One suggestion for sequestering CO₂ is to synthesize carbonate polymers. Polycarbonate is well known for its strength and transparency. To gauge the feasibility of this approach, consider the synthesis of dimethyl carbonate (DMC) from methanol and CO₂ at 350 K.

(a) Write a balanced stoichiometric equation for this reaction. Highlight any by-products.

(b) Estimate the K_a value for the reaction. What pressure is required to achieve P·K_a = 0.1?

(c) Methanol and DMC are both liquids at this temperature. Explain how to estimate their partial pressures at a given extent of conversion. You may neglect the CO₂ in the liquid for this question.