Final answer:
To double the volume of the solvent, the effect on the reaction rate depends on the reaction order. For first-order reactions, doubling reactant concentration doubles the reaction rate. Doubling solvent volume dilutes reactant concentration, commonly decreasing the reaction rate.
Step-by-step explanation:
The factor by which you multiply the reaction rate when you double the volume of the solvent depends on the order of the reaction. Assuming we are dealing with first-order reactions, where the rate is directly proportional to the concentration of one reactant, when the concentration is doubled, the reaction rate also doubles, as seen in the provided examples with cyclopropane and CH3CH2Cl.
However, if you double the solvent volume rather than the reactant concentration, the effect on the reaction rate isn't as straightforward. Doubling the solvent volume generally dilutes the reactant concentration, assuming you keep the same amount of reactant. In a diluted solution, the reaction rate would decrease because there are fewer reactant particles per unit volume, which may lead to fewer collisions between reactants and a lower chance of successful reaction events. So, without additional information about the reaction or changes to the amount of solute, one cannot accurately state a specific factor by which to multiply the reaction rate after simply doubling the solvent volume.