Respuesta :
Answer : The concentration of Si in kilograms is, [tex]19.55kg/m^3[/tex]
Explanation :
As we are given that, the concentration of Si in an Fe-Si alloy is 0.25 wt% that means:
Weight of Si = 0.25 g = 0.00025 kg
Weight of Fe = 100 - 0.25 = 99.75 g = 0.09975 kg
Density of Si = [tex]2.32g/cm^3=2.32\times 10^6g/m^3[/tex]
Density of Fe = [tex]7.87g/cm^3=7.87\times 10^6g/m^3[/tex]
Now we have to calculate the concentration in kilograms of Si per cubic meter of alloy.
Concentration of Si in kilograms = [tex]\frac{\text{Weight of Si in 100 g of alloy}}{\text{Volume of 100 g of alloy}}[/tex]
Concentration of Si in kilograms = [tex]\frac{\text{Weight of Si in 100 g of alloy}}{\frac{\text{Wight of Fe}}{\text{Density of Fe}}+\frac{\text{Wight of Si}}{\text{Density of Si}}}[/tex]
Now put all the given values in this expression, we get:
Concentration of Si in kilograms = [tex]\frac{0.00025kg}{\frac{99.75g}{7.87\times 10^6g/m^3}+\frac{0.25g}{2.23\times 10^6g/m^3}}[/tex]
Concentration of Si in kilograms = [tex]19.55kg/m^3[/tex]
Thus, the concentration of Si in kilograms is, [tex]19.55kg/m^3[/tex]
