Respuesta :
Answer : The molecular formula of the sample is, [tex]X_4Y_6Z_4[/tex]
Solution :
If percentage are given then we are taking total mass is 100 grams.
So, the mass of each element is equal to the percentage given.
Mass of X = 15.0 g
Mass of Y = 75.0 g
Mass of Z = 10.0 g
Molar mass of X = 45.0 g/mole
Molar mass of Y = 150 g/mole
Molar mass of Z = 30.0 g/mole
Step 1 : convert given masses into moles.
Moles of X = [tex]\frac{\text{ given mass of X}}{\text{ molar mass of X}}= \frac{15.0g}{45.0g/mole}=0.33moles[/tex]
Moles of Y = [tex]\frac{\text{ given mass of Y}}{\text{ molar mass of Y}}= \frac{75.0g}{150g/mole}=0.5moles[/tex]
Moles of Z = [tex]\frac{\text{ given mass of Z}}{\text{ molar mass of Z}}= \frac{10.0g}{30.0g/mole}=0.33moles[/tex]
Step 2 : For the mole ratio, divide each value of moles by the smallest number of moles calculated.
For X = [tex]\frac{0.33}{0.33}=1[/tex]
For Y = [tex]\frac{0.5}{0.33}=1.5[/tex]
For Z = [tex]\frac{0.33}{0.33}=1[/tex]
The ratio of X : Y : Z = 1 : 1.5 : 1
To make in the whole number we multiply the ratio by 2, we get:
The ratio of X : Y : Z = 2 : 3 : 2
The mole ratio of the element is represented by subscripts in empirical formula.
The Empirical formula = [tex]X_2Y_3Z_9[/tex]
The empirical formula weight = 2(45.0) + 3(150) + 2(30.0) = 600 gram/eq
Now we have to calculate the molecular formula of the compound.
Formula used :
[tex]n=\frac{\text{Molecular formula}}{\text{Empirical formula weight}}[/tex]
[tex]n=\frac{1200}{600}=2[/tex]
Molecular formula = [tex](X_2Y_3Z_2)_n=(X_2Y_3Z_2)_2=X_4Y_6Z_4[/tex]
Therefore, the molecular of the sample is, [tex]X_4Y_6Z_4[/tex]
