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Chemistry Forums for Students => Physical Chemistry Forum => Topic started by: YuliaSnow on September 25, 2016, 07:08:45 PM

Title: Thermodynamics - First Law Problem
Post by: YuliaSnow on September 25, 2016, 07:08:45 PM

I have been trying to figure out how to do this problem for a few hours, hoping someone can help me out. :)

Question:

An air mattress (of volume 50L) is inflated using a solid called  "A" with a molar mass of 10g/mol. "A" decomposes and produces "B", a gas at a ratio of 1:1.5. Each mole of A also produces an enthalpy of ΔH=-10kJ. Assume 70% of this energy is deposited in "B" and decomposition is instantaneous. Also let "B" be an ideal gas with C_p,m=30J/mol/K. In order for the mattress to work properly, it should reach a pressure of 3 atm when fully inflated.

a) Estimate the mass in g of "A" needed to use the air mattress. State any assumptions or approximations being made.
Hint: Treat the decomposition of "A" and the expansion of "B" as two separate processes.

b) Find the temperature of "B" after the mattress is fully inflated.
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Here is my attempt at it:

I assumed the temperature is at room temp (298K) and pressure is starting at 1 atm.

I used q=(10kJ/mol*1000J/kJ*30%*2/3*n) since 70% was put in "B".
Some equations I used:
PV=nRT
dU=C_vdT for ideal gas
C_v=C_p-nR


U=q+w
dU=C_vdT=dq+PdV
Integrate
(nC_p,m-nR)(T₂-T₁)=(10kJ/mol*1000J/kJ*30%*2/3*n)+0
T₂=(10kJ/mol*1000J/kJ*30%*2/3)/(C_p,m-R)+T₁=390K

n=PV/RT=(3atm)(50L)/(0.082057Latm/mol/K)/390K=4.687mol

mass_A=(M_A)(1/1.5)*n_B
=31.2g
T₂=390K