The price of gold is $625 per troy ounce at this writing. How much heat (in J) is needed to raise the temperature of $5000.00 worth of gold from 29.5 oC to 70.5 oC?
(1 troy oz = 31.10 g and the specific heat of Au is 25.42 J/(moloC).)
Please help!
$625/oz x ?oz = $5,000.
? oz x 31.1 g/oz = x grams.
q = grams x specific heat x (Tfinal-Tinitial)
Substitute and solve for q.
Great thanks!
To calculate the amount of heat required to raise the temperature of gold, we can use the formula:
Q = m * c * ΔT
In this formula:
- Q represents the heat energy in joules (J)
- m represents the mass of the gold in grams (g)
- c represents the specific heat capacity of gold (J/(mol·°C))
- ΔT represents the change in temperature (°C)
First, let's calculate the mass of the gold in grams using the given information that 1 troy ounce is equal to 31.10 g:
Mass of gold = $5000.00 / ($625 per troy ounce) * (31.10 g per troy ounce)
Mass of gold = (5000.00 / 625) * 31.10 g
Next, let's calculate the change in temperature:
ΔT = Final temperature - Initial temperature
ΔT = 70.5°C - 29.5°C
Now that we have the mass of gold and the change in temperature, we can calculate the heat energy:
Q = Mass of gold * specific heat capacity * ΔT
Q = (Mass of gold) * 25.42 J/(mol·°C) * ΔT
Substituting the values we calculated earlier, we can find the heat energy:
Q = (Mass of gold) * 25.42 J/(mol·°C) * ΔT
Q = [((5000.00 / 625) * 31.10 g) / (31.10 g/mol)] * 25.42 J/(mol·°C) * (70.5°C - 29.5°C)
Simplifying the equation gives us the final answer.
Note: Make sure to convert the mass of gold from grams to moles by dividing by the molar mass of gold (31.10 g/mol).