A #3 L# container holds #30 # mol and #15 # mol of gasses A and B, respectively. Groups of three of molecules of gas B bind to five molecules of gas A and the reaction changes the temperature from #320^oK# to #480^oK#. How much does the pressure change?

Question

A #3 L# container holds #30 # mol and #15 # mol of gasses A and B, respectively.  Groups of three of molecules of gas B bind to five molecules of gas A and the reaction changes the temperature from #320^oK# to #480^oK#. How much does the pressure change?

Nora Arzate · Accepted Answer

The final pressure is three times whatever the initial pressure was.

#5A + 3B → A_5B_3# With an initial ratio of 2:1 gas B is the limiting reagent. Only 15 * 5/3 = 25 moles of A will be combined with 15 moles of B. Thus, the final composition in the container will be 5 moles of A and 5 moles of #A_5B_3# for a total of 10 moles. The original number of moles was 45. The ratio of the temperature change in oK is equal to the ratio of the change in the total number of moles of gas in the container times the inverse ratio of the pressures, assuming ideal gas behavior where n = PV/RT and a constant volume. #(n_1*(PV)/T)_1 = (n_2*(PV)/T)_2# ; #(n_1/n_2)*(T_1/T_2) = P_2/P_1# #P_1/P_2 = (n_2/n_1)*(T_2/T_1)# #P_1/P_2 = (10/45)*(480)/(320)# #P_1/P_2 = 0.3333 ; P_2 = P_1 * 3# so the final pressure is three times whatever the initial pressure was (exothermic reaction!).

Xavier Adame · Answer

undefined To solve this problem, we can use the ideal gas law, $ PV = nRT $, where $ P $ is pressure, $ V $ is volume, $ n $ is the number of moles, $ R $ is the gas constant, and $ T $ is temperature in Kelvin.

First, we need to find the initial pressure using the initial conditions and then calculate the final pressure using the final conditions. Finally, we subtract the initial pressure from the final pressure to find the change in pressure.

Initial pressure ($ P_i $) can be calculated using the initial number of moles of gas and initial temperature.

Final pressure ($ P_f $) can be calculated using the final number of moles of gas and final temperature.

Then, the change in pressure ($ \Delta P $) can be found by subtracting the initial pressure from the final pressure.

Given:
Initial temperature ($ T_i $) = 320 K
Final temperature ($ T_f $) = 480 K
Initial number of moles of gas A ($ n_A $) = 30 mol
Initial number of moles of gas B ($ n_B $) = 15 mol

Molar ratios:
Gas B molecules bind to gas A molecules in a 3:5 ratio.

Gas constant ($ R $) is a constant value.

Using these values, we can calculate the initial and final pressures and then find the change in pressure.