86.3 g of water in a calorimeter have an initial temperature of 24 degrees C. The temperature increased to 33.1 degrees C when 54.3 g of a sample of metal initially at 99.7 degrees C is added to the calorimeter and allowed to equilibrate with the water.

Calculate the specific heat of the metal in joules/g degrees C.

qH2O + qmetal = 0

qH2O = mass H2O x specific heat water x (Tfinal-Tinitial).

qmetal = mass metal x specific heat metal x(Tfinal-Tinitial).

Just plug in the numbers and solve for specific heat metal.

23

No, it isn't 23.

is it 186.1?

To calculate the specific heat of the metal, we can use the equation:

Heat gained by water = Heat lost by metal

The heat gained or lost can be calculated using the formula:

Q = m * c * ΔT

Where:
Q is the heat gained or lost,
m is the mass,
c is the specific heat, and
ΔT is the change in temperature.

Let's calculate the heat gained by the water first. In this case, the water is gaining heat because its temperature increases from 24°C to 33.1°C. The mass of the water is 86.3 g, and the change in temperature is ΔT = 33.1°C - 24°C = 9.1°C.

Now, we substitute the values into the formula:

Q_water = (86.3 g) * c_water * (9.1°C)

Now, we calculate the heat lost by the metal. The mass of the metal is 54.3 g, and its temperature decreases from 99.7°C to reach the final equilibrium temperature of 33.1°C. The change in temperature is ΔT = 99.7°C - 33.1°C = 66.6°C.

Note that in the equation, the specific heat of the metal is denoted as c_metal.

Now, we substitute the values into the formula:

Q_metal = (54.3 g) * c_metal * (-66.6°C)

Since the heat gained by the water is equal to the heat lost by the metal (according to the principle of conservation of energy), we can equate the two expressions:

(86.3 g) * c_water * (9.1°C) = (54.3 g) * c_metal * (-66.6°C)

Simplifying the equation:

c_metal = ((86.3 g) * c_water * (9.1°C)) / ((54.3 g) * (-66.6°C))

Now, we substitute the value of c_water, which is the specific heat capacity of water (4.184 J/g°C):

c_metal = ((86.3 g) * (4.184 J/g°C) * (9.1°C)) / ((54.3 g) * (-66.6°C))

Simplifying further:

c_metal = - (4.184 J/g°C) * (86.3 g) * (9.1°C) / (54.3 g) * (66.6°C)

Calculating the numerical result will give you the specific heat of the metal in joules per gram degree Celsius.