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Chapter 3: Problem 15

Explain which of the following statement(s) is (are) correct concerning glucose (blood sugar), \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\) (a) The percentages, by mass, of \(\mathrm{C}\) and \(\mathrm{O}\) are the same as in CO. (b) The ratio of \(\mathrm{C}: \mathrm{H}: \mathrm{O}\) atoms is the same as in dihydroxyacetone, \(\left(\mathrm{CH}_{2} \mathrm{OH}\right)_{2} \mathrm{CO}\) (c) The proportions, by mass, of \(C\) and \(O\) are equal. (d) The highest percentage, by mass, is that of H.

Short Answer

Expert verified
Only statement (b) is correct.

Step by step solution

01

Understanding the Compound Structure

Glucose has a molecular formula of \(C_6H_{12}O_6\) and dihydroxyacetone has a molecular formula of \((CH_2OH)_{2}CO\). The total atomic masses of carbon (C), hydrogen (H), and oxygen (O) are 12 g/mol, 1 g/mol, and 16 g/mol respectively.
02

Evaluating Statement (a)

In CO, there is one atom each of carbon and oxygen. As the atomic masses of carbon and oxygen are 12 g/mol and 16 g/mol respectively, the percentage mass of carbon is approximately 43% and that of oxygen is approximately 57%. However, in glucose, one must first calculate the total mass of glucose molecule by adding the atomic masses of all constituent atoms together, which equals 180 g/mol. Then, the percentage mass of carbon and oxygen in glucose are calculated. For carbon, it is \( (6 \cdot 12 / 180) \cdot 100 = 40% \) and for oxygen, it is \( (6 \cdot 16 / 180) \cdot 100 = 53.3% \). These percentages are not the same as in CO. Therefore, statement (a) is incorrect.
03

Evaluating Statement (b)

For glucose, the ratio of C:H:O is 6:12:6 or 1:2:1 when simplified. For dihydroxyacetone or \((CH_2OH)_{2}CO\), there are 3 Carbon atoms, 6 Hydrogen atoms and 3 Oxygen atoms, so the ratio of C:H:O is 3:6:3 or 1:2:1 when simplified. Therefore, statement (b) is correct.
04

Evaluating Statement (c)

In glucose, the proportion mass of carbon and oxygen has been calculated previously in Step 2 as 40% and 53.3% respectively. The proportions are not equal. Therefore, statement (c) is incorrect.
05

Evaluating Statement (d)

In glucose, the proportion mass of hydrogen is calculated as \( \left(\frac{12 \times 1 }{180}\right) \times 100 = 6.7% \) which is not greater than the proportions of either carbon or oxygen. Therefore, statement (d) is incorrect.

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