Predict the relative rates for the reaction of butadiene and (a) ethene, (b) methyl propenoate, (c) maleic anhydrid.

To predict the relative rates of a reaction, we usually consider the reaction mechanism and the factors that affect the reaction rate. Some of the key factors that can influence the rate of a reaction include the nature of the reactants, the concentration of reactants, temperature, and the presence of a catalyst.

In this case, we need to compare the relative rates of the reaction of butadiene with ethene, methyl propenoate, and maleic anhydride.

(a) Butadiene and Ethene:
To predict the relative rates of the reaction between butadiene and ethene, we need to consider the reaction mechanism and the nature of the reactants.

Butadiene and ethene are both alkenes, and the reaction between alkenes typically involves a pi-bond breaking and forming a new pi-bond. Since both butadiene and ethene have the same functional group (C=C double bond), their reaction mechanism would be similar.

The relative rate of the reaction between butadiene and ethene will depend on the reactivity of the double bonds within each molecule. Butadiene has two double bonds (conjugated system), while ethene has only one double bond. Due to the presence of conjugation, the double bonds in butadiene are more reactive compared to the double bond in ethene.

Therefore, the reaction of butadiene with ethene will likely have a higher rate compared to the reaction of ethene alone.

(b) Butadiene and Methyl Propenoate:
To predict the relative rates of the reaction between butadiene and methyl propenoate, again, we need to consider the reaction mechanism and the nature of the reactants.

Methyl propenoate is an ester which contains an ester functional group, while butadiene is an alkene. The reaction between an alkene and an ester typically involves the nucleophilic addition of the alkene to the carbonyl group of the ester, followed by elimination of the leaving group.

The relative rate of the reaction between butadiene and methyl propenoate will depend on the reactivity of the double bond in butadiene and the electrophilicity of the carbonyl group in the ester. Without further information about the specific reactants, it's difficult to determine the exact relative rates.

(c) Butadiene and Maleic Anhydride:
To predict the relative rates of the reaction between butadiene and maleic anhydride, we need to consider the reaction mechanism and the nature of the reactants.

Maleic anhydride is a cyclic anhydride which contains a reactive carbonyl group. The reaction between butadiene and maleic anhydride is a Diels-Alder reaction, a type of cycloaddition reaction.

The Diels-Alder reaction between butadiene and maleic anhydride is generally highly exothermic and occurs rapidly. Therefore, the reaction between butadiene and maleic anhydride is likely to have a relatively high rate.

In summary, the relative rates of the reactions involving butadiene will depend on various factors such as the nature of the reactants, reaction mechanism, and the reactivity of the functional groups involved. Further specific information about the reactants and conditions would be necessary to give more precise predictions.