A 15.00 g chunk of lustrous silver metal is heated to 50.0 degrees C and is then placed in a coffee cup calorimeter containing 50.0 mL of water at 15.30 degrees C. After equilibrium, the water temperature is measured to be 16.56 degree C. Suggest which metal or metals could have been used.
In the calorimeter, the sum of heats gained is zero.
Heat gained by metal+heatgained by water=0
15*cmetal*(16.56-50.0)+50*cwater*(16.56-15.30)=0
solve for specific heat of the metal, then look at various metals to see a match.
To determine which metal or metals could have been used, we need to calculate the heat exchanged between the metal and the water.
The heat transferred can be calculated using the formula:
q = mcΔT
Where:
q is the heat transferred
m is the mass of the substance (water or metal)
c is the specific heat capacity of the substance
ΔT is the change in temperature
First, let's calculate the heat transferred from the metal to the water.
The mass of water used is 50.0 mL. The density of water is 1 g/mL, so the mass of the water is also 50.0 g.
The specific heat capacity of water is 4.18 J/g°C.
Using the formula above, we can calculate the heat transferred from the metal to the water:
q_water = (50.0 g) * (4.18 J/g°C) * (16.56°C - 15.30°C)
Next, let's calculate the heat transferred by the metal.
The mass of the metal used is 15.00 g.
Assuming the metal has a specific heat capacity of 0.385 J/g°C (which is close to the specific heat capacity of silver), we can calculate the heat transferred from the metal to the water:
q_metal = (15.00 g) * (0.385 J/g°C) * (50.0°C - 16.56°C)
Now we compare the values of q_water and q_metal to determine the corresponding metal(s).
If q_water is equal to q_metal, then the metal is silver.
If q_water is less than q_metal, then the metal is something with a higher specific heat capacity than silver.
If q_water is greater than q_metal, then the metal is something with a lower specific heat capacity than silver.
Calculate the values of q_water and q_metal, and compare them to determine the possible metal(s) used in the experiment.