Question

A compound has a general formula \( C_aH_bO_cN_d \) and molecular weight 187. A 935 mg/l solution of the compound is prepared in distilled deionized water. The Total Organic Carbon (TOC) is measured as 360 mg/l (as C). The Chemical Oxygen Demand (COD) and the Total Kjeldahl Nitrogen (TKN) are determined as 600 mg/l (as O\(_2\)) and 140 mg/l (as N), respectively (as per the chemical equation given below). Which of the following options is/are CORRECT?

• A. \( a = 6 \)
• B. \( b = 7 \)
• C. \( c = 5 \)
• D. \( d = 3 \)

Hint:

When solving problems with molecular formulas and stoichiometric equations, use the given data to set up equations based on atomic weights and balances, then solve for the unknowns algebraically.

Answer 1

The Correct Option is A, B, C

Given Data:
- Molecular weight of \( C_aH_bO_cN_d \) = 187 g. 
- Solution concentration in distilled water = 935 mg/L. 
- TOC = 360 mg/L (as C). 
- COD = 600 mg/L (as O\(_2\)). 
- TKN = 140 mg/L (as N). 
Step 1: Chemical Equation
The general chemical equation for oxidation is: \[ C_aH_bO_cN_d + \left( \frac{4a + b - 2c - 3d}{4} \right) O_2 \rightarrow aCO_2 + \frac{b - 3d}{2} H_2O + dNH_3 \] Step 2: Atomic Weights
- Carbon (C) = 12 - Hydrogen (H) = 1 - Oxygen (O) = 16 - Nitrogen (N) = 14 
Step 3: Calculate \( d \) (Nitrogen content)
\[ d = \frac{140}{935} \times 187 = 2 \] Step 4: Calculate \( a \) (Carbon content)
\[ a = \frac{360}{935} \times 187 = 6 \] Step 5: Solve for \( b \) and \( c \) using the Oxygen Balance Equation
\[ \frac{4a + b - 2c - 3d}{4} = \frac{600 \times 187}{935} \] Rearranging, \[ b + 16c = 87 \] Solving for \( b \) and \( c \): \[ b = 7, \quad c = 5 \] Step 6: Verify Molecular Weight
\[ 12a + b + 16c + 14d = 187 \] \[ 12(6) + 7 + 16(5) + 14(2) = 187 \] Final Answer:
The correct values are \( a = 6 \), \( b = 7 \), \( c = 5 \), and \( d = 2 \). The correct options are (a), (b), and (c). ✅