed with 100ml of water for the mole fraction (X) of ethyl alcohol to be 0.2.
Hence, the correct option is (D).
Note: The sum of mole fraction of all the components in the solution mixture is always equal to unity. Since it is a fraction of moles i.e. the ratio of same quantity, it is unitless. Other concentration terms can be calculated using mole fraction such as molarity, molality, etc.
Complete step-by-step solution:
Mole fraction is the ratio of moles of one substance in a solution mixture to the total number of moles of all substances in the same mixture. For a mixture of two substances, A and B, we can write the mole fractions of each as follows:
\[mole{\text{ }}fraction{\text{ }}of{\text{ }}A = \dfrac{{{n_A}}}{{{n_A} + {n_B}}}\]
We can calculate number of moles of each substance using the below formula:
\[moles = \dfrac{{given{\text{ }}mass}}{{molar{\text{ }}mass}}\]
Number of moles of water are
\[moles = \dfrac{{100}}{{18}} = 5.55moles\]
We are provided that the mole fraction of ethyl alcohol is 0.2 and molecular weight of ethyl alcohol is 46 grams, putting these values in mole fraction formula, we get
\[0.2 = \dfrac{{{m_x}/46}}{{{m_x}/46 + 5.55}}\]
Solving this equation, we get the value of \[{m_x}\]= 64.4 grams.
Therefore, 64.4 grams of ethyl alcohol must be mixed with 100ml of water for the mole fraction (X) of ethyl alcohol to be 0.2.
Hence, the correct option is (D).
Note: The sum of mole fraction of all the components in the solution mixture is always equal to unity. Since it is a fraction of moles i.e. the ratio of same quantity, it is unitless. Other concentration terms can be calculated using mole fraction such as molarity, molality, etc.
Recently Updated Pages
JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

Chemical Properties of Hydrogen - Important Concepts for JEE Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

JEE Isolation, Preparation and Properties of Non-metals Important Concepts and Tips for Exam Preparation

Trending doubts
The stability of the following alkali metal chlorides class 11 chemistry JEE_Main

The atomic weight of Ne is 202 Ne is a mixture of Ne20 class 11 chemistry JEE_Main

IIIT JEE Main Cutoff 2024

Photoelectric Effect and Stopping Potential with Work Function and Derivation for JEE

Newton’s Laws of Motion: Three Laws of Motion Explanation with Examples

Difference Between Metals and Non-Metals for JEE Main 2024

Other Pages
JEE Advanced 2025 Revision Notes for Mechanics

Ideal and Non-Ideal Solutions Raoult's Law - JEE

JEE Main 2025: Conversion of Galvanometer Into Ammeter And Voltmeter in Physics

NCERT Solutions for Class 11 Chemistry Chapter 7 Redox Reaction

Hydrocarbons Class 11 Notes: CBSE Chemistry Chapter 9

Number of sigma and pi bonds in C2 molecule isare A class 11 chemistry JEE_Main
