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?
[mass M x sp.h.M x (Tfinal-Tinitial)] + [mass H2O x specific heat water x (Tfinal-Tinitial)] = 0
solve for sp.h. M
I don't think it's Au.
Note the correct spelling of celsius.
To find the specific heat of the metal, we can use the formula:
q = m × c × ΔT
Where:
q is the heat absorbed or released by the substance (in this case, water)
m is the mass of the substance (in this case, water)
c is the specific heat capacity of the substance
ΔT is the change in temperature of the substance
In this question, the metal is initially heated to 62 degrees Celsius and then transferred to the water in the coffee cup calorimeter, causing the water temperature to rise from 19.2 degrees Celsius to 21.0 degrees Celsius. Therefore, the change in temperature of the water is:
ΔT = Final temperature - Initial temperature = 21.0°C - 19.2°C = 1.8°C
The mass of the water is given as 85.0g, and we can assume the specific heat capacity of water is 4.18 J/g°C.
Now, we need to calculate the heat gained by the water:
q = m × c × ΔT
q = 85.0g × 4.18 J/g°C × 1.8°C
Calculating this, we find that q = 636.06 J (Joules).
According to the law of conservation of energy, the heat lost by the metal should be equal to the heat gained by the water. Therefore, the heat lost by the metal is also 636.06 J.
Now, we can use the formula for heat:
q = m × c × ΔT
Rearranging the equation to solve for the specific heat capacity (c) of the metal:
c = q / (m × ΔT)
c = 636.06 J / (40.0g × 1.8°C)
Calculating this, we find that c ≈ 8.84 J/g°C.
Now, to determine if the metal is gold, we can compare the specific heat capacity we calculated (8.84 J/g°C) to the known specific heat capacity of gold (0.129 J/g°C).
Since the value we calculated is significantly different from the known specific heat capacity of gold, it is unlikely that the metal is gold.