Calculating Mass in a Calorimetry Problem

[Branflake]

Homework Statement

What is the mass of a piece of nickel metal if it is heated to 100.0°C and placed into 250.0 grams of water at 21.52°C in a calorimeter with a heat capacity of 95.3J/K and the temperature stabilizes at 25.82°C?

Homework Equations

-qnickel=+qwater

The Attempt at a Solution

Well this problem is on our review for thermochemistry, but non of the examples we have done or seen (even in the book) really go this far. Here is my first attempt.
-(cnickel X massnickel XΔTnickel)=cwater X masswater X ΔTwater
Plugging in the knowns I get :
Mass of nickel=(4.184J/g*K X 250.0g X 4.3K)/(0.444J/g*K X 74.18K)=136.6g of nickel
I got the specific heat for water through memorization and the specific heat for nickel through a periodic table. Was able to solve it, but for some reason it doesn't feel right. Can't find an example of something similar anywhere.
Am I on the right track at least?

 

[Simon Bridge]

Where does your feeling come from? Can you pin it down?
Does the figure feel too high or too low?

Your reasoning is correct, heat lost by sample is gained by the water.
The calculation followed that. So the places you could make a mistake are in the constants (did you try verifying them?) or an arithmetic error or something like that.

Examples of this problem are easy to come by online.
Did you try looking?
http://www.chemteam.info/Thermochem/MixingMetal&Water.html

 

[Branflake]

Where does your feeling come from? Can you pin it down?
Does the figure feel too high or too low?

Your reasoning is correct, heat lost by sample is gained by the water.
The calculation followed that. So the places you could make a mistake are in the constants (did you try verifying them?) or an arithmetic error or something like that.

Examples of this problem are easy to come by online.
Did you try looking?
http://www.chemteam.info/Thermochem/MixingMetal&Water.html

Thanks this makes me feel a little better about it. Honestly the main reason why I doubted myself is because in the lab we made similar calculations for finding everything but the mass of the metal, but the mass was always between 20g and 70g so my higher value made me concerned.

Also I found that same webpage earlier today, but only the first two problems would load. Thanks for posting it.

 

[Borek]

In general you are on the right track, but seems to me like you ignored heat capacity of the calorimeter.

 

[DeeNos]

Your initial attempt at solving the problem is on the right track. However, there are a few things that can be improved upon. Firstly, in the equation -qnickel=+qwater, the negative sign should be on the heat capacity of the water, not the nickel. This is because the heat lost by the nickel is equal to the heat gained by the water. Secondly, the specific heat for water is not 0.444 J/g*K, it is 4.184 J/g*K, as you correctly used in your calculation. Lastly, the units for specific heat should be J/g*K, not J/K.

Using the corrected equation, we can solve for the mass of the nickel:

-(0.444J/g*K X massnickel X (100.0°C-25.82°C)) = 4.184J/g*K X 250.0g X (25.82°C-21.52°C)

Solving for massnickel, we get:

Massnickel = (4.184J/g*K X 250.0g X 4.3K) / (0.444J/g*K X 74.18K) = 136.6g of nickel

This is the same answer you got, so your initial attempt was correct. It's always good to double check your units and make sure they are consistent throughout the calculation. Additionally, it's helpful to include the correct units in your final answer, so the mass of the nickel would be 136.6g. Well done on solving the problem!