A #5 L# container holds #16 # mol and #6 # mol of gasses A and B, respectively. Every three of molecules of gas B bind to four molecule of gas A and the reaction changes the temperature from #320^oK# to #450 ^oK#. By how much does the pressure change?

Question

A #5 L# container holds #16 # mol and #6 # mol of gasses A and B, respectively.  Every three of molecules of gas B bind to four molecule of gas A and the reaction changes the temperature from #320^oK# to #450  ^oK#. By how much does the pressure change?

Adrian Ayala · Accepted Answer

#56.4%# increase

Caution : Dont write #X^o # if it is in kelvin, write #X K# straightaway. Considering they are ideal gases, they follow #PV = nRT# Here, #V# is constant and #R# is anyway constant, so we are left with #P_1/(n_1 T_1)=P_2/(n_2 T_2)# Note that, #16/6>4/3#. So gas B gets totally consumed up. So, #6/3 = 2# moles of new has was formed, so in the process #8# moles of gas A was taken up and #8# moles of A is remaining. So in the reaction, total #n_1 (=16+6 = 22)# moles of gas is transformed into #n_2(=2+8=10)# moles of gas. we are given, #T_1 = 320 K# #T_2 = 450K# So, #P_1/P_2 = (n_1T_1)/(n_2T_2) = (22*320)/(10*450) ~~1.564 # So pressure is about #56.4%# increased.

Parker Abbott · Answer

undefined To solve this problem, we first need to calculate the initial and final number of molecules of each gas using the ideal gas law. Then, we can use the given stoichiometry of the reaction to determine the final number of molecules of each gas after the reaction. Finally, we can use the ideal gas law again to calculate the final pressure and compare it to the initial pressure to find the change in pressure.

1. Calculate the initial and final number of molecules of each gas:
Initial number of moles of gas A (n_A) = 16 mol
Initial number of moles of gas B (n_B) = 6 mol
Total initial number of moles (n_total) = n_A + n_B = 16 mol + 6 mol = 22 mol

Initial number of molecules of gas A (N_A) = n_A * Avogadro's number
Initial number of molecules of gas B (N_B) = n_B * Avogadro's number

2. Calculate the final number of molecules of each gas after the reaction:
Every 3 molecules of B bind to 4 molecules of A.
Let x be the number of molecules of B that react.
Number of molecules of A remaining = N_A - (4/3)*x
Number of molecules of B remaining = N_B - x

3. Use the ideal gas law to calculate the initial and final pressure:
Initial pressure (P_initial) = (n_total * R * T_initial) / V
Final pressure (P_final) = (n_total * R * T_final) / V

4. Calculate the change in pressure:
Change in pressure (ΔP) = P_final - P_initial

After these calculations, we can determine the change in pressure.