Problem 1847 with feedback 21 of 24 Constants Periodic Tabl

Problem 18.47 with feedback

21 of 24

Constants | Periodic Table

You may want to reference (Page) Section 18.4 while completing this problem.

The organic anion shown in the figure (Figure 1) is found in most detergents. Assume that the anion undergoes aerobic decomposition in the following manner:

2C18H29SO3(aq)+51O2(aq)36CO2(aq)+28H2O(l)+2H+(aq)+2SO42(aq)

Part A

What is the total mass of O2 required to biodegrade 2.0 g of this substance?

Express the mass in grams to two significant digits.

Solution

Balanced reaction is

2C₁₈H₂₉SO_3(aq) + 51O_2(aq)   36CO_2(aq)  + 28H₂O_(l)  + 2H⁺_(aq) + 2SO₄²_(aq)

molar mass of C₁₈H₂₉SO₃^- = 325.4861 g/mol then 2 gm C₁₈H₂₉SO₃^- = 2/325.4861 = 0.0061446556 mole

According to reaction to decompose 2 mole of C₁₈H₂₉SO₃^- require 51 mole of O₂ then to decopose 0.0061446556 mole of C₁₈H₂₉SO₃^- required O₂ = 0.0061446556 X 51 / 2 = 0.1566887 mole of O₂

molar mass of O₂ = 31.9988 g/mole

then  0.1566887 mole of O₂ =  0.1566887 X 31.9988 = 5.01 gm

to biodegrade 2 gm C₁₈H₂₉SO₃^- require 5.01 gm O₂