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

_{v}dT for ideal gas

C

_{v}=C

_{p}-nR

U=q+w

dU=C

_{v}dT=dq+PdV

Integrate

(nC

_{p,m}-nR)(T

_{2}-T

_{1})=(10kJ/mol*1000J/kJ*30%*2/3*n)+0

T

_{2}=(10kJ/mol*1000J/kJ*30%*2/3)/(C

_{p,m}-R)+T

_{1}=390K

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

mass

_{A}=(M

_{A})(1/1.5)*n

_{B}=

**31.2g**T

_{2}=

**390K**