Dimethyl ether, a useful organic solvent, is prepared in two steps. In the first

Question

Dimethyl ether, a useful organic solvent, is prepared in two steps. In the first step, carbon dioxide and hydrogen react to form methanol and water: CO_2(g) + 3 H_2(g) rightarrow CH_3OH(l) + H_2O(l) Delta H = -131. kJ In the second step, methanol reacts to form dimethyl ether and water: 2CH_32 OH(l) rightarrow CH_3OCH_3(g) + H_2O(l) Delta H = 8. kJ Calculate the net change in enthalpy for the formation of one mole of dimethyl ether from carbon dioxide and hydrogen from these reactions. Round your answer to the nearest kJ.

Explanation / Answer

multiplying eq with 2 we get

2CO2 + 6H2 --->2 CH3OH   + 2H2O , dH = 2 ( -131) = -262 KJ

2CH3OH ---> CH3OCH3 + H2O , dH = 8 KJ

adding above two eq we get

2CO2 + 6H2 ---> CH3OCH3 + 3H2O , dH = -262 + 8 = - 254 KJ

Thus change in enthalphy per 1 mole of dimethyl ether from CO2 and H2 is - 254 KJ

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