A large, complex piece of apparatus has built into it a cooling system containin

Question

A large, complex piece of apparatus has built into it a cooling system containing an unknown volume of cooling liquid. It is desired to measure the volume of the coolant without draining the lines. To the coolant was added 10.0 mL of methanol whose molecules included atoms of 14C and that had specific activity of 580 counts per minute per gram (cpm/g), determined using a Geinger counter.The coolant was permitted to circulate to assure complete mixing before a sample was withdrawn that was found to have a specific activity of 29 cpm/g. Calculate the volume of the coolant in the system in millileters (Make sure to show your work) The density of methanol is 0.792 g/mL and the density of the coolant is 0.884 g/mL.

Explanation / Answer

Total weight of methanol added (g) = density x volume = 0.792 x 10 = 7.92 g

Suppose a (ml) is volume of coolant.

Total weight of coolant present (g) = volume x density = a x 0.884

Total weight when methanol is added = 0.884 a + 7.92

Specific activity is inversely proportional to weight/ mass

weight of coolant/ weight of methanol = 580/29

(0.884 a + 7.92)/7.92 = 20

On solving a = 170.22 ml

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