Respuesta :
Answer:
The concentration of Li (in wt%) is 3,47g/mol
Explanation:
To obtain the 2,42g/cm³ of density:
2,42g/cm³ = 2,71g/cm³X + 0,534g/cm³Y (1)
Where X is molar fraction of Al and Y is molar fraction of Li.
X + Y = 1 (2)
Replacing (2) in (1):
Y = 0,13
Thus, X = 0,87
The weight of Al and Li is:
0,87*26,98g/mol = 23,4726 g of aluminium
0,13*6,941g/mol = 0,84383 g of lithium
The concentration of Li (in wt%) is:
0,84383g/(0,84383g+23,4726g) ×100= 3,47%
The concentration of Li in the aircraft is 3.47 %.
Density can be defined as the mass of the substance per unit volume. The density can be expressed as:
[tex]\rm Density=\dfrac{Mass}{Volume}[/tex]
Computation for the concentration of Li
The density of the aircraft is given as 2.42 g per cubic centimeter.
The density of aluminum is 2.71 g per cubic cm.
The density of lithium is 0.534 grams per cubic cm.
The aircraft is made of aluminum and Li, thus the density of aircraft is given as:
[tex]\rm Aircraft =Al+Li\\2.42=2.71\;\times\;x+0.543\;\times y[/tex]
Where x and y are the molar concentrations of the constituent elements.
The sum of x and y is 1. Thus, the concentration in terms of y is given as:
[tex]x+y=1\\x=1-y[/tex]
Substituting the values of x and y in the equation
[tex]2.42=2.71(1-y)-0.543y\\2.42-2.71=-2.71y-0.543y\\y=0.13[/tex]
The value of x is given as:
[tex]x+y=1\\x+0.13=1\\x=0.87[/tex]
The x is the concentration of Al in the aircraft, and y is the concentration of Li in the aircraft.
The mass of Al is given as:
[tex]\rm 0.87\;\times\;27\;g/mol=23.47\;g[/tex]
The mass of Li is given as:
[tex]\rm 0.13\;\times\;6.941\;g/mol=0.84\;g[/tex]
The total mass of aircraft is :
[tex]\rm Mass=Al+Li\\Mass=23.47+0.84\;g\\Mass=24.31\;g[/tex]
The concentration of Li in the aircraft is given as:
[tex]\rm Li \%=\dfrac{0.84}{24.31}\;\times\;100\\\\ Li \%=3.47\;\%[/tex]
The concentration of Li in the aircraft is 3.47 %.
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