To solve this problem, let's break it down into several steps:

Step 1: Calculate the molecular weight of biomass (C₅H₇O₂N)

The molecular formula of biomass is C₅H₇O₂N.

Using the given atomic weights:

Carbon (C) = 12 g/mol
Hydrogen (H) = 1 g/mol
Oxygen (O) = 16 g/mol
Nitrogen (N) = 14 g/mol

The molecular weight of biomass is calculated as follows:

Molecular weight = (5 × 12) + (7 × 1) + (2 × 16) + (1 × 14)

Molecular weight = 60 + 7 + 32 + 14 = 113 g/mol

Step 2: Determine the initial concentration of biomass in terms of total organic carbon (TOC)

TOC represents the amount of carbon in the biomass:

Carbon atoms in C₅H₇O₂N = 5

Molecular weight of carbon in the biomass = 5 × 12 = 60 g/mol

So, TOC is:

TOC = 60 / 113

Step 3: Calculate BOD₅ using first-order reaction kinetics

The reaction rate constant (k) is given as 0.23/d. The first-order reaction equation for BOD at time t is:

$$BOD_t = L_0 \left(1 - e^{-kt}\right)$$

where:

$$BOD_t$$ = Biochemical Oxygen Demand at time t
$$L_0$$ = Ultimate Biochemical Oxygen Demand (Ultimate BOD)
$$k$$ = Reaction rate constant
$$t$$ = Time (in days)

We are interested in BOD₅, so t = 5 days:

$$BOD_5 = L_0 \left(1 - e^{-0.23 \times 5}\right)$$

$$BOD_5 = L_0 \left(1 - e^{-1.15}\right)$$

Using a calculator to find the exponential term:

$$e^{-1.15} \approx 0.316$$

Therefore:

$$BOD_5 = L_0 \left(1 - 0.316\right) = L_0 \times 0.684$$

Step 4: Determine the ultimate BOD (L₀)

Ultimate BOD (L₀) is the total oxygen demand if the biomass is fully oxidized. From the given reaction, the complete oxidation of C₅H₇O₂N consumes 5 moles of O₂:

Molecular weight of O₂ = 2 × 16 = 32 g/mol

Oxygen required per mole of biomass = 5 × 32 = 160 g/mol

So, $$L_0 = 160 / 113 = 1.415$$ g O₂/g of biomass

Step 5: Calculate BOD₅

$$BOD_5 = 1.415 \times 0.684 = 0.968$$ g O₂ per g of biomass

Step 6: Calculate the ratio of BOD₅ to TOC

We previously found that TOC = 60 / 113 = 0.531 g C per g of biomass

The ratio of BOD₅ to TOC is:

BOD₅ / TOC = 0.968 / 0.531

$$\text{Ratio} ≈ 1.82$$

So, the ratio of BOD₅ at 20ºC to total organic carbon (TOC) of biomass is 1.82.

Waste Water Characteristics · Environmental Engineering · GATE CE

Marks 2