AP Chemistry Question of the Day--68

I was tutoring a student and came across the following question, I found it to be a good question regarding several concepts in chemistry.

A 2cm Mg ribbon was reacted with 100ml 0.10M HCl and at the end of the reaction, all the Mg ribbon has dissolved. The temperature of the reaction mixture increased by 20 degrees. Another 1cm Mg ribbon was reacted with 0.1M HCl in a separate reaction. How much HCl solution is required to make the temperature increase 10 degrees?

A. 50mL
B. 100mL
C. 200mL
D. Could not be decided.

The correct answer is B.
Mg reacts with HCl and produces MgCl2 and Hydrogen gas. If at the end of the reaction, all the Mg has dissolved, it means that Mg was the limiting agent. If half the length of Mg was used in the second experiment, then the amount of heat released should also be halfed.
According to q=mc(deltaT), both the q and delta T were half of the original, the m should stay the same. m here is the mass of the total reaction mixture. If we assume the reaction mixture has the same density as water, then we can deduce that the mass of the reaction mixture depends on the volume of the HCl solution. As a result, the volume of the HCl solution should remain as 100mL.
A common mistake would think the m in q=mc(deltaT) refers to the mass of the reactants. Because the temperature increase occurs to the overall reaction mixture, the mass should always be the mass of the total reaction mixture, not the mass the reactants themselves.

Hope this helps with your AP review. Good luck in your exam in May.