A 15g sample of what appears to be gold that was heated from 22 degrees C to 39 degrees C, required 26.3 J of energy. If the specific heat of gold is .129 J/(g x degrees C), is the metal pure gold? Defend your answer with calculations.
q = mass metal x specific heat metal x (Tfinal-Tinitial)
Substitute q, mass metal, Tfinal and Tinitial and solve for specific heat. Compare with that of pure Au.
To determine if the metal is pure gold, we need to calculate the amount of energy required based on the specific heat of gold and compare it with the given value.
The formula to calculate the energy change is:
Q = m * C * ΔT
Where:
Q is the energy change
m is the mass of the substance
C is the specific heat of the substance
ΔT is the change in temperature
Given:
m = 15g (mass of the sample)
C = 0.129 J/(g °C) (specific heat of gold)
ΔT = 39°C - 22°C = 17°C (change in temperature)
Now, let's calculate the amount of energy required using the given specific heat:
Q = 15g * 0.129 J/(g °C) * 17°C
Q = 33.1 J
Comparing the calculated energy change of 33.1 J with the given value of 26.3 J, we can see that they are not equal. This discrepancy suggests that the sample is not pure gold.
The reason for this discrepancy could be impurities in the sample, which cause a variation in the specific heat value. Pure gold should have a consistent specific heat value, and any deviation indicates the presence of other substances in the sample.
Therefore, based on the calculations, we can conclude that the metal sample is likely not pure gold.