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Andru [333]
3 years ago
5

A rigid, closed vessel of volume V =648 liters maintained at constant temperature T=365 K is loaded with 112 mol of n-hexane, 15

5 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.
Chemistry
1 answer:
Marrrta [24]3 years ago
6 0

Answer:

P = 2.92 atm

Explanation:

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

  • A liquid phase containing n-hexane and n-heptane, and
  • A gaseous phase containing n-hexane vapor, n-heptane vapor, and nitrogen gas.

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

  • n-hexane:

P = 0.199 MPa ⇒ 0.199 * 1.869 = 1.964 atm

  • 1.964 atm * 648 L = n * 0.082 atm·L·mol⁻¹·K⁻¹ * 365 K
  • n = 42.52 moles
  • n-heptane:

P = 0.083 MPa ⇒ 0.083 * 1.869 = 0.155 atm

  • 0.155 atm * 648 L = n * 0.082 atm·L·mol⁻¹·K⁻¹ * 365 K
  • n = 3.358 moles

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

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

  • n-hexane:
  • n = 112 mol - 42.52 mol = 69.48 mol
  • 69.48 mol * 0.146 L/mol = 10.14 L
  • n-heptane:
  • n = 155 mol - 3.358 mol = 151.642 mol
  • 151.642 mol * 0.162 L/mol = 24.57 L

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

Finally, to<u> calculate the pressure in the vessel</u>, 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

  • P * 613.29 L = 59.87 mol *  0.082 atm·L·mol⁻¹·K⁻¹ * 365 K
  • P = 2.92 atm
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