Derive an expression for the compression factor of a gas thatobeys the equation

Question

Derive an expression for the compression factor of a gas thatobeys the equation of state p(V-nb) = nRT, where b and R areconstants. If the pressure and temperature are such that Vm=10b,what is the numerical value of the compression factor? Please show work, thanks. Derive an expression for the compression factor of a gas thatobeys the equation of state p(V-nb) = nRT, where b and R areconstants. If the pressure and temperature are such that Vm=10b,what is the numerical value of the compression factor? Please show work, thanks.

Explanation / Answer

I got something different...

[Eqn 1]: P(V-nb) = nRT

we also know that:

[Eqn 2]: Z = P(Vm)/RT (where Vm = molar volume).

Multiplying out [Eqn 1]:

PV - Pnb = nRT

Then dividing by n:

PV/n - Pb = RT

Therefore, we can say that,

[Eqn 3]: RT = P(Vm) - Pb = P[(Vm) - b]

RT appears in the denominator of [Eqn 2], so we can substitute [Eqn 3] into [Eqn 2] to get:

Z = P(Vm) / P[(Vm) - b]

P cancels out:

[Eqn 4]: Z = Vm / Vm - b

Then substitute the given Vm = 10b into [Eqn 4]:

Z = 10b / 10b - b

= 10b / 9b

= 10/9

That's what I got.

Related Questions

Navigate

• Browse (All)
• Browse D
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.