Question

1. Consider the following reaction:

3CH4(g)→C3H8(g)+2H2(g)

Calculate ΔG at 298 K if the reaction mixture consists of 41 atm of CH4, 0.011 atm of C3H8, and 2.1×10⁻² atm of H2.

Express the Gibbs free energy in kilojoules to two significant digits.

2. The element gallium (Ga) freezes at 29.8 ∘C, and its molar enthalpy of fusion is ΔHfus = 5.59 kJ/mol.

Calculate the value of ΔS when 61.0 g of Ga(l) solidifies at 29.8 ∘C. in J/K

Answer 1

Answer – 1)

We are given, pressure of each reactant and product and we need to calculate the ΔG

Reaction - 3CH₄(g) ---> C₃H₈(g)+2H₂(g)

Step 1) Calculate the reaction quotient

Q = P(H₂ (g))² * P (C₃H₈(g)) / P(CH₄(g))³

     = (0.021)²* 0.011 / (41)³

     = 7.04*10^-11

Now we need to calculate the standard Gibb’s frre energy for this reaction

We know,

ΔG^o = sum of the ΔG^o of product - sum of the ΔG^o of reactant

       = [ΔG^oC₃H₈(g) + 2*ΔG^o H₂(g)] – [3* ΔG^oCH₄(g)]

      = (-23.56 kJ + 2*0.00 kJ) – ( 3*-50.84 kJ)

       = 128.96 kJ

       = 1.289*10⁵ J

We know formula

ΔG = ΔG^o+ RTlnQ

      = 1.289*10⁵ J + 8.314 J/mol.K * 298 K * ln 7.04*10^-11

     = 71042

ΔG = 71 kJ

2) Given, ΔHfus = 5.59 kJ/mol., T = 29.8 +273 = 302.8 K

Mass of Ga(l) = 61 g

First we need to convert given mass of Ga(l) to its moles

We know, moles = mass / molar mass

                            = 61 g / 69.723 g.mol^-1

                            = 0.875 moles

Now we are given ΔHfus per mole means

1 mole of Ga = 5.59 kJ

So, 0.875 mole = ?

= 4.89 kJ

We need to calculate ΔS

We know , when liquid converted to solid then there is ΔG^ois zero

So, ΔS = ΔHfus / T

We need to convert the ΔHfus kJ to J

We know,

1 kJ = 1000 j

So, 4.89 kJ = ?

= 4.89*10³ J

Now plugging the value in the fromula-

ΔS = ΔHfus / T

      = 4.89*10³ J / 302.8 K

       = 16.15 J/k