5.00g of an unknown solid was heated to 99.7 degrees C and placed in a calorimeter with 1.25L H20. The initial temp of the water was 25.0 degrees C. During the experiment, the temperature of the water rose to 63.5 degrees C. what is the specific heat of the sample? Do you think the solid is a metal or nonmetal?
Heat lost by solid + heat gained by H2O = 0
[mass solid x specific heat solid x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Solve for specific heat solid.
To calculate the specific heat of the unknown solid, we can use the formula:
q = m * c * ΔT
Where:
q = heat absorbed or released by the substance (in this case, the water)
m = mass of the substance (water) in grams
c = specific heat of the substance (water) in J/g°C
ΔT = change in temperature of the substance (water) in °C
First, let's calculate the heat absorbed by the water:
q = m * c * ΔT
The mass of the water (m) is given as 1.25 L, but we need it in grams. 1 L of water weighs approximately 1000 grams, so:
m = 1.25 L * 1000 g/L = 1250 g
ΔT is the change in temperature, which is the final temperature minus the initial temperature:
ΔT = 63.5°C - 25.0°C = 38.5°C
We can rearrange the equation to solve for c:
q = m * c * ΔT
c = q / (m * ΔT)
Now, let's calculate the heat absorbed by the water using the specific heat formula:
q = m * c * ΔT
q = 1250 g * c * 38.5°C
Next, we need to calculate the heat released by the unknown solid. We assume that there is no heat exchange with the surroundings and that the heat lost by the solid is equal to the heat gained by the water:
q solid = -q water
Substituting the values:
q solid = - (1250 g * c * 38.5°C)
We know that q solid = ΔH, which is the enthalpy change. Since the solid is heated, the enthalpy change is positive. Therefore, we have:
ΔH = 1250 g * c * 38.5°C
Now, we have all the information we need to calculate the specific heat (c) of the unknown solid. Rearranging the equation:
c = ΔH / (m * ΔT)
c = (1250 g * c * 38.5°C) / (5.00 g * 38.5°C)
Simplifying the equation:
c = (1250 g * c) / 5.00 g
c = 250
From the final calculation, the specific heat of the unknown solid is approximately 250 J/g°C.
To determine whether the solid is a metal or nonmetal, we need some additional information. Generally, metals have lower specific heats than nonmetals. However, based on the specific heat value alone, it is not sufficient to determine whether the unknown solid is a metal or nonmetal. Additional experiments or information about the substance is needed to make a conclusive determination.