A #5 L# container holds #5 # mol and #10 # mol of gasses A and B, respectively. Every five of molecules of gas B bind to two 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 #5 # mol and #10 # mol of gasses A and B, respectively.  Every five of molecules of gas B bind to two molecule of gas A and the reaction changes the temperature from #320^oK# to #450  ^oK#. By how much does the pressure change?

Julia Aguilar · Accepted Answer

There is a change of #-56.649# atmospheres.

To solve for #DeltaP#, we need two values: #P_"initial"# and #P_"final"#. First, we calculate the initial pressure using the Ideal Gas Law: #P_iV=n_iRT_i# Here, #V=5"L"# #n_i=15"mol"# #T_i=320"K"# #R=0.0821"L atm K"^-1"mol"^_1# To solve for #P_i#, we rearrange: #P_i=(n_iRT_i)/V# And input: #P_i=(15*0.0821*320)/5# #P_i=78.816"atm"# Now, we need the equation that took place. It is: #5"A"+10"B"rarr2"A"_2"B"_5+"A"#. Here, one mole of #"A"# is left unreacted. In the products side, we find we now have #3# moles of gas. Use the Ideal Gas Law again: #P_fV=n_fRT_f# Here, #n_f=3"mol"# #T_f=450"K"# Rearranging to solve for #P_f#: #P_f=(n_fRT_f)/V# and inputting: #P_f=(3*0.0821*450)/5# #P_f=22.167"atm"# We know that #DeltaP=P_f-P_i#. Inputting: #DeltaP=22.167-78.816# #DeltaP=-56.549"atm"#

Emily Abbate · Answer

undefined To solve this problem, we first need to calculate the initial and final number of moles of gas A and B, using the ideal gas law. Then, we can determine the initial and final volumes of the gases at the given temperature. Finally, we can use the ideal gas law again to find the initial and final pressures, and then calculate the change in pressure.

1. Calculate initial moles of A and B:
Initial moles of A = 5 mol
Initial moles of B = 10 mol

2. Calculate final moles of A and B after the reaction:
For every 5 molecules of B, 2 molecules of A react.
So, after the reaction, the number of remaining molecules of B = 10 mol - (10 mol / 5) * 2 = 6 mol
Remaining moles of A = 5 mol - (10 mol / 5) = 3 mol

3. Use the ideal gas law to find the initial and final volumes of the gases:
Initial volume = 5 L
Initial temperature = 320 K
Final temperature = 450 K

4. Calculate the initial and final pressures using the ideal gas law:
$P_1V_1 = n_1RT_1$ and $P_2V_2 = n_2RT_2$

5. Calculate the change in pressure:
$\Delta P = P_2 - P_1$

By calculating the values using the given information and equations above, you can find the change in pressure.