Textbook Question
An aqueous solution contains 25% HCl by mass. Calculate the molality and mole fraction of the solution.
14. Solutions
Mole Fraction of Solutions
Multiple Choice
If mole fraction of urea is 4.55 x 10-1, what is the mass of urea needed to dissolve in 38.0 g of water? The molar mass of urea is 60.062 g/mol.
A
26.7 g
B
106 g
C
39.6 g
D
8.19 g
Verified step by step guidance1
Understand the concept of mole fraction: The mole fraction is the ratio of the number of moles of a component to the total number of moles in the solution. In this problem, the mole fraction of urea is given as 4.55 x 10^-1.
Calculate the number of moles of water: Use the formula \( n = \frac{m}{M} \), where \( n \) is the number of moles, \( m \) is the mass, and \( M \) is the molar mass. The molar mass of water is approximately 18.015 g/mol. Substitute the mass of water (38.0 g) into the formula to find the moles of water.
Set up the equation for mole fraction: The mole fraction of urea (\( X_{urea} \)) is given by \( X_{urea} = \frac{n_{urea}}{n_{urea} + n_{water}} \). Rearrange this equation to solve for the number of moles of urea (\( n_{urea} \)).
Calculate the number of moles of urea: Substitute the mole fraction of urea (4.55 x 10^-1) and the calculated moles of water into the rearranged mole fraction equation to find \( n_{urea} \).
Determine the mass of urea: Use the formula \( m = n \times M \), where \( m \) is the mass, \( n \) is the number of moles, and \( M \) is the molar mass of urea (60.062 g/mol). Substitute the number of moles of urea into this formula to find the mass of urea needed.
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