Calculate the final temperature (once the ice has melted) of a mixture made up initially of 75.0 mL liquid water at 29.0 Celsius and 7.0 g ice at 0.0 Celsius?
heat gained by ice + heat gained by melted ice + heat lost by 75 mL liquid H2O = 0
(mass ice x heat fusion) + (mass melted ice x specific heat liquid H2O x (Tfinal-Tintial) + (mass 75 mL H2O x specific heat liquid H2O x (Tfinal-Tinitial) = 0
Substitute all of the numbers and solve for Tfinal.
To calculate the final temperature of the mixture once the ice has melted, we can use the principle of energy conservation.
Step 1: Calculate the heat gained by liquid water during the heating process.
We can use the equation Q = mcΔT, where Q is the heat gained, m is the mass of the liquid water, c is the specific heat capacity of water, and ΔT is the change in temperature.
Given:
- Mass of water, m = 75.0 mL.
Density of water, ρ = 1 g/mL.
Mass (m) = ρ × volume (V) = 1 g/mL × 75.0 mL = 75.0 g.
- Specific heat capacity of water, c = 4.184 J/g°C (at constant pressure).
- Initial temperature of water, T1 = 29.0°C.
- Final temperature, T2 = unknown.
Using the equation Q = mcΔT, we can rewrite it as:
Q1 = mcΔT1.
Step 2: Calculate the heat lost by the ice during the cooling process.
We can also use the equation Q = mcΔT to calculate the heat lost by the ice during the cooling process.
Given:
- Mass of ice, m = 7.0 g.
- Specific heat capacity of ice, c = 2.09 J/g°C (at constant pressure).
- Initial temperature of ice, T1 = 0.0°C.
- Final temperature, T2 = unknown.
Using the equation Q = mcΔT, we can rewrite it as:
Q2 = mcΔT2.
Step 3: Set up an equation using the principle of energy conservation.
According to the principle of energy conservation, the heat gained by the liquid water must be equal to the heat lost by the ice.
Q1 = Q2.
Step 4: Solve the equations to find the final temperature.
Substituting the equations Q1 = mcΔT1 and Q2 = mcΔT2 into the energy conservation equation, we get:
mcΔT1 = mcΔT2.
Canceling out the mass and specific heat capacity on both sides of the equation, we have:
ΔT1 = ΔT2.
Combining the equations, we get:
T2 - T1 = T1 - T0,
T2 = T1 - T0 + T1,
Substituting the values,
T2 = 29.0°C - 0.0°C + 29.0°C,
Calculating,
T2 = 58.0°C.
Therefore, the final temperature of the mixture after the ice has melted is 58.0°C.
To calculate the final temperature of the mixture once the ice has melted, we can use the principle of conservation of energy.
First, let's determine the heat absorbed by the liquid water.
The heat gained or lost by a substance can be calculated using the equation:
Q = m * c * ΔT
Where:
Q is the heat gained or lost (in joules or calories)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g°C or cal/g°C)
ΔT is the change in temperature (in °C)
For the liquid water, we have:
m = 75.0 mL * density of water
c = specific heat capacity of water
ΔT = final temperature - initial temperature = TF - 29.0°C
Next, let's determine the heat released by the ice.
The heat released by the ice as it melts can be calculated using the equation:
Q = m * ΔHf
Where:
Q is the heat released (in joules or calories)
m is the mass of the substance (in grams)
ΔHf is the heat of fusion of the substance (in J/g or cal/g)
For the ice, we have:
m = 7.0 g
ΔHf = heat of fusion of ice
Now, we can set up an equation to solve for the final temperature:
Q gained by liquid water = Q released by ice
m1 * c1 * (TF - 29.0°C) = m2 * ΔHf
Where:
m1 = mass of liquid water
c1 = specific heat capacity of water
m2 = mass of ice
Substituting the given values:
75.0 mL * density of water * specific heat capacity of water * (TF - 29.0°C) = 7.0 g * heat of fusion of ice
Now, we can solve this equation to find the final temperature (TF).