We are asked to calculate the concentration of each isomer present at 25 °C once equilibrium is established.

Recall that the equilibrium concentrations are determined by the equilibrium constant (K):

$\overline{){\mathbf{K}}{\mathbf{}}{\mathbf{=}}\frac{\mathbf{products}}{\mathbf{reactants}}}$

Recall that **ΔG˚ _{rxn} and K** are related to each other:

$\overline{){\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{-}}{\mathbf{RTlnK}}}$

With this, we can derive expressions of K.

We can use the following equation to solve for ** ΔG˚_{rxn}**:

$\overline{){\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{{\mathbf{rxn}}}{\mathbf{=}}{\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{prod}}{\mathbf{-}}{\mathbf{\Delta G}}{{\mathbf{\xb0}}}_{\mathbf{f}\mathbf{,}\mathbf{}\mathbf{react}}}$

We go through the following steps to solve the problem:

**Step 1:** Calculate ΔG°_{rxn }for (1) → (2) and (1) → (3)

**Step 2:** Derive K expressions for (1) → (2) and (1) → (3)

**Step 3:** Calculate the concentrations of each

At 25 °C, 1.0 M methylpropene (1) was added to a reaction vessel. Upon addition of a suitable catalyst, an equilibrium mixture of three isomeric compounds formed. Methylpropene (1), cis-2-butene (2), and trans-2 butene (3) are isomers with formula C_{4}H_{8}, with ΔG°_{f} = +58.07 kJ/mol, +65.86 kJ/mol and +62.97 kJ/mol, respectively. What will be the concentration of each isomer present at 25 °C once equilibrium is established? Please circle your answer(s)

Hint: The sum of the equilibrium concentrations of the three species will still total 1.0 M.

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