Questions regarding kinetics

[cccc]

The question is this: at 25 degrees C, 200 cm^3 of 1 mol dm^3 of nitric acid is added to 5g of magnesium powder. If experiment is repeated using same mass of magnesium powder, which conditions will result in the same initial reaction rate? 

 

I chose 100 cm^3 of nitric acid , 2 mol dm^3 as conc and 25 degrees C.

However, the answer is 100 cm ^3 of 1 mol dm^3 HNO3. How is it the case? If it is so, then in 200 cm^3, there would be 2 mol dm^3. As there is a higher conc, then the reaction rate should be higher, so it doesn't give the same rate?

[kw0573]

I do think you know the thought process and you only tripped up because the question gave extraneous information.
The original conditions had 1 mol dm^-3 as [HNO₃] so the correct choice also have 1 mol dm^-3 as [HNO₃]_.Note that "in theory" solids don't contribute to rate so [HNO₃] is the only species affecting rate so its concentration must remain unchanged. The volumes provided are completely irrelevant; they are there to confuse you. Your choice said instead 2 mol dm^-3; I haven't done any calculations these are directly from the questions.
 

[Vioh]

I totally agree with kw0573. This question is so simple, yet I have seen many people failing at it.

1 hour ago, cccc said:

However, the answer is 100 cm ^3 of 1 mol dm^3 HNO3. How is it the case? If it is so, then in 200 cm^3, there would be 2 mol dm^3.

@cccc Your calculation is incorrect here. If you double the volume, you don't double the concentration; only the amount will be doubled. So if you have 100 cm3 of 1 mol/dm3 nitric acid, then the number of moles of nitric acid that you have is 0.1 moles. Now if you increase the same solution to the volume of 200 cm3, the amount will be doubled (in other words you will have 0.2 moles of nitric acid). However, the concentration still remains the same, namely at 1 mol/dm3.

[Msj Chem]

The initial rate of reaction is determined by factors such as temperature, concentration and surface area. The amount of product produced depends on the amount of the limiting reactant. 

For example, a solution of 1.00 moldm^-3 HCl and 2.00 moldm^-3 HCl (both reacted with powered magnesium at 25^oC) with have different initial rates of reaction, with the higher concentration having the faster initial rate of reaction. The amount of product produced depends on the amount of the limiting reactant (which is not relevant in this question). 

Maybe this video will help:

 

Edited April 6, 2016 by Msj Chem