question_answer

For the chemical equilibrium, \[CaC{{O}_{3}}(s)\] ⇌ \[CaO(s)+C{{O}_{2}}(g),\ \Delta H_{r}^{{}^\circ }\] can be determined from which one of the following plots      [AIIMS 2005]

A)           

B)  

C)       

D)  

Correct Answer: A

Solution :

       For the reaction,                    CaCO3(g) ⇌ CaO(s) + CO2(g)                    Kp = \[{{P}_{C{{O}_{2}}}}\] and KC  = [CO2]                    (Q [CaCO3] = 1 and [CaO] = 1 for solids]                    According to Arrhenius equation we have                    \[K=A{{e}^{-\Delta H{{{}^\circ }_{r}}/RT}}\]                    Taking logarithm, we have                    \[\log {{K}_{p}}=\log A-\frac{\Delta H_{r}^{o}}{RT(2.303)}\]                    This is an equation of straight line. When log Kp is plotted against 1 / T. we get a straight line.                    The intercept of this line = log A, slope = ?∆H°r / 2.303 R                    Knowing the value of slope from the plot and universal gas constant R, ∆Hr° can be calculated.                    (Equation of straight line : Y = mx + C. Here,                    \[\log {{K}_{p}}=-\frac{\Delta H_{r}^{o}}{2.303R}\left( \frac{1}{T} \right)+\log A\]                                 Y              m            x              C