Respuesta :
Formula used for determining the number of moles:
number of moles =[tex]\frac{mass}{molar mass}[/tex] -(1)
Mass of [tex]CO_2[/tex] = 14.41 mg (given)
Mass of [tex]H_2O[/tex] = 3.93 mg (given)
Number of moles of [tex]C[/tex] from [tex]CO_2[/tex] = [tex]\frac{14.41 \times 10^{-3} g}{44 g/mol}[/tex]
= [tex]0.3275\times 10^{-3} mol[/tex]
Number of moles of [tex]H[/tex] from [tex]H_2O[/tex] = [tex]\frac{2 \times 3.93 \times 10^{-3} g}{18 g/mol}[/tex]
= [tex]0.437\times 10^{-3} mol [/tex]
Mass of carbon = [tex]0.3275\times 10^{-3} mol \times 12 g /mol [/tex]
= [tex]3.93 \times 10^{-3} g[/tex]
Mass of hydrogen = [tex]0.437 \times 10^{-3} mol \times 1 g /mol [/tex]
= [tex]0.437 \times 10^{-3} g[/tex]
Mass of oxygen = total mass of the compound - mass of carbon- mass of hydrogen
=[tex]9.612 \times 10^{-3} g- 3.93 \times 10^{-3} g - 0.437 \times 10^{-3} g[/tex]
= [tex]5.245 \times 10^{-3}g[/tex]
Now, number of moles of oxygen = [tex]\frac{5.245 \times 10^{-3} g}{16 g/mol}[/tex]
= [tex]0.328 \times 10^{-3}g[/tex]
To identify the empirical formula; divide the number of moles of carbon, hydrogen and oxygen with least number of moles.
Thus,
[tex]C_{\frac{0.3275\times 10^{-3} }{0.3275\times 10^{-3} }}[/tex]
[tex]H_{\frac{0.437\times 10^{-3} }{0.3275\times 10^{-3} }}[/tex]
[tex]O_{\frac{0.328\times 10^{-3} }{0.3275\times 10^{-3} }}[/tex]
[tex]C_{1}H_{1.33}O_{1.00}[/tex]
Now, multiply the numbers with 3 to get the hydrogen number in whole number, we get
The empirical formula = [tex]C_{3}H_{4}O_{3}[/tex]
The empirical weight = [tex]3\times 12 g/mol+4\times 1 g/mol+3\times 16 g/mol[/tex]
= [tex]88 g/mol[/tex]
Divide the molecular weight with empirical weight to find the factor between empirical formula and molecular formula , we get
[tex]\frac{molecular weight}{empirical weight}[/tex] = [tex]\frac{176.1 g/mol}{88 g/mol}[/tex]
= [tex]2[/tex]
Now, multiply the numbers of carbon, hydrogen and oxygen with 2 to get molecular formula, we get
Number of carbon = 6
Number of hydrogen = 8
Number of oxygen = 6
Thus, molecular formula is [tex]C_{6}H_{8}O_{6}[/tex].
