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.mol. The temperature of a block of lead (MM 207.2) was raised by 13.1 degrees when 99.0 J of heat were added to it. What is the mass of the lead block? Enter your answer with three significant figures.

J = mass x specific heat x (Tfinal-Tinitial) = 0

99 J = mass Pb x 24.92 J/mol
Solve for mass Pb in mols.
Convert to grams. mol = g/molar mass

To find the mass of the lead block, we can use the equation:

q = n * C * ΔT

Where:
q is the heat added to the system
n is the number of moles of the substance
C is the molar heat capacity of the substance
ΔT is the temperature change

First, let's calculate the number of moles (n) of lead using its molar mass (MM) and the given mass.

MM of lead (Pb) = 207.2 g/mol
Let's assume the mass of the lead block is 'x' grams.

n = x / MM

Now, rearranging the equation, we can solve for x (mass):

x = n * MM

Next, we need to calculate the number of moles. Rearranging the equation, we have:

n = q / (C * ΔT)

Now, substituting the given values:

ΔT = 13.1 degrees Celsius = 13.1 K
q = 99.0 J
C = 24.92 J/K.mol

n = 99.0 J / (24.92 J/K.mol * 13.1 K)

Solving this equation will give us the number of moles (n). Finally, using the value of n, we can calculate the mass of the lead block (x) using the equation:

x = n * MM

To get the answer, simply follow these steps and perform the necessary calculations with the provided values.