How Can I Calculate the Heat of Reaction Using Hess' Law and a Calorimeter?

[Greyt]

Hello there,

I am supposed to experimentally determine (with the use of a calorimeter) the overall heat of reaction per mole of calcium metal in two cases:

1. When I mix HCL, calcium and water in that order.
2. When I mix water, calcium and HCL in that order.

In each case, I am supposed to treat the overall reaction as a single process and determine a ΔH for the two-step process using my determined overall change in temperature.

I've purposefully left out the provided numerical values, hoping to understand more where to start than to solve the actual problem at the moment; however I can provide them if desired.

From what I understand, I'm supposed to basically sum up the overall reaction in an equation and that both ways should theoretically result in the release of the same amount of energy... but how on Earth would I go about calculating the heat of reaction using the overall temperature change?

I will mention that we are provided with the following:

1. Mass of the solution
2. Initial and final temperature
3. Mass of each reagent and the calorimeter itself
4. Heat capacity of the calorimeter

Depressing as it is, I'm fairly lost and any information would be appreciated, thanks.

NOTE: My current attempt revolves around treating the solution as having a heat capacity similar to water, and having the ΔH = CmΔT(water) + CΔT (calorimeter). I don`t know if it`s very appropriate to assume such a thing however and would like to see if there`s any other ideas.

 

[Mandelbroth]

Hello there,

I am supposed to experimentally determine (with the use of a calorimeter) the overall heat of reaction per mole of calcium metal in two cases:

1. When I mix HCL, calcium and water in that order.
2. When I mix water, calcium and HCL in that order.

In each case, I am supposed to treat the overall reaction as a single process and determine a ΔH for the two-step process using my determined overall change in temperature.

I've purposefully left out the provided numerical values, hoping to understand more where to start than to solve the actual problem at the moment; however I can provide them if desired.

From what I understand, I'm supposed to basically sum up the overall reaction in an equation and that both ways should theoretically result in the release of the same amount of energy... but how on Earth would I go about calculating the heat of reaction using the overall temperature change?

I will mention that we are provided with the following:

1. Mass of the solution
2. Initial and final temperature
3. Mass of each reagent and the calorimeter itself
4. Heat capacity of the calorimeter

Depressing as it is, I'm fairly lost and any information would be appreciated, thanks.

NOTE: My current attempt revolves around treating the solution as having a heat capacity similar to water, and having the ΔH = CmΔT(water) + CΔT (calorimeter). I don`t know if it`s very appropriate to assume such a thing however and would like to see if there`s any other ideas.

Important to remember in this case is that the reaction is taking place at what we can assume to be constant pressure. In this case, for which we chemists use the fancy term "isobaric", the heat of the reaction is equal to the enthalpy of the reaction. Thus, you are on the right track with your above attempt.

We can assume that the heat capacity is similar to water if your solution is dilute enough, though you have not given us enough information to confirm that. However, your change in enthalpy should be for the whole solution. Thus, we can just write $\Delta H = Q_{reaction} = (c_{H_{2}O})(m_{sol'n})(\Delta T_{sol'n})$.

 

[Greyt]

Important to remember in this case is that the reaction is taking place at what we can assume to be constant pressure. In this case, for which we chemists use the fancy term "isobaric", the heat of the reaction is equal to the enthalpy of the reaction. Thus, you are on the right track with your above attempt.

We can assume that the heat capacity is similar to water if your solution is dilute enough, though you have not given us enough information to confirm that. However, your change in enthalpy should be for the whole solution. Thus, we can just write $\Delta H = Q_{reaction} = (c_{H_{2}O})(m_{sol'n})(\Delta T_{sol'n})$.

First off, thank you for the swift reply.

It seems that is the correct method of solving the problem, but I am curious as to when I can use the heat capacity of water. Is there a general guideline as to how concentrated a solution has to be before you can no longer say its heat capacity is similar to that of water? At the moment, I seem to rely on that method unless I am dealing with a solution that's stated to be nearly void of water.

 

[Mandelbroth]

First off, thank you for the swift reply.

It seems that is the correct method of solving the problem, but I am curious as to when I can use the heat capacity of water. Is there a general guideline as to how concentrated a solution has to be before you can no longer say its heat capacity is similar to that of water? At the moment, I seem to rely on that method unless I am dealing with a solution that's stated to be nearly void of water.

Heat capacity is the amount of heat (energy transfer) required to change the temperature of a substance by some amount. We are using specific heat capacity, which is the heat capacity per unit of mass.

Because our "heat capacity" depends on mass, we can infer that it changes with the increase of solute (more solute implies more mass). You will likely study the colligative properties of solutions. By adding more solute to a solution, you are reducing the chemical potential, which both lowers the freezing point and raises the boiling point. The concept is rooted in this. However, I think that the change in your accuracy by using the specific heat of water rather than a more exact value for your solution will not be a problem for now.

 

[LudusRex]

Hello,

It seems like you are working with Hess' Law, which states that the enthalpy change of a reaction is independent of the pathway taken from reactants to products. In other words, the total enthalpy change of a reaction is the same whether it occurs in one step or multiple steps. This law is useful in cases where it is difficult or impossible to directly measure the enthalpy change of a reaction, such as in your experiment.

To begin, you will need to write out the balanced chemical equations for each of the two reactions. Then, using the given information, you can calculate the moles of each reactant and product. From there, you can use the specific heat capacity of water to calculate the heat released or absorbed by the reaction (q = mCΔT). Remember to also take into account the heat absorbed by the calorimeter itself.

Once you have calculated the heat for each individual reaction, you can use Hess' Law to determine the overall heat of reaction per mole of calcium metal. This can be done by subtracting the heat of the first reaction from the heat of the second reaction, as the net enthalpy change should be the same regardless of the pathway taken.

As for your approach of using the heat capacity of water, it is a valid approximation as long as the solution is mostly water. However, if there are other components in the solution that may significantly affect its heat capacity, you may need to consider those as well.

I hope this helps and good luck with your experiment!