A #5 L# container holds #9 # mol and #12 # 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 #320^oK# to #210 ^oK#. By how much does the pressure change?

1 Answer
May 7, 2018

The Pressure within the container decreases by
#Delta P=9.43*10^6color(white)(l)"Pa"#

Explanation:

Number of moles of gaseous particles before the reaction:
#n_1=9+12=21color(white)(l)"mol"#

Gas A is in excess.
It takes #9*3/2=13.5color(white)(l)"mol">12 color(white)(l)"mol"# of gas B to consume all gas A and #12*2/3=8 color(white)(l)"mol"<9 color(white)(l)"mol"# vice versa.
#9-8=1color(white)(l)"mol"# of gas A would be in excess.

Assuming that every two molecules of A and three molecules of B combine to yield a single gaseous product molecule, the number of moles of gas particles present in the container after the reaction would equal to
#color(darkblue)(n_2)=12*color(darkblue)(1)/3+1=color(darkblue)(5)color(white)(l)"mol"#

The volume of the container in the appropriate SI unit would be
#V=5 color(white)(l)"dm"^3=5*10^(-3) color(white)(l)m^3#

The temperature drops from #T_1=320 color(white)(l)"K"# to #T_2=210 color(white)(l)"K"# during the reaction. Apply the ideal gas law with

#R=8.314color(white)(l)"m" ^3* "Pa"* "mol" ^(-1)* "K" ^(-1)#

gives

#P_1=(n_1*R*T_1)/(V)=1.12*10^7 color(white)(l)"Pa"#

#color(darkblue)(P_2)=(color(darkblue)(n_2)*R*T_1)/(V)=color(darkblue)(1.75*10^6) color(white)(l)"Pa"#

#color(darkblue)(Delta P)=color(darkblue)(P_2)-P_1=color(darkblue)(-9.43*10^6)color(white)(l)"Pa"#

Hence the pressure decrease by #color(darkblue)(9.43*10^6)color(white)(l)"Pa"#.

Note that the figures in dark blue are dependent on the assumption that every two moles of gas A and three moles of gas B combine to form one mole of product, which is also a gas. See if you can find the right #Delta P# based on further information given in the question.

Reference
[1] The Ideal Gas Law, http://www.science.uwaterloo.ca/~cchieh/cact/c120/idealgas.html