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 11.5 K when the copper block released 32.5 J of heat. What is the mass of the copper block?

To solve this problem, we need to use the concept of heat capacity. The heat capacity (C) is defined as the amount of heat required to raise the temperature of a substance by 1 Kelvin or 1 degree Celsius.

In this case, we are given the molar heat capacity of copper (C) as 24.92 J K^(-1) mol^(-1). This means that it takes 24.92 Joules of heat to raise the temperature of 1 mole of copper by 1 Kelvin.

The heat released by the copper block is given as 32.5 J and the temperature change is given as -11.5 K (negative indicating a decrease in temperature).

First, we need to find the number of moles of copper. We can use the molar mass (M) to convert the mass of copper to moles.

The molar mass of copper is given as 63.55 g mol^(-1).

Let's use the formula:
moles = mass / molar mass

moles = mass of copper / molar mass of copper
moles = mass of copper / 63.55 g mol^(-1)

Now, we can determine the mass of copper by rearranging the formula to solve for mass:

mass of copper = moles * molar mass of copper

Since we now know the moles, we can substitute this value into the equation:

mass of copper = moles * 63.55 g mol^(-1)

To find the moles of copper, we need to determine the number of moles from the given heat and heat capacity relationship:

heat = moles * molar heat capacity * temperature change

Rearranging the equation to solve for moles:

moles = heat / (molar heat capacity * temperature change)

Substituting the given values:

moles = 32.5 J / (24.92 J K^(-1) mol^(-1) * -11.5 K)

Finally, substitute the value of moles back into the mass equation:

mass of copper = moles * 63.55 g mol^(-1)

Now, let's calculate the mass of the copper block:

mass of copper = (32.5 J / (24.92 J K^(-1) mol^(-1) * -11.5 K)) * 63.55 g mol^(-1)

Calculating this expression will give us the mass of the copper block.