Solving Basic Che Question Homework on Hexadecane Yield Coefficient

[gloryofgreece]

Homework Statement

The aerobic growth of an organism on hexadecane (C16H34) is given by the following stoichiometric relationship:
C16H34 + 12.43O2 + 2.07NH3  2.42C4.4H7.3N0.86O1.2 + 12.43H2O + 5.33CO2
Calculate the mass yield coefficient YX/S (gdw cells/g substrate) for this biological reaction.

Homework Equations

My question is what is does mean by C4.4? Those notation are really confusing. What would cell's grams dry weight and the substrate?
I am just really confused at the whole problem statement.

The Attempt at a Solution

 

[KataKoniK]

Hi there, thank you for your question. The notation used in the stoichiometric equation is a shorthand way of indicating the chemical formula for the products and reactants involved in the biological reaction. In this case, C4.4H7.3N0.86O1.2 represents the chemical formula for the cells produced during the aerobic growth of the organism on hexadecane.

To calculate the mass yield coefficient YX/S, we need to first determine the mass of cells produced (X) and the mass of substrate consumed (S). The units for YX/S are gdw cells/g substrate, which means it is the mass of cells produced per gram of substrate consumed.

To find the mass of cells produced, we can use the chemical formula given in the stoichiometric equation. C4.4H7.3N0.86O1.2 has a molar mass of approximately 85 g/mol. Since the stoichiometric coefficient for this product is 2.42, we can calculate the mass of cells produced as (2.42 mol)(85 g/mol) = 205.7 g.

To find the mass of substrate consumed, we can use the chemical formula for hexadecane (C16H34). Its molar mass is approximately 226 g/mol, and the stoichiometric coefficient for this reactant is 1. Therefore, the mass of substrate consumed is (1 mol)(226 g/mol) = 226 g.

Now, we can calculate the mass yield coefficient YX/S as (205.7 g cells)/(226 g substrate) = 0.91 gdw cells/g substrate.

I hope this helps clarify the problem statement and how to approach finding the mass yield coefficient. Let me know if you have any further questions. Good luck with your calculations!

 

[piercas]

I understand that the notation C4.4 represents a specific compound with a molecular formula of C4.4H7.3N0.86O1.2. This compound is likely a product of the biological reaction and is being used to represent the overall yield of the organism on hexadecane. The notation can be read as 4.4 carbon atoms, 7.3 hydrogen atoms, 0.86 nitrogen atoms, and 1.2 oxygen atoms in the compound.

To calculate the mass yield coefficient YX/S, we need to first determine the mass of the cells and the substrate. The mass of the cells can be represented as gdw (grams dry weight) and the substrate is hexadecane (C16H34).

Using the stoichiometric relationship given, we can see that for every mole of hexadecane consumed, 2.42 moles of C4.4H7.3N0.86O1.2 are produced. We can use this ratio to calculate the mass of C4.4H7.3N0.86O1.2 produced from the mass of hexadecane consumed.

Next, we can determine the mass of the cells produced by using the molar mass of C4.4H7.3N0.86O1.2 and the mole ratio of cells to C4.4H7.3N0.86O1.2 (2.42 moles of cells produced for every mole of C4.4H7.3N0.86O1.2 produced).

Finally, we can calculate the mass yield coefficient YX/S by dividing the mass of cells produced by the mass of substrate consumed.

Overall, the homework problem is asking you to use stoichiometry and basic chemistry principles to calculate the yield of an organism on hexadecane. It may seem confusing at first, but by breaking it down and using the given information, you can find the solution.