For pure (anyhydrous) hydrogen chloride (HCl) the ctricial pressure p c = 81.5 a

Question

For pure (anyhydrous) hydrogen chloride (HCl) the ctricial pressure pc = 81.5 atm and the critical temperature Tc = 325K.

(a) using this data alone, predit the pressure exhibited by HCl when confined to a mmolar volume of .075 L at a temperature of 300K, assuming that HCl can be described with a van der Waals Equation of State.

(b) Under these conditions, is HCl best decribed as a liquid, a gas, or a supercritical liquid?

Please show work, i think i know what i'm supposed to do but i keep getting lost.

Explanation / Answer

Tc = 8a / 27bR = 325 a/b = 325*R*27 / 8 = 91.04 = a/b

Pc = a/(27b^2) = 81.5 a/b^2 = 27*81.5 = 2200.5 = a/b^2

Tc / Pc = a/b / a/b^2 = b = 91.04 / 2200.5 = 0.0413

a/0.0413 = 91.04 a = 91.04*0.0413 = 3.76

volume = .075 L

temperature = 300K

P = nRT/(V - nb) - a * (n^2/v^2)

= 0.083* 300 / (0.075 - 0.0413) - 3.76 * (1/(0.075)^2) = 70.427atm

a) Pressure of gas 70.427atm

b) it is well below Pc and Tc so we have to tell it is gaseous form

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