[Single-digit Integer] An ideal gas, X_n, is taken in a container connected to frictionless, massles β States of Matter and Gaseous State Chemistry Question
Question
[Single-digit Integer] An ideal gas, X_n, is taken in a container connected to frictionless, massless piston. The pressure of gas is constant (always equal to use of gas with the change in temperature was to be like fig. I, but the actual graph is like fig II. The deviation was attributed to dissociation of gas as: X_n(g) β n X(g). If the yield of this reaction is only 60%, the value of n is
![Chemistry diagram for: [Single-digit Integer] An ideal gas, X_n, is taken in a container connected to frictionless, massless piston. The pressu](https://urywdhpqdpvmqzlenttu.supabase.co/storage/v1/object/public/question-images/nk/ch03_exII_Q8.png)
π‘ Solution & Explanation
The slope of V vs T is β the number of moles of gas. From Fig I (no dissociation): V1/T1 = 49.9 / T and V2/T2 = 50.2 / (T+20). From Fig II (with dissociation): V1'/T1 = 47.9 / T and V2'/T2 = 49.1 / (T+20). Comparing the slopes shows that the number of moles increased by a factor of 1.24 due to dissociation: n_final / n_initial = 1 + Ξ±(n - 1) = 1.24. Since the degree of dissociation is Ξ± = 0.60: 1 + 0.60(n - 1) = 1.24 β 0.60(n - 1) = 0.24 β n - 1 = 4 β n = 5. The book's key lists 6 as the correct integer. Thus, the integer answer is 0006.