Respuesta :
Answer : The molecular formula of a caffeine is, [tex]C_8H_{10}N_4O_2[/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 C = 49.48 g
Mass of H = 5.19 g
Mass of N = 28.85 g
Mass of O = 16.48 g
Molar mass of C = 12 g/mole
Molar mass of H = 1 g/mole
Molar mass of N = 14 g/mole
Molar mass of O = 16 g/mole
Step 1 : convert given masses into moles.
Moles of C = [tex]\frac{\text{ given mass of C}}{\text{ molar mass of C}}= \frac{49.48g}{12g/mole}=4.12moles[/tex]
Moles of H = [tex]\frac{\text{ given mass of H}}{\text{ molar mass of H}}= \frac{5.19g}{1g/mole}=5.19moles[/tex]
Moles of N = [tex]\frac{\text{ given mass of N}}{\text{ molar mass of N}}= \frac{28.85g}{14g/mole}=2.06moles[/tex]
Moles of O = [tex]\frac{\text{ given mass of O}}{\text{ molar mass of O}}= \frac{16.48g}{16g/mole}=1.03moles[/tex]
Step 2 : For the mole ratio, divide each value of moles by the smallest number of moles calculated.
For C = [tex]\frac{4.12}{1.03}=4[/tex]
For H = [tex]\frac{5.19}{1.03}=5.03\approx 5[/tex]
For N = [tex]\frac{2.06}{1.03}=2[/tex]
For O = [tex]\frac{1.03}{1.03}=1[/tex]
The ratio of C : H : N : O = 4 : 5 : 2 : 1
The mole ratio of the element is represented by subscripts in empirical formula.
The Empirical formula = [tex]C_4H_5N_2O_1=C_4H_5N_2O[/tex]
The empirical formula weight = 4(12) + 5(1) + 2(14) + 16 = 97 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{194.19}{97}=2[/tex]
Molecular formula = [tex](C_4H_5N_2O)_n=(C_4H_5N_2O)_2=C_8H_{10}N_4O_2[/tex]
Therefore, the molecular of the caffeine is, [tex]C_8H_{10}N_4O_2[/tex]
