A 5 L5L container holds 8 8 mol and 10 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 360^oK360oK to 270 ^oK270oK. By how much does the pressure change?

1 Answer
Feb 2, 2018

The total pressure PP inside the V = 5 LV=5L container is due to the pressures of both gasses AA and BB:

P = P_A + P_BP=PA+PB.

According to the ideal gas law:

PV = nRTPV=nRT.

If we consider gasses AA and BB to be ideal, then this equation must apply to each one of them. For the total pressure, this means that:

P = (n_ART_A)/V_A + (n_BRT_B)/V_BP=nARTAVA+nBRTBVB.

If we also assume that both gasses can occupy all the container's volume and that they will always be at thermal equilibrium with each other, then:

P = (RT)/V(n_A + n_B)P=RTV(nA+nB).

This means that we can obtain the pressure's value if we know the above quantities. Since R = 8,2 J/(molK)R=8,2JmolK is constant and we know the values for TT and VV, we must figure out what happens to the number of mols of each gas after the reaction takes place.

Since it takes 5 molecules of gas BB to bind to 2 molecules of gas AA, we can extend this proportion to their corresponding number of mol. Since initially we have n_(1A) = 8n1A=8 mol and n_(1B) = 10n1B=10 mol, then, after the reaction takes place, we will end up with n_(2A) = 4 moln2A=4mol, n_(2B) = 0n2B=0 mol and n_C = 2nC=2 mol of the new gas, the product of the AA and BB reaction.

Then, our final pressure will be described by:

P_2 = (RT)/V(n_A + n_B + n_C)P2=RTV(nA+nB+nC).

(Remember that P_1 = (RT)/V(n_A + n_B)P1=RTV(nA+nB).

Taking the values to perform the calculations:

P_1 = (0.082 (atm cancel(L))/(cancel(mol)cancel(K)) * 360 cancel(K))/(5 cancel(L)) * (8 + 10) cancel(mol);

P_1 = 106.3 atm.

After the reaction takes place:

P_2 = (0.082 (atm cancel(L))/(cancel(mol)cancel(K)) * 270 cancel(K))/(5 cancel(L)) * (4 + 0 + 2) cancel(mol);

P_2 = 26.6 atm.

Therefore, the change in pressure, DeltaP, is:

DeltaP = P_2 - P_1;

DeltaP = -79,7 atm.