A 40.0g sample of an unknow, yellowish-brown, pure metal was heated to 62degrees Celcius and put into a coffee cup calorimeter containing 85.0g of watera at 19.2 degrees Celcius. The water was heated by the hot metal to a temperature of 21.0 degrees Celcius. What is the specific heat of the metal? Is it possible that the metl is gold?
See above.
1st find the heat of water in Joules. Heat absorbed by water is heat lost by metal.
Use this to find Specific heat of metal:
SH = J/mass*Change in Temp of metal
SH = 640.152J/40g*41C
SH = 390.33658854 x 10^-3
SH = .390 J/gC
It's not gold whose SPHeat is .131...it is likely copper perhaps.
To find the specific heat of the metal, we can use the formula:
q = mcΔT
Where:
q is the heat absorbed or released (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g°C)
ΔT is the change in temperature (in °C)
From the given data:
Mass of the metal (m1) = 40.0g
Temperature change of the metal (ΔT1) = 21.0°C - 62.0°C = -41.0°C (Note: negative because the metal lost heat)
Mass of water (m2) = 85.0g
Temperature change of water (ΔT2) = 21.0°C - 19.2°C = 1.8°C
Now, we can calculate the heat absorbed by the metal (q1) and the heat absorbed by the water (q2):
q1 = m1c1ΔT1
q2 = m2c2ΔT2
Since the metal loses heat and the water gains heat, the heat gained by the water is equal in magnitude but opposite in sign to the heat lost by the metal:
|q1| = |q2|
Now we can substitute the formulas and solve for the specific heat of the metal (c1):
m1c1ΔT1 = m2c2ΔT2
c1 = (m2c2ΔT2) / (m1ΔT1)
Substituting the given values:
c1 = (85.0g * 4.18 J/g°C * 1.8°C) / (40.0g * (-41.0°C))
By evaluating this expression, we can find the specific heat of the metal.
Regarding whether the metal is gold, we can compare the calculated specific heat with the known specific heat of gold (0.128 J/g°C). If the calculated specific heat differs significantly from the known value of gold, then it is unlikely that the metal is gold.