A 11.6 g sample of an unknown metal was heated to 100.0 oC and then added to 25.0 g of water at 23.0 degrees Celsius in an insulated calorimeter. At thermal equilibrium, the temperature of the water in the calorimeter was 24.8 degrees Celsius.

What is the heat absorbed or lost by the water? In joules
How much heat is absorbed or lost by the metal? In joules
What's the specific heat of metal? (Joules/ grams x degrees Celsius )

q absorbed by water = mass x specific heat x (Tfinal-Tintial)

q lost by metal = heat absorbed by water

[mass metal x specific heat metal x (Tfinal-Tintial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0

Substitute and solve for sp. h. metal.

To calculate the heat absorbed or lost by the water, we can use the formula:

q = m × c × ΔT

Where:
q is the heat absorbed or lost by the water (in joules),
m is the mass of the water (in grams),
c is the specific heat capacity of water (4.18 J/g°C), and
ΔT is the change in temperature of the water (final temperature - initial temperature).

Given:
Mass of water (m) = 25.0 g
Specific heat capacity of water (c) = 4.18 J/g°C
Change in temperature of water (ΔT) = 24.8°C - 23.0°C = 1.8°C

Substituting the values into the formula:

q = 25.0 g × 4.18 J/g°C × 1.8°C
q = 188.1 J

Therefore, the heat absorbed or lost by the water is 188.1 joules.

To calculate the heat absorbed or lost by the metal, we can use the formula:

q = m × c × ΔT

Where:
q is the heat absorbed or lost by the metal (in joules),
m is the mass of the metal (in grams),
c is the specific heat capacity of the metal (unknown in this case), and
ΔT is the change in temperature of the metal (final temperature - initial temperature).

Given:
Mass of metal (m) = 11.6 g
Change in temperature of metal (ΔT) = 100.0°C - 24.8°C = 75.2°C

To find the specific heat capacity of the metal (c), we need to divide the heat absorbed or lost by the metal (q) by the product of its mass and change in temperature:

c = q / (m × ΔT)

Substituting the values into the formula:

c = (188.1 J) / (11.6 g × 75.2°C)
c ≈ 0.215 J/g°C

Therefore, the specific heat capacity of the metal is approximately 0.215 J/g°C.