a 225.0g sample of an unknown, silver, pure metal was heated to 95.5 degrees Celsius and then put into 150.50g of water at 22.5 degree Celsius. the water was heated by the hot metal to a temp. of 31.4 degree Celsius. what is the specific heat of the metal and what is the metal?
heat lost by metal + heat gained by H2O = 0
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for specific heat metal, then look in specific heat tables and identify the metal with that specific heat .
thank you , but what do I substitute the specific heat metal for to find out what it is?
To find the specific heat of the metal and identify the metal, we can follow the principles of calorimetry.
First, let's calculate the energy absorbed by the water using the formula:
Qwater = mwater * cwater * ΔTwater
Where:
Qwater is the energy absorbed by the water
mwater is the mass of the water
cwater is the specific heat capacity of water (which is approximately 4.18 J/g°C)
ΔTwater is the change in temperature of the water (final temperature - initial temperature)
Given:
mwater = 150.50g
cwater = 4.18 J/g°C
ΔTwater = 31.4°C - 22.5°C = 8.9°C
Plugging in the values:
Qwater = 150.50g * 4.18 J/g°C * 8.9°C
Qwater ≈ 55835.97 J
According to the law of conservation of energy, the energy lost by the metal is equal to the energy gained by the water. Therefore:
Qmetal = -Qwater
The negative sign indicates that the energy lost by the metal is transferred to the water.
Qmetal = -55835.97 J
Now, we can calculate the specific heat of the metal (cmetal) using the formula:
Qmetal = mm * cm * ΔTmetal
Where:
Qmetal is the energy lost by the metal
mm is the mass of the metal
cm is the specific heat capacity of the metal
ΔTmetal is the change in temperature of the metal (final temperature - initial temperature)
Given:
mm = 225.0g
ΔTmetal = 31.4°C - 95.5°C = -64.1°C (Note: Negative sign indicates a drop in temperature)
Plugging in the values:
-55835.97 J = 225.0g * cm * -64.1°C
Simplifying:
cm ≈ -55835.97 J / (225.0g * -64.1°C)
cm ≈ 3.825 J/g°C
The specific heat capacity of the metal is approximately 3.825 J/g°C.
To identify the metal, we can compare its specific heat capacity with the known values of different metals. Looking up values for specific heat capacity, we find that it closely matches the specific heat capacity of silver, which is around 0.24 J/g°C.
Therefore, based on the specific heat capacity, the metal is likely to be silver.
Note: It's important to mention that this calculation assumes no heat loss to the surroundings, and it assumes that the density of the water remains constant throughout the process.