A 5.00-wt% aqueous sulfuric acid solution (p=1.03 g/ml) flows through a 45-m long pipe with a 6.0 cm diameter at a rate of 82 L/min. a) What is the molarity of sulfuric acid in the solution? b) How long in seconds) would it take to fill a 55-gallon drum, and how much sulfuric acid (lbm) would the drum contain? c) The mean velocity of a fluid in a pipe equals the volumetric flow rate divided by the cross-sectional area normal to the direction of flow. Use this information to estimate how long (in seconds) it takes the solution to flow from the pipe inlet to the outlet.

Explanation:

a )

5 gram of sulfuric acid in 100 gram of solution

volume of 100 gram of solution = 100 / 1.03 ml

= 97.08 ml = .097 L

5 gram of sulfuric acid = 5 / 98 moles = .051 moles

.051 moles in .097 L solution

molarity = .051 / .097 = .525 M .

b ) 55 gallon = 3.7854 x 55  L = 208 L

rate of flow = 82 L / min

time taken to fill the drum = 208 / 82 min = 2.536 min .

volume of sulfuric acid = 208 L

mass = volume x density = 208 x 1000 x 1.03 gram = 214.24 kg

214.24 kg = 214.24 x 2.2 lb = 471.33 lb

c )

cross sectional area = 3.14 x 3² = 28.26 cm²

rate of flow = 82 L / min = 82 x 1000 cm³ / min

= 82000 / 60  cm³ / sec = 1366.67 cm³ / s

velocity = 82 x 1000 / 1366.67 = 60 cm / s  = .6 m / s

length of pipe = 45 m

time taken = 45 / .6 = 75 s