To calculate the total body water (TBW) in the patient, we can use the concentration of antipyrine before and after equilibrium.
The initial amount of antipyrine injected can be calculated using the formula:
\[ \text{Amount of antipyrine injected} = \text{Volume} \times \text{Concentration} \]
Given that the volume is 10 ml and the concentration is 150 mg/ml:
\[ \text{Amount of antipyrine injected} = 10 , \text{ml} \times 150 , \text{mg/ml} = 1500 , \text{mg} \]
After equilibrium, the concentration of antipyrine in the blood is given as 0.03 mg/ml. We can then calculate the total volume of distribution (which in this case represents total body water) using the following equation:
\[ \text{Total body water (TBW)} = \frac{\text{Amount of antipyrine injected}}{\text{Concentration after equilibrium}} \]
Plugging in the values we have:
\[ \text{Total body water (TBW)} = \frac{1500 , \text{mg}}{0.03 , \text{mg/ml}} = 50000 , \text{ml} \]
To convert this to liters (since 1 liter = 1000 ml):
\[ \text{Total body water (TBW)} = \frac{50000 , \text{ml}}{1000} = 50 , \text{liters} \]
Therefore, the total body water in the patient is 50 liters.