Dimethyl ether, CH₃OCH₃(𝑔), is an industrially useful organic compound that is a gas at room temperature. Consider the following balanced thermochemical equations:

CH₃OCH₃(g) + 3 O₂(g) → 2 CO₂(g) + 3 H₂O(g) ΔH° = −1328 kJ          

CH₄(g) + 2 O₂(g) → CO₂(g) + 2 H₂O(g) ΔH° = −802 kJ      

2 C₂H₆(g) + 7 O₂(g) → 4 CO₂(g) + 6 H₂O(g) ΔH° = −2855 kJ

a. All three of the above reactions produce H2O(𝑔). If they were written to produce H2O(𝑙) instead, would the values of Δ𝐻° become more negative, become less negative, or stay the same?

b. By using Hess’s law and the reactions provided, calculate Δ𝐻° for the following balanced reaction between dimethyl ether and methane to produce ethane and water:

CH₃OCH₃(g) + 2 CH₄(g) → 2 C₂H₆(g) + H₂O(g)