A #3 L# container holds #5 # mol and #5 # mol of gasses A and B, respectively. Groups of three of molecules of gas B bind to two molecules of gas A and the reaction changes the temperature from #340^oK# to #320^oK#. How much does the pressure change?

Question

A #3 L# container holds #5 # mol and #5 # mol of gasses A and B, respectively.  Groups of three of molecules of gas B bind to two molecules of gas A and the reaction changes the temperature from #340^oK# to #320^oK#. How much does the pressure change?

William Audy · Accepted Answer

We have to take two things into account:
the change in moles and the change in temperature.

(1) change caused by change in number of molecules: Reaction equation: #2A+3B->A_2B_3# So #5# moles of B will react with #2/3xx5=3 1/3# moles of A. #1 2/3# moles of A will be left. Since every 3 moles of B will form 1 mole of #A_2B_3#: #5/3=1 2/3# mole of #A_2B_3# will be formed Total moles before reaction: #5+5=10# moles Total moles after reaction: #1 2/3 + 1 2/3=3 1/3# moles (mixture of #A_2B_3# and left-over #A#) Pressure change because of amount of matter: #3 1/3div5=10/3div5=xx2/3# (2) Change caused by temperature change: Temperature goes down from #34oK# to #320K# Pressure change: #320/340=xx16/17# Total change: Pressure is decreased by a factor of #2/3xx16/17=32/51~~xx0.63# Or: pressure decreases to #63%# of original (or by #37%#) Note: Of course you could have used the general gas-formula #p=(nRT)/V# to calculate both pressures.

Adam Arnold · Answer

undefined To find the change in pressure, you can use the ideal gas law, which states:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin

Given:
Initial temperature (T1) = 340 K
Final temperature (T2) = 320 K
Initial number of moles of gas A (nA) = 5 mol
Initial number of moles of gas B (nB) = 5 mol
Initial total number of moles (n_total) = nA + nB
Volume (V) = 3 L

To find the initial pressure (P1), you can use the initial conditions:

P1 = (n_total * R * T1) / V

To find the final pressure (P2), you need to use the final conditions:

P2 = (n_total * R * T2) / V

Then, the change in pressure (ΔP) can be calculated as:

ΔP = P2 - P1