Select the correct answer.
What is the percent composition of carbon in glucose ($C_6H_{12}O_6$)?
(The molar mass of $C = 12.01, H = 1.0079$ and $O = 16.00$.)
A. $3.36 \%$
B. $6.71 \%$
C. $15.20 \%$
D. $40 \%$
E. $53.29 \%$
Answer (1)
Calculate the molar mass of glucose ( C 6 H 12 O 6 ): 6 × 12.01 + 12 × 1.0079 + 6 × 16.00 = 180.1548 g/mol.
Calculate the mass of carbon in glucose: 6 × 12.01 = 72.06 g.
Determine the percent composition of carbon: 180.1548 72.06 × 100 .
The percent composition of carbon in glucose is approximately 40% .
Explanation
Understanding the Problem We want to find the percent composition of carbon in glucose ( C 6 H 12 O 6 ). We are given the molar masses of carbon, hydrogen, and oxygen as C = 12.01 g/mol, H = 1.0079 g/mol, and O = 16.00 g/mol, respectively.
Calculating Molar Mass of Glucose First, we need to calculate the molar mass of glucose ( C 6 H 12 O 6 ). This is done by summing the masses of each element multiplied by the number of atoms of that element in the molecule:
Molar mass of glucose = 6 × ( 12.01 ) + 12 × ( 1.0079 ) + 6 × ( 16.00 )
Molar Mass Calculation Molar mass of glucose = 72.06 + 12.0948 + 96.00 = 180.1548 g/mol
Calculating Mass of Carbon Next, we calculate the total mass of carbon in one mole of glucose. Since there are 6 carbon atoms, the mass of carbon is:
Mass of carbon = 6 × 12.01 = 72.06 g
Calculating Percent Composition Now, we can calculate the percent composition of carbon in glucose using the formula:
Percent composition of carbon = Molar mass of glucose Mass of carbon × 100
Final Calculation Percent composition of carbon = 180.1548 72.06 × 100 = 39.998934249878445 ≈ 40.00%
Conclusion Therefore, the percent composition of carbon in glucose is approximately 40% .
Examples
Understanding percent composition is crucial in various fields. For instance, in nutrition, it helps determine the amount of carbohydrates, fats, and proteins in food. In environmental science, it's used to analyze the composition of pollutants. In pharmaceuticals, it ensures the correct formulation of drugs. Knowing the percent composition allows for accurate calculations and informed decisions in these areas.
