Calculate the specific heat of the metal

[nate808]

I have a chem test 2mor and i keep getting stuck on this problem

A 150.0g sample of metal at 75.0 degrees C is added to 150.0g of water at 15.0 degrees C. The temperature of water rises to 18.3 degrees C. Calculate the specific heat of the metal, assuming that all the heat lost by the metal is gained by the water

What I tried to do was use the formula for woork q=mc delta T, and found the m=300.0g c=4.18 T=3.3 C and found the number of Joules to be 4138.2. Then I divided by the number of grams of metal, 150g, and the temperature of the metal, 75.0 C. I keep getting .36Kj/mol--but the back of my book says that the answer is .25kJ/mol-----Can someone please tell me what i am doing wrong and possiblibly guide me in the right direction

Thanks in advance

 

[GCT]

You'll need to find the equilibrium "heat value (q)" gained by water given off by the metal (qmetal=-qwater), also the final temperature of the metal will be the same as that of the final temperature of water

 

[Blueshift5]

Hello,

First of all, great job using the formula q=mcΔT to solve this problem. Your approach is correct, but there is a small error in your calculation.

When dividing by the number of grams of metal, you should use the mass of the metal that was added to the water, which is 150.0g. However, you used the total mass of the water and the metal (300.0g) in your calculation. This is why you are getting a slightly higher value for the specific heat.

The correct calculation would be:

q = (150.0g)(4.18 J/g°C)(18.3°C - 15.0°C)

q = 1863.6 J

To find the specific heat of the metal, we need to divide this value by the mass of the metal and the change in temperature of the metal.

Specific heat of metal = (1863.6 J) / (150.0g)(75.0°C - 18.3°C)

Specific heat of metal = 0.25 kJ/mol

As you can see, the answer matches with the one given in the back of your book. So, the specific heat of the metal is 0.25 kJ/mol.

I hope this helps and good luck on your test tomorrow! Remember to always double check your calculations and use the correct values in your formula.