Metal Specific Heat (J/g-C)
Al (s) 0.900
Au(s) 0.129
Cu(s) 0.385
Fe(s) 0.444
Hg(l) 0.139
H2O(l) 4.184
C2H5OH(l) 2.46
A piece of metal at a temp of 95.0oC and a mass of 67.0 g is dropped into a beaker of water containing 100 g at a temp. of 30.0oC. If the final temperature reached is 42.7.0oC, what is the identity of the metal?
the sum of the heats gained is zero.
heatgainedmetal+heatgainedwater=0
95*cm*(30-95)=100*4.18(42.7-30)
1.28
would it be Au?
To determine the identity of the metal, you need to calculate the heat gained by the metal and the heat gained by the water. Since the sum of the heats gained is zero, you can set up the equation:
heat gained by metal + heat gained by water = 0
The heat gained by the metal can be calculated using the formula:
heat gained by metal = mass of metal * specific heat of metal * change in temperature of the metal
The heat gained by the water can be calculated using the formula:
heat gained by water = mass of water * specific heat of water * change in temperature of the water
Substituting the given values into the equation, you can set up the equation:
67g * specific heat of metal * (42.7oC - 95oC) + 100g * 4.184 J/g-oC * (42.7oC - 30oC) = 0
Simplifying the equation gives:
67g * specific heat of metal * (-52.3oC) + 100g * 4.184 J/g-oC * (12.7oC) = 0
Dividing both sides of the equation by -1 to remove the negative sign gives:
67g * specific heat of metal * 52.3oC = 100g * 4.184 J/g-oC * 12.7oC
Simplifying further, you get:
67g * specific heat of metal = 100g * 4.184 J/g-oC * 12.7oC / 52.3oC
Now, you can substitute the specific heat values from the table to determine which metal has a specific heat that matches the calculated value.
For Au (gold): 0.129 J/g-oC
For Cu (copper): 0.385 J/g-oC
For Fe (iron): 0.444 J/g-oC
Calculating the value for each metal:
67g * 0.129 J/g-oC = 100g * 4.184 J/g-oC * 12.7oC / 52.3oC
8.643 J/oC = 50.83 J/oC
This value does not match the calculated value, so Au is not the correct metal.
67g * 0.385 J/g-oC = 100g * 4.184 J/g-oC * 12.7oC / 52.3oC
26 J/oC = 50.83 J/oC
This value does not match the calculated value, so Cu is not the correct metal.
67g * 0.444 J/g-oC = 100g * 4.184 J/g-oC * 12.7oC / 52.3oC
29.748 J/oC = 50.83 J/oC
This value does not match the calculated value, so Fe is not the correct metal.
Therefore, the correct identity of the metal cannot be determined based on the specific heats provided.