Tetrodotoxin is a toxic chemical found in fugu pufferfish, a popular but rare delicacy in Japan. This compound has an LD 50 (the amount of substance that is lethal to 50.% of a population sample) of 10. μ g per kg of body mass. Tetrodotoxin is 41.38% carbon by mass, 13.16% nitrogen by mass, and 5.37% hydrogen by mass, with the remaining amount consisting of oxygen. What is the empirical formula of tetrodotoxin? If three molecules of tetrodotoxin have a mass of 1.59 × 10 −21 g, what is the molecular formula of tetrodotoxin? What number of molecules of tetrodotoxin would be the LD 50 dosage for a person weighing 165 lb?

Interpretation: The empirical formula, molecular formula and the number of molecules of Tetrodotoxin are to be calculated.

Concept introduction: The empirical formula of an element is defined as the simplest formula that expresses the percentage composition of the element and the molecular formula of an element defines the total number of atoms present in a molecule.

To determine: The empirical formula, molecular formula and the number of molecules of Tetrodotoxin.

Explanation

Given

The mass percent of carbon is 41.38% .

The mass percent of nitrogen is 13.16% .

The mass percent of hydrogen is 5.37% .

The remaining amount consists of oxygen. The mass percent of oxygen is calculated as,

Mass percent of oxygen=Total percent−(Mass percent of C+Mass percent of N+Mass percent of H)

Substitute the value of mass percent of carbon, nitrogen and hydrogen in the above expression, the mass percent of oxygen is calculated.

Mass percent of oxygen=Total percent−(Mass percent of C+Mass percent of N+Mass percent of H)=100−(41.38+13.16+5.37)=40.09%

The mass percent of oxygen is 40.09% .

Therefore,

Mass of sample is 100 g

Mass of carbon is 41.38 g

Mass of nitrogen is 13.16 g

Mass of hydrogen is 5.37 g

Mass of oxygen is 40.09 g

The molar mass of carbon is 12 g/mol .

The molar mass of nitrogen is 14 g/mol .

The molar mass of hydrogen is 1 g/mol .

The molar mass of oxygen is 16 g/mol .

The number of moles is calculated by the formula,

Number of moles=Given massMolar mass

Substitute the value of the given mass and the molar mass, to calculate the number of moles of carbon, nitrogen, hydrogen, and oxygen in the above equation.

For carbon,

Number of moles of carbon=Given massMolar mass=41.38 g12 g/mol=3.45 mol

For nitrogen,

Number of moles of nitrogen=Given massMolar mass=13.16 g14.0 g/mol=0.939 mol

For hydrogen,

Number of moles of hydrogen=Given massMolar mass=5.37 g1 g/mol=5.33 mol

For oxygen,

Number of moles of oxygen=Given massMolar mass=40.09 g16 g/mol=2.51 mol

The calculated values are divided by the smallest number of moles to determine the simplest whole number ratio of moles of each constituent.

For carbon (C) ,

C=3.45 mol0.939 mol=3.67

For nitrogen (N) ,

N=0.939 mol0.939 mol=1

For hydrogen (H) ,

H=5.33 mol0.939 mol=5.67

For oxygen (O) ,

O=2.51 mol0.939 mol=2.67

Multiply each of the numbers by 3 in order to get whole number.

Carbon=11Nitrogen=3Hydorgen=17Oxygen=8

So the empirical formula of Tetrodotoxin is C11H17N3O8 .

Three molecules of Tetrodotoxin has a mass of 1.59×10−21 g .

The molar mass is the mass of one mole or 6.022×1023 molecules

The molar mass of Tetrodotoxin is calculated by using the expression,

Molar mass=MassNumber of Moles

Substitute the value of mass and number of molecules of Tetrodotoxin the above expression, the molar mass of Tetrodotoxin is calculated