Question

Part of Dr. Ritchey’s work in her previous job involved boiling and condensing hydrocarbon mixtures. In one of her experiments, she used a binary mixture of n-pentane (density 39.1 lbm/ft^3) and p-xylene (density 53.8 lbm/ft^3). One outlet stream of her condenser was measured to have a flow rate of 32 ft^3/min and a concentration of 30/70 n-pentane/p-xylene by volume. The other outlet stream was measured to have a flow rate of 24 ft^3/min and a concentration of 50/50 n-pentane/p-xylene by volume. If the system operates at steady state and the only inlet to her condenser has a flow rate of 56 ft^3/min, what is the inlet concentration of n-pentane in % by volume?

Your answer should be between 0 and 100. Round your answer to 1 decimal place for entry into eCampus. Do not enter units. Example: 12.3

Note: 30/70 by volume means that 30% of the volume is n-pentane and 70% of the volume is p-xylene.

Answer 1

it is a material balance problem, wherein one input stream and two output streams are present.

where, xP = volume fraction of pentane

xX = volume fraction of xylene

multipying 100 to the fractions will give us the volume%.

it is a steady state process and with no generation and consumption terms. therefore the mass entering will be equal to the mass leaving.

mass flowrates and density of each component is constant, therefore, their volumetric flowrates will also be constant.

thus we can do a volume balance, as density terms on both the sides will be cancelled out.

hence, in inlet stream: volume% of pentane = 38.6%

and volume% of xylene = 61.4%