A #5 L# container holds #5 # mol and #6 # mol of gasses A and B, respectively. Every three of molecules of gas B bind to two molecule of gas A and the reaction changes the temperature from #360^oK# to #210 ^oK#. By how much does the pressure change?

Question

A #5 L# container holds #5 # mol and #6 # mol of gasses A and B, respectively.  Every three of molecules of gas B bind to two molecule of gas A and the reaction changes the temperature from #360^oK# to #210  ^oK#. By how much does the pressure change?

Elena Albarran · Accepted Answer

The pressure decreases by either 54.65 atm or 61.543 atm, depending on whether the product is gaseous or solid.

To keep everything straight, let's create a table of the initial and final states: We are changing three parameters in this situation: pressure, temperature, and the number of moles of gas. According to the Ideal Gas Law, these are P, T, and n. V and R stay constant. #V" "5.0 l" "5.0 l# #R" "0.082054 (l*(atm)/(mol*K))" "0.082054 (l*(atm)/(mol*K))# #n" "11 mol" "3 mol or 1 mol #(see below) #T" "360 K" "210 K# #P" "TBD" "TBD# A couple of points. 1) The question does not specify whether the product of the reaction is gaseous or not. If it is gaseous, then you will be left with three moles (you will lose 4 A and 6 B, leaving one mole of A and two moles of #A_2B_3#). If it is not gaseous, then you are simply left with one mole of A. 2) Just a note on proper notation: the temperature is in kelvins, not "degrees kelvin". No degree symbol is used with K. We can easily calculate the initial pressure: #P = nRT/V# #P = 11mol xx 0.082057(l*(atm)/(mol*K)) xx (360K) / (5l) = 64.989 atm# The question did not specify whether the final product was a gas (unlikely, given the temperature) or a solid, so we will calculate both answers. Now for the final pressure: #P_3 = 3mol xx 0.082057(l*(atm)/(mol*K)) xx (210K) / (5l) = 10.339 atm# or #P_1 = 1mol xx 0.082057(l*(atm)/(mol*K)) xx (210K) / (5l) = 3.446 atm# in the #P_3# case (product remains gaseous) the pressure decreases by 54.65 atm, or #(54.65)/(64.989) xx 100% = 84%# in the #P_1# case (product is solid) the pressure decreases by 61.543 atm, or #(61.543)/(64.989) xx 100% = 95%#

Nora Arzate · Answer

undefined To find the change in pressure, you 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. Rearrange the equation to $ P = \frac{nRT}{V} $, then calculate the initial and final pressures using the given temperatures and moles of gas. Finally, find the difference between the initial and final pressures to determine the change.