Data collected from the calorimetry of a metal
mass of the metal = 110.62g
initial temperature of the water in the cup = 23.0 C
initial temperature of the metal in the boiling water = 99.02 C
final temperature of the metal AND water in the cup=25.54C
volume of the water =100.0ml
1. What is the mass of the water?
2. What is the change in temperature of the water?
3. What is the change in temperature of the metal?
4. What is the specific heat of the metal?
I assume the density of the water is 1.00 g/mL but there is nothing in the problem to support that.
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass water x specific heat water x (Tfinal-Tinital)] = 0
I believe the only unknown is specific heat metal.
Let's go through each question step by step:
1. To find the mass of the water, we need to convert the volume from milliliters (ml) to grams (g), as the density of water is 1 g/ml. Since the volume is given as 100.0 ml, the mass of the water is 100.0 g.
2. The change in temperature of the water can be calculated by subtracting the initial temperature from the final temperature. So the change in temperature of the water is:
Final temperature - Initial temperature = 25.54°C - 23.0°C = 2.54°C.
3. Similarly, the change in temperature of the metal is calculated by subtracting the initial temperature from the final temperature. So the change in temperature of the metal is:
Final temperature - Initial temperature = 25.54°C - 99.02°C = -73.48°C.
Notice here that the change in temperature of the metal is negative because it lost heat (decrease in temperature).
4. To find the specific heat of the metal, we need to use the heat transfer equation:
q = m * c * ΔT, where q is the amount of heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Since the heat lost by the metal is equal to the heat gained by the water (in calorimetry), we can write:
m_water * c_water * ΔT_water = m_metal * c_metal * ΔT_metal.
Assuming the specific heat of water is approximately 4.18 J/g°C, and rearranging the equation, we have:
c_metal = (m_water * c_water * ΔT_water) / (m_metal * ΔT_metal).
Substituting the given values, we get:
c_metal = (100.0g * 4.18 J/g°C * 2.54°C) / (110.62g * -73.48°C).
Calculating this expression will give us the specific heat of the metal.
To answer the given questions, we can use the principles of calorimetry. Calorimetry is the science of measuring heat flow and can be used to determine various properties, such as the mass of a substance, temperature changes, and specific heat.
1. To find the mass of the water, we can use the given volume and the density of water, which is approximately 1 gram per milliliter (g/mL). Therefore, the mass of the water is 100.0 grams.
2. The change in temperature of the water can be calculated by subtracting the initial temperature from the final temperature. In this case, the change in temperature of the water is 25.54°C - 23.0°C = 2.54°C.
3. The change in temperature of the metal can also be calculated using the same principle. It is the difference between the initial temperature of the metal and the final temperature of the metal and water in the cup. In this case, the change in temperature of the metal is 25.54°C - 99.02°C = -73.48°C. Note that a negative sign indicates a decrease in temperature.
4. To determine the specific heat of the metal, we can use the equation:
Heat gained/lost by the metal = mass of the metal × specific heat of the metal × change in temperature of the metal
Since the metal is losing heat (decreasing temperature), we can express the equation as:
Heat lost by the metal = - (heat gained by the water)
The heat gained by the water can be calculated using the equation:
Heat gained by the water = mass of the water × specific heat of water × change in temperature of the water
We can rearrange the equations to solve for the specific heat of the metal:
Specific heat of the metal = (mass of the water × specific heat of water × change in temperature of the water) / (mass of the metal × change in temperature of the metal)
Now, let's plug in the given values to calculate the specific heat of the metal:
Specific heat of the metal = (100.0 g × 1 cal/g°C × 2.54°C) / (110.62 g × -73.48°C)
Evaluate the above expression to find the specific heat of the metal in cal/g°C.