Question

Saccharin, an artificial sweetener that is 300 times sweeter than sugar, is composed of 45.9% carbon, 2.73% hydrogen, 26.23% oxygen, 7.65% nitrogen, and 17.49% sulfur. Each packet of Sweet

Answer 1

let the molecular weight of saccharin be x , and the no.of atoms of oxygen , hydrogen , oxygen , nitrogen and sulphur present be n1 , n2,n3,n4 and n5 resp. , so

x= n1(12) + n2(1) +n3(16) + n4(14) +n5(32) ----- eq. (1)

now , framing equations by taking the % of each element present in the compound ,

for carbon , (n1 (12) /x ) *100 = 45.9 --------eq.(2)

for hydrogen , (n2 (1)/x) * 100 = 2.73 -------eq.(3)

for oxygen , (n3(16)/x) * 100 = 26.23 -------eq.(4)

for nitrogen , (n4(14)/x) * 100 = 7.65 ------eq.(5)

for sulphur , (n5(32)/x) *100 = 17.49 ------eq.(6)

we have 5 unknowns and 6 variables , solving this system of equations by matrix ,

we get the values of n1 , n2 , n3 , n4 and n5 as 7,5,3,1,1 resp.

so the formula of saccharin is C₇H₅O₃NS

weight of the molecule is hence 183g/mol

weights of carbon , hydrogen , oxygen , nitrogen and sulphur are 84g/mol , 5g/mol ,48g/mol ,14g/mol & 32g/mol resp.

1.packet contains 36mg of saccharin , so weights of carbon , hydrogen , oxygen , nitrogen and sulphur here are

16.548mg , 0.985mg , 9.456mg , 2.758mg and 6.304mg resp.

2. no.of moles of carbon in a packet = 1.379millimoles

no.of moles of hydrogen in a packet= 0.985millimoles

no.of moles of oxygen in a packet=0.591millimoles

no.of moles of nitrogen in a packet=0.197millimoles

no.of moles of sulphur in a packet=0.197millimoles