Question

A sample of protein was analysed for metal content and analysis revealed that it contained magnesium and titanium in equal amounts, by mass. If these are the only metallic species present in the protein and it contains \(0.016 \%\) metal, by mass, the minimum possible molar mass of the protein is \((\mathrm{Mg}=24, \mathrm{Ti}=48)\) (a) \(6,00,000\) (b) \(1,50,000\) (c) \(3,00,000\) (d) \(12,00,000\)

Short answer

The minimum possible molar mass of the protein is (b) 1,50,000.

Step-by-step solution

Identify the mass percentages of magnesium and titanium

Given that magnesium and titanium are present in equal amounts by mass, and they together constitute 0.016% of the protein by mass, then both magnesium and titanium each make up half of this percentage, which is 0.008% of the protein by mass.

Calculate the mass of magnesium and titanium in 100g of protein

If we consider a 100g sample of protein, the mass of magnesium would be 0.008% of 100g, which is 0.008g. Since the amount of titanium is equal to that of magnesium, it also has a mass of 0.008g in 100g of protein.

Convert mass to moles for magnesium and titanium

Using the molar mass of magnesium (24g/mol) and titanium (48g/mol), calculate the number of moles of each metal in the protein. The number of moles of magnesium is 0.008g divided by 24g/mol, and the number of moles of titanium is 0.008g divided by 48g/mol.

Determine the molar ratio and the molar mass of the protein

The molar ratio of magnesium to titanium will be the same as their molar amounts since they are present in equal masses. Using this molar ratio and the given metallic species, calculate the minimum possible molar mass of the protein. If we have 1 mole of protein containing x moles of magnesium and x moles of titanium, it will have a molar mass Mg (x · 24) + Ti (x · 48). The sum of the mole fractions should equal the metal content (0.016%), and from there we can solve for the molar mass of the protein.

Perform the calculations and derive the minimum molar mass

If the metallic content is 0.016%, which corresponds to 0.016g of metal in 100g of protein, and knowing that each metal contributes equally to this mass, we can calculate the minimum molar mass by solving for x in the equation 0.016g = x (24g/mol + 48g/mol) and then finding the total mass of protein that contains this amount of metal.

Key concepts

Stoichiometry

Stoichiometry is a section of chemistry that involves determining the quantities of reactants and products in a chemical reaction. It is a powerful tool that is based on the conservation of mass and the concept of the mole. Stoichiometry calculations help to balance chemical equations, which means ensuring that the number of atoms for each element is the same on both the reactant and product sides of the equation.

For example, in the protein metal content analysis, stoichiometry involves understanding how the mass of metals relates to the molar mass of the entire protein. By knowing the mass percentage of magnesium and titanium in the protein and their individual molar masses, one can determine the total molar mass of the protein using stoichiometric calculations.

Percent Composition

Percent composition refers to the percent by mass of each element in a compound. It is an essential concept in determining the formula of an unknown compound and in finding its molar mass. In the given exercise, percent composition is used to find out how much magnesium and titanium, by mass, is in the protein.

To calculate the percent composition, the mass of the individual element is divided by the molar mass of the compound and then multiplied by 100. In this case, since the mass of magnesium and titanium each contributes 0.008% to the protein mass, you initially identify the percent composition of these metals in the protein, which lays the groundwork for finding out the molar mass of the protein.

Mole Concept

The mole concept is a fundamental principle in chemistry that relates the mass of substances to the amount of substance present. A mole is defined as the amount of substance that contains as many entities (atoms, molecules, ions, etc.) as there are atoms in 12 grams of carbon-12. The mole provides a link between the macroscopic world of the laboratory and the microscopic world of atoms and molecules.

In the context of our example, the mole concept allows us to convert the mass of magnesium and titanium to moles by dividing the mass by their respective molar masses. It is this calculation that helps in finding the molar ratio of magnesium to titanium and subsequently determining the molar mass of the protein, which is the goal of the exercise. The result from these calculations is crucial to understanding the protein's composition and its possible functions.