GATE 2026 BT – Question 62
It is desired to cultivate 150 mg (dry weight) microbial cells with an empirical formula of $C_5H_7O_2N$. If the phosphorus requirement for the cells is 20% of the nitrogen requirement (on a weight/weight basis), the minimum amount of phosphorous required to be added to the cultivation medium is ________ mg. (rounded off to one decimal place)
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Correct answer: 3.68 to 3.72
Explanation
The molar mass of $C_5H_7O_2N$ is $5 \times 12 + 7 + 2 \times 16 + 14 = 113$ g/mol, so the nitrogen is $\frac{14}{113} \times 150 = 18.58$ mg. The phosphorus is 20% of this, $0.2 \times 18.58 = 3.7$ mg.