Question

In a calorimetry experiment, an unknown metal with a mass of 24.2 g that has been heated to a temperature of 90.1 °C is placed in a coffee cup calorimeter containing 74.0 g of water initially at a temperature of 23.5 °C. After the water and metal have reached thermal equilibrium, the final temperature reading of the calorimeter is 27.2 °C. Calculate the specific heat of the unknown metal in J/g°C.

a) 0.392 J/g°C
b) 0.486 J/g°C
c) 0.675 J/g°C
d) 0.824 J/g°C

Answer 1

To calculate the specific heat of the unknown metal, we can use the formula q = mcΔT. By plugging in the given values and solving for c, we find that the specific heat of the unknown metal is 0.392 J/g°C.

Step-by-step explanation:

In order to calculate the specific heat of the unknown metal, we can use the formula:

q = mcΔT

Where q is the heat absorbed or released, m is the mass of the substance, c is the specific heat capacity of the substance, and ΔT is the change in temperature.

First, let's calculate the heat released by the water:

qwater = mcΔT = (74.0 g)(4.18 J/g°C)(27.2 °C - 23.5 °C) = 1022.88 J

Next, let's calculate the heat absorbed by the unknown metal:

qmetal = mcΔT

We know the mass of the metal is 24.2 g, the final temperature is 27.2 °C, and the initial temperature is 90.1 °C. Plugging in these values, we can solve for c:

1022.88 J = (24.2 g)c(27.2 °C - 90.1 °C)

c = 0.392 J/g°C

Therefore, the specific heat of the unknown metal is 0.392 J/g°C.