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Vapor pressure in mm of mercury of solid and liquid ammonia is given by ​InP=23.1–(3749/T) and InP=19.6–(3049/T),I_nP = 23.1 – (3749/T) \s
Question

Vapor pressure in mm of mercury of solid and liquid ammonia is given by

InP=23.1(3749/T) and InP=19.6(3049/T),I_nP = 23.1 – (3749/T) \space{ and }\space I_nP = 19.6 –(3049/T), find out the triple point.

A.

700 K

B.

231 K

C.

200 K

D.

180 K

Correct option is C

We are given two equations for vapor pressure of solid and liquid ammonia in terms of temperature T,and asked to find the triple point, i.e., where both phases coexist:lnPsolid=lnPliquidWrite given equationslnPsolid=23.13749TlnPliquid=19.63049TEquating the two23.13749T=19.63049TSolveSubtract:23.119.6=37493049T=>3.5=700T=>T=7003.5=200 K\begin{aligned}&\text{We are given two equations for vapor pressure of solid and liquid ammonia in terms of temperature } T, \\&\text{and asked to find the triple point, i.e., where both phases coexist:} \\&\ln P_{\text{solid}} = \ln P_{\text{liquid}} \\[1.5em]&\textbf{Write given equations} \\&\ln P_{\text{solid}} = 23.1 - \frac{3749}{T} \\&\ln P_{\text{liquid}} = 19.6 - \frac{3049}{T} \\[1.5em]&\textbf{Equating the two} \\&23.1 - \frac{3749}{T} = 19.6 - \frac{3049}{T} \\[1.5em]&\textbf{Solve} \\&\text{Subtract:} \\&23.1 - 19.6 = \frac{3749 - 3049}{T} \Rightarrow 3.5 = \frac{700}{T} \Rightarrow T = \frac{700}{3.5} = \boxed{200\, \text{K}}\end{aligned}​​

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