A rigid, closed vessel of volume V =648 liters maintained at constant temperature T=365 K is loaded with 112 mol of n-hexane, 155 mol of n-heptane, and 14 mol of nitrogen. Calculate the pressure in the vessel and the composition of all phases present at equilibrium. Make the following three assumptions: a) n-hexane and n-heptane form an ideal liquid solution, b) the vapor phase is ideal, c) nitrogen has negligible solubility in the liquid phase at the conditions of interest. The vapor pressures of n-hexane and n-heptane at T=365 K are P1=0.199 MPa and P2=0.083 MPa, respectively. Their (liquid) molar volumes are V¯ 1=0.146 l/mol and V¯ 1=0.162 l/mol, respectively.

P = 2.92 atm

Explanation:

With the three assumptions in mind, the system consists of:

First we use PV=nRT to calculate the moles of n-hexane and n-heptane in the gaseous phase:

P = 0.199 MPa ⇒ 0.199 * 1.869 = 1.964 atm

P = 0.083 MPa ⇒ 0.083 * 1.869 = 0.155 atm

So the gaseous phase consists of 42.52 moles of n-hexane, 3.358 moles of n-heptane, and 14 mol of nitrogen.

For the liquid phase, we calculate the remaining moles of n-hexane and n-heptane. Then we convert to liters, using their molar volumes:

So the liquid phase occupies (10.14+24.57) = 34.71 L, and contains 69.48 mol of n-hexane and 151.64 mol of n-heptane.

Finally, to calculate the pressure in the vessel, we use PV=nRT:

P = ?

V = 648 - 34.71 = 613.29 L

n = 42.52 mol hexane + 3.35 mol heptane + 14 mol nitrogen = 59.87 mol

T = 365 K

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