The heat lost or gained by a system is related to its temperature change by a property called its heat capacity. The molar heat capacity of metals at or above room temperature equals 24.92 J K-1mol-1.
The temperature of a block of copper metal (molar mass 63.55 g mol-1) fell by 9.56 K when the copper block released 23.6 J of heat. What is the mass of the copper block?
q = mass Cu x specific heat Cu x delta T
To find the mass of the copper block, we need to use the equation:
q = m * C * ΔT
where:
- q is the heat released or gained by the system (in joules, J)
- m is the mass of the substance (in grams, g)
- C is the molar heat capacity of the substance (in J K-1 mol-1)
- ΔT is the temperature change (in Kelvin, K)
Given:
- q = 23.6 J (heat released by the copper block)
- C = 24.92 J K-1 mol-1 (molar heat capacity of copper)
- ΔT = -9.56 K (temperature change, negative because the temperature of the block fell)
First, we need to calculate the number of moles (n) of copper using its molar mass:
molar mass of copper = 63.55 g mol-1
We can calculate the number of moles using the formula:
n = m / molar mass
Rearranging the formula:
m = n * molar mass
To find the number of moles (n), we can use the equation:
n = q / (C * ΔT)
Substituting the given values:
n = 23.6 J / (24.92 J K-1 mol-1 * -9.56 K)
After calculating n, we can substitute it into the equation:
m = n * molar mass
Substituting the values for molar mass and n, we can find the mass of the copper block.