Find the relative uncertainty in the half-life.

1.  The flow rate of water through a cylindrical pipe is given by Q = πr 2v, where r is the radius of the pipe and v is the flow velocity.


a.  Assume that r = 3.00 ± 0.03 m and v = 4.0 ± 0.2 m/s. Estimate Q, and find the uncertainty in the estimate.

b.   Assume that r = 4.00 ± 0.04 m and v = 2.0 ± 0.1 m/s. Estimate Q, and find the uncertainty in the estimate.

c.    If r and v have not been measured, but it is known that the relative uncertainty in r is 1% and that the relative uncertainty in v is 5%, is it possible to compute the relative uncertainty in Q? If so, compute the relative uncertainty. If not, explain what additional information is needed.


2.    The conversion of cyclobutane (C4H8 ) to ethylene (C2H4 ) is a first-order reaction. This means that the concentration of cyclobutane at time t is given by ln C = ln C0 − kt, where C is the concentration at time t, C0 is the initial concentration, t is the time since the reaction started, and k is the rate constant. Assume that C0 = 0.2 mol/L with negligible uncertainty. After 300 seconds at a constant temperature, the concentration is measured to be C = 0.174 ± 0.005 mol/L. Assume that time can be measured with negligible uncertainty.


a.   Estimate the rate constant k, and find the uncertainty in the estimate.

b.  The units of k will be s−1 . Find the relative uncertainty in k. The half-life t1/2 of the reaction is the time it takes for the concentration to be reduced to one-half its initial value.

c.   The half-life is related to the rate constant by t1/2 = (ln 2)/k. Using the result found in part (a), find the uncertainty in the half-life.

d.  Find the relative uncertainty in the half-life.


find the cost of your paper

Determine the outlet concentration x1 in the water solution and in the trichloroethane solution using an analytical equation.

Predicting Extraction for an Existing Tower with a Given Number of Steps. An existing tower contains 5.0 theoretical steps. It is desired to predict its performance under the following conditions….

Calculate the minimum solvent that can be used. [Hint: In this case, the tie line through the feed L0 represents the condition for minimum solvent flow rate.

Minimum Solvent and Countercurrent Extraction of Acetone. An aqueous feed solution of 1000 kg/h containing 23.5 wt % acetone and 76.5 wt % water is being extracted in a countercurrent….

Determine the break-point time, the fraction of total capacity used up to the break point, the length of the unused bed, and the saturation loading capacity of the solid.

Drying of Nitrogen and Scale-Up of a Column. Using molecular sieves, water vapor was removed from nitrogen gas in a packed bed (C1) at 28.3°C. The column height was 0.268….