The molar entropy of helium gas at 258C and 1.00 atm is 126.1 J K21 mol21. Assuming ideal behavior, calculate the entropy of the following. a. 0.100 mole of He(g) at 258C and a volume of 5.00 L b. 3.00 moles of He(g) at 258C and a volume of 3000.0 L

Part  (a) 0.100 mole of He(g) at 258°C and a volume of 5.00 L, entropy = 12.6117 J/K

Part (b) 3.00 moles of He(g) at 258°C and a volume of 3000.0 L, entropy = 379.089 J/K

Explanation:

ΔS = n*R*ln(V₂/V₁)

where;

ΔS is change in entropy

n is number of moles

R is ideal gas constant = 0.08206 L*atm/mol*K

V₂ is final volume

V₁ is the initial volume

Part  (a) 0.100 mole of He(g) at 258°C and a volume of 5.00 L

Initial volume of  0.1 mole of helium gas at 258°C (495K)

V₁ = n*R*T/P = (0.100mol)(0.08206 L*atm/mol*K)*(495K)/(1atm) = 4.06 L

ΔS = n*R*ln(V₂/V₁) = 0.1*0.08206*ln(5/4.06) = 0.0017 J/K

ΔS = 0.0017 J/K

S₁ = 0.100 mol* 126.1(J/K*mol) = 12.61 J/K

S₂ = ΔS + S₁

S₂ = 0.0017 J/K + 12.61 J/K = 12.6117 J/K

Part (b) 3.00 moles of He(g) at 258°C and a volume of 3000.0 L

Initial volume of 3.00 moles of helium gas at 258°C (495K)

V₁ = n*R*T/P = (3.00 mol)(0.08206 L*atm/mol*K)*(495K)/(1atm) = 121.8591 L

ΔS = n*R*ln(V₂/V₁) = 3.0*0.08206 *ln(3000/121.859) = 0.789 J/K

ΔS = 0.789 J/K

S₁ = 3.0 mol* 126.1(J/K*mol) = 378.3 J/K

S₂ = ΔS + S₁

S₂ = 0.789 J/K + 378.3 J/K = 379.089 J/K

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