A 108g piece of unknown metal is heated to 100 degrees C in boiling water. The heated sample of metal is then dropped into 50ml of H20, which is initially at 23.0 degrees C. After a few minutes the temp. of water raises to 37.5 degrees C. What is the specific heat capacity of the metal and what is the identity of the metal?
Thank You in advance.
heat lost by metal + heat gained by water = 0.
[mass metal x specific heat M x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for specific heat. Then look in your text or on-line for a list of specific heats of metals and identify the one in this problem.
To find the specific heat capacity of the metal and identify the metal, we can use the equation:
m1c1ΔT1 = m2c2ΔT2
where:
m1 = mass of the metal (108 g)
c1 = specific heat capacity of the metal (unknown)
ΔT1 = change in temperature of the metal (final temperature - initial temperature of the metal)
m2 = mass of water (50 g, assuming 50 ml of water has a density of 1 g/ml)
c2 = specific heat capacity of water (4.18 J/g°C, which is a constant value for water)
ΔT2 = change in temperature of the water (final temperature of the water - initial temperature of the water)
Let's substitute the given values into the equation:
(108 g)(c1)(100°C - 23.0°C) = (50 g)(4.18 J/g°C)(37.5°C - 23.0°C)
Now, let's solve the equation to find the specific heat capacity of the metal (c1):
(108 g)(c1)(77.0°C) = (50 g)(4.18 J/g°C)(14.5°C)
(108 g)(c1)(77.0) = (50 g)(60.41 J)
833.6c1 = 3020.5 J
c1 = 3.62 J/g°C
Therefore, the specific heat capacity of the metal is 3.62 J/g°C.
Unfortunately, with the information given, we cannot determine the exact identity of the metal. Different metals have different specific heat capacities, but without additional information or comparisons to known values, it is not possible to identify the metal specifically.