The rate at which water flows out of a biuret is directly proportional to the amount of water, W, remaining above the exit valve:
ln W = kt + C, where C is a constant.
But at t = 0, W = 54.3 ml. This applies to a 50.0 ml biuret. The volume is greater than 50.0 ml because there is an additional 4.3 ml between the 50.0 ml line and the valve.
ln(54.3) = k(0) + C.
C = ln(54.3) = 3.994524227
If it takes 300 s for 50.0 ml of water to flow out of the burette, then there will be only 4.3 mL remaining:
ln(4.3) = k(300) + 3.994524227
k = -0.008453030680
ln W = -0.008453030680 t + 3.994524227
In exponential form:
W = e-0.008453030680 t + 3.994524227
It is more convenient to measure the volume, V, flowing out of the burette. V = 54.3 – W, or substituting,
V = 54.3 - e-0.008453030680 t + 3.994524227