A 5.00-wt% aqueous sulfuric acid solution ( density = 1.03 g/ML ) flows through

Question

A 5.00-wt% aqueous sulfuric acid solution ( density = 1.03 g/ML ) flows through a 45-m long pipe with a 6.0 cm diameter at a rate of 87L/min.

What is the molarity of sulfuric acid in the solution?

How long (in seconds) would it take to fill a 55 gallon drum, and how much sulfuric acid (lb_m) would the drum contain? (use two dimensional equations)?

The mean velocity of a fluid in a pipe equal 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 / Answer

a)..................................

Sulfuric acid has a molecular mass of 98.08 g/mol

1.03 g/mL = 1030 g/L

( 5 g H2SO4 / 100g solution )( 1030 g/L ) / 98.08 g/mol = 0.5250 moles/L

b)..................................

1 liter = 0.264 gallon

(87 L/min)(0.264 gallon/L)( 1 min/60 sec ) = 0.3828 gal/sec

( 55 gal ) / ( 0.3828 gal/sec ) = 144 seconds

? = ( 1030 g/L )( 1 L/0.264 gallon )( 1 lbm/453.6 g ) = 8.601 lbm/gal

( 55 gal )( 8.601 lbm/gal ) = 473 lbm

c)..................................

A = ?D/4 = ?(6)/4 = 9? = 28.274 cm

87 L/min = 87,000 cm/min

( 87,000 cm/min )( 1 min/60 sec ) = 1450 cm/sec

V = Q/A = ( 1450 cm/sec )( 28.274 cm )( 1 m / 100 cm ) = 0.5128 m/sec

45 m / 0.5128 m/sec = 87.75 sec

Note: chaosjmf - I have 98.08 g/mol
I would think a 55 gallon filled drum would weigh more than 4.73 lbm, as the specific weight of H2SO4 is greater than water.

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