A sample of unknown metal has a mass of 36.7 g. This metal was placed in boiling water at 96.0oC until the metal had reached the temperature of the water. The metal was then placed in a foam cup with 50.0 g of water in it at 20.0oC. The cup absorbs 42.0 J/oC, and the temperature of the water went up to 24.0oC. What is the specific heat of the metal?

Chemistry - DrBob222, Sunday, November 10, 2013 at 7:35pm
heat lost be warm metal + heat gained by water + heat gained by foam cup = 0

[mass warm metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] + [Ccup x (Tfinal-Tinitial)]
Substitute and solve for specific heat metal.
Post your work if you get stuck.

To find the specific heat of the metal, we can use the formula provided:

heat lost by warm metal + heat gained by water + heat gained by foam cup = 0

This equation takes into account the heat lost by the warm metal as it cools down, the heat gained by the water as it heats up, and the heat gained by the foam cup.

Let's substitute the given values into the equation:

mass of the metal = 36.7 g
initial temperature of the metal = 96.0°C
final temperature of the metal = 20.0°C (since it reaches the temperature of the water)

mass of the water = 50.0 g
initial temperature of the water = 20.0°C
final temperature of the water = 24.0°C

heat absorbed by the foam cup = 42.0 J/°C

Now we can plug in the values:

[36.7 g x specific heat metal x (20.0°C - 96.0°C)] + [50.0 g x specific heat water x (24.0°C - 20.0°C)] + [42.0 J/°C x (24.0°C - 20.0°C)] = 0

Simplifying further:

[-76.7 g x specific heat metal] + [200.0 g x specific heat water] + [168.0 J] = 0

To find the specific heat of the metal, we need to isolate the term involving the metal:

[-76.7 g x specific heat metal] = -[200.0 g x specific heat water] - [168.0 J]

Divide both sides by -76.7 g:

specific heat metal = (-[200.0 g x specific heat water] - [168.0 J]) / (-76.7 g)

Now you can plug in the specific heat of water (which is typically 4.18 J/g°C) and calculate the specific heat of the metal.