The human body can get energy by metabolizing proteins, carbohydrates or fatty acids, depending on the circumstances. Roughly speaking, the energy it gets comes mostly from allowing all the carbon atoms in the food molecules to become oxidized to carbon dioxide CO2 by reaction with oxygen from the atmosphere. Hence the energy content of food is roughly proportional to the carbon content. Let's consider alanine, C3H7NO2, one of the amino acids from which proteins are made, and glucose C6H12O6, one of the simplest carbohydrates. Using the idea above about energy content, calculate the ratio of the energy the body gets metabolizing each gram of alanine to the energy the body gets metabolizing each gram of glucose.

the ratio of the energy the body gets metabolizing each gram of alanine to the energy the body gets metabolizing each gram of glucose is 1.0111

Explanation:

Given the data in the question;

To determine the ratio of the energy the body gets metabolizing each gram of alanine to the energy the body gets metabolizing each gram of glucose, first we get the molar masses of both alanine and glucose

we know that;

Molar mass of alanine ( C₃H₇NO₂ ) = 89.09 g/mol

Molar mass of glucose ( C₆H₁₂O₆ ) = 180.16 g/mol

now, { metabolizing each gram }

moles of alanine = mass taken / molar mass

= 1g / 89.09 g/mol = 1/89.09 moles

moles of glucose = mass taken / molar mass

= 1g / 180.16 g/mol = 1/180.16 moles

In each molecule of alanine, we have 3 atoms  of carbon.

Also, in each molecules of glucose, we have 6 atoms of carbon

so,

number of moles of Carbons in alanine = 3 × 1/89.09 moles = 0.03367

number of moles of Carbons in glucose = 6 × 1/180.16 moles = 0.0333

so ratio of energy will be the ratio of carbon atoms, which is;

⇒ 0.03367 / 0.0333 = 1.0111

Therefore, the ratio of the energy the body gets metabolizing each gram of alanine to the energy the body gets metabolizing each gram of glucose is 1.0111

the density of gold = 19.3 g/cm3

the relation between density and mass and volume is

density = mass / volume

given :

mass of gold = 13 g

density = 13g / volume = 19.3

volume = 13 /19.3 = 0.67 cm^3

thus volume of gold nugget = 0.67 cm^3

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