9.4.11 Evaluate the solution The problem: A deflated balloon starts with 0.017 m

Question

9.4.11 Evaluate the solution

The problem: A deflated balloon starts with 0.017 mol of air inside of it, an internal volume of 3.0 cm3 , and an inside pressure of 1.0 atm. You add air so that when filled, the balloon contains 0.33 mol of air and has a volume of 30 cm3. The process occurs at constant temperature. Determine the final pressure in the balloon.

Proposed solution: For a constant temperature process, P0V0 = PV. Thus: P = P0V0 / V = (1.0 atm)(3.0 cm3) / (30 cm3 ) = 0.10 atm

a. Identify any missing elements or errors in the solution.

b. Provide a corrected solution or missing elements if you find errors.

Explanation / Answer

number of moles=n1=0.017

internal volume=V1=3 cm^3=3*10^(-6) m^3

inside pressure=P1=1 atm=101325 N/m^2

when filled with air, mols of air=n2=0.33

volume=V2=30 cm^3=30*10^(-6) m^3

pressure=P2

assuming it is an ideal gas, P*V=n*R*T

as temperature is constant, P1*V1/(n1)=P2*V2/n2

==>P2=P1*V1*n2/(V2*n1)

=1.9969*10^5 N/m^2

=1.9412 atm

answers are:

part a:

as number of moles are not constant, the proposed solution does not include number of moles and it has to.

part b:

correct solution is given above and final pressure is 1.9412 atm.

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