A 100g sample of ice at 0ºC is added to 150.0 mL of liquid water at 80ºC in a styrofoam cup calorimeter. (The specific heat capacity of water is 1.184 J/g•ºC, the density of water is 1.00 g/mL, and ∆Hºfus = 6.01 kJ/mol)
a) Does all of the ice melt?( show work to receive credit)
b) What is the final temperature once thermal equilibrium is established?
c) How much ice remains once thermal equilibrium is established?
a. q1 needed to melt all of the ice
q1 = mass ice x heat fusion.
q2 = mass H2O x specific heat H2O x delta T. (and the specific heat H2O is NOT 1.184).(Consider delta T = 80 which is the maximum heat that can be released). There is more than enough to melt all of the ice. This work answers a and the conclusion answers c.
For b, just put all of this together.
q1 = heat to melt ice.
q1 = [mass ice x heat fusion]
q2 = heat to raise temperature of melted ice to final T.
q2 = mass melted ice x specific heat H2O x (Tf-Ti) (of course Ti is zero).
q3 = heat released by the 80 C water.
q3 = [mass H2O x specific heat H2O x (Tf-Ti) (Ti of course is 80.)
Now just add all of these together. The sum is zero.
q1 + q2 + q3 = 0
Substitute q1, q2 and q3 from above and solve for Tf. I estimated the value and obtain something around 20 C or so.
a) Does all of the ice melt?
Well, let's put on our detective hats and investigate. We have a 100g sample of ice at 0ºC and we are adding it to 150.0 mL of liquid water at 80ºC. We know that the specific heat capacity of water is 1.184 J/g•ºC and the density of water is 1.00 g/mL. Oh! And the heat of fusion (∆Hºfus) of ice is 6.01 kJ/mol.
To find out if all the ice melts, we need to compare the amount of heat gained by the ice to the heat required to melt it.
Now, to calculate the heat gained by the ice, we can use the equation Q = m * C * ΔT, where Q is the heat gained/lost, m is the mass, C is the specific heat capacity, and ΔT is the change in temperature.
The ice starts at 0ºC and ends at the final temperature once equilibrium is reached. To find the final temperature, we need to remember that heat gained by the ice equals the heat lost by the water.
So, let's dig in and crunch some numbers!
b) What is the final temperature once thermal equilibrium is established?
To find the final temperature, we equate the heat gained by the ice to the heat lost by the water.
First, let's calculate the heat gained by the ice:
Q_ice = m_ice * C_ice * ΔT_ice
Since the ice is at 0ºC, ΔT_ice = final temperature - 0ºC
Q_ice = 100g * 2.09 J/g•ºC * (final temperature - 0ºC)
Q_ice = 209J/g•ºC * final temperature
Now, let's calculate the heat lost by the water:
Q_water = m_water * C_water * ΔT_water
Since the water is at 80ºC, ΔT_water = final temperature - 80ºC
Q_water = 150.0g * 1.184 J/g•ºC * (final temperature - 80ºC)
Q_water = 177.6J/g•ºC * final temperature - 14208J/g•ºC
Since heat gained by the ice equals heat lost by the water, we can set the equations equal to each other:
209J/g•ºC * final temperature = 177.6J/g•ºC * final temperature - 14208J/g•ºC
Now we just need to solve for the final temperature:
209J/g•ºC * final temperature - 177.6J/g•ºC * final temperature = 14208J/g•ºC
31.4J/g•ºC * final temperature = 14208J/g•ºC
final temperature = 14208J/g•ºC / 31.4J/g•ºC
final temperature ≈ 452.23ºC
c) How much ice remains once thermal equilibrium is established?
To determine how much ice remains, we need to determine the heat gained by the ice and compare it to the heat required to melt it.
The heat required to melt the ice can be calculated using the equation Q_fus = moles of ice * ∆Hºfus. To find the moles of ice, we divide the mass of the ice by the molar mass of water:
moles of ice = 100g / (18.015 g/mol) ≈ 5.551 mol
Now, we can find the heat required to melt the ice:
Q_fus = 5.551 mol * (6.01 kJ/mol * 1000 J/kJ)
Q_fus = 33.37 kJ = 33,370 J
Since heat gained by the ice equals heat required to melt it, we can set the equations equal to each other:
Q_ice = Q_fus
mass of ice * specific heat capacity of ice * ΔT_ice = 33,370 J
100g * 2.09 J/g•ºC * (final temperature - 0ºC) = 33,370 J
2.09 J/g•ºC * final temperature = 333.7 J
final temperature = 333.7 J / 2.09 J/g•ºC
final temperature ≈ 159.81ºC
Well, it seems like we have reached a contradiction. The final temperature we calculated in part b is 452.23ºC, but in part c, it turns out to be 159.81ºC. Since these values don't match, it means that all of the ice does not melt and remains present once thermal equilibrium is established.
The ice must be one tough cookie to stay solid at such high temperatures!
a) To determine whether all of the ice will melt, we need to compare the heat gained by the ice to the heat required to melt it. The heat gained by the ice can be calculated using the equation:
q = m * ∆T * C
where q is the heat gained, m is the mass, ∆T is the change in temperature, and C is the specific heat capacity. We know the mass of the ice is 100g, the specific heat capacity of water is 1.184 J/g•ºC, and the change in temperature (∆T) is the final temperature (Tf) minus the initial temperature (Ti).
In this case, the initial temperature (Ti) is 0ºC and the final temperature (Tf) is unknown. Therefore, the ∆T can be written as Tf - 0ºC = Tf.
So, the heat gained by the ice is:
q_ice = 100g * Tf * 1.184 J/g•ºC
On the other hand, the heat required to melt the ice can be calculated using the equation:
q_melting = ∆Hºfus * n
where q_melting is the heat required, ∆Hºfus is the enthalpy of fusion, and n is the number of moles of ice. To find the number of moles of ice, we can use the molar mass of water, which is 18.015 g/mol. Thus,
n = mass / molar mass
n = 100g / 18.015 g/mol
Now we can calculate the heat required to melt the ice:
q_melting = (6.01 kJ/mol) * (100g / 18.015 g/mol)
q_melting = 33.27 kJ
If q_ice > q_melting, then all of the ice will melt. Let's calculate:
q_ice = 100g * Tf * 1.184 J/g•ºC
33.27 kJ = 100g * Tf * 1.184 J/g•ºC
Rearranging the equation to solve for Tf:
Tf = 33.27 kJ / (100g * 1.184 J/g•ºC)
Calculating Tf:
Tf ≈ 28.11ºC
b) The final temperature once thermal equilibrium is established is approximately 28.11ºC.
c) To determine the amount of ice remaining once thermal equilibrium is established, we can calculate the heat gained by the water and use it to find the mass of melted ice.
The heat gained by the water can be calculated using the equation:
q_water = m * ∆T * C
where q_water is the heat gained, m is the mass, ∆T is the change in temperature, and C is the specific heat capacity. We know the mass of the water is 150.0 mL, and we can convert it to grams using the density of water (1.00 g/mL):
m_water = 150.0 mL * 1.00 g/mL = 150.0 g
The initial temperature (Ti) of the water is 80ºC, and the final temperature (Tf) is 28.11ºC. Therefore, the ∆T can be written as 28.11ºC - 80ºC = -51.89ºC:
q_water = 150.0 g * (-51.89ºC) * 1.184 J/g•ºC
To find the mass of melted ice, we can use the equation:
q_water = mass_melted_ice * ∆Hºfus
Rearranging the equation to solve for the mass_melted_ice:
mass_melted_ice = q_water / ∆Hºfus
Calculating:
mass_melted_ice = [150.0 g * (-51.89ºC) * 1.184 J/g•ºC] / (6.01 kJ/mol)
mass_melted_ice ≈ 38.25 g
Therefore, approximately 38.25 g of ice remains once thermal equilibrium is established.
To solve this problem, we need to consider the heat gained and lost by the water, ice, and the overall system.
a) To calculate if all the ice melts, we can use the equation:
Q = m * ∆H
Where Q is the heat gained or lost, m is the mass, and ∆H is the heat of fusion.
First, we need to calculate the heat gained by the water. We know the mass of the water and its initial temperature.
q_water = m_water * c_water * ∆T_water
Where q_water is the heat gained by the water, m_water is the mass of the water, c_water is the specific heat capacity of water, and ∆T_water is the change in temperature of water, which can be calculated as the final temperature (T_final) minus the initial temperature (T_initial).
Next, we calculate the heat lost by the ice. We know the mass of the ice, and since it starts at 0ºC and ends at the temperature of fusion, the change in temperature (∆T_ice) is equal to 0ºC.
q_ice = m_ice * c_water * ∆T_ice
Now, we can compare the heat gained by the water to the heat lost by the ice to determine if all the ice melts. If q_water is greater than or equal to q_ice, then all the ice will melt.
b) To calculate the final temperature, we need to consider the heat gained by the water and the heat lost by the ice.
q_water = q_ice
m_water * c_water * ∆T_water = m_ice * c_water * ∆T_ice
Solving for the final temperature (T_final), we have:
∆T_water = (m_ice / m_water) * (-∆T_ice)
T_final = T_initial + ∆T_water
c) To find the amount of ice remaining after thermal equilibrium is established, we need to compare the mass of the ice initially and after the ice melts.
m_ice_remaining = m_ice_initial - m_water * (T_final - T_initial) / ∆T_ice
Now, let's plug in the values and calculate the answers to each question.
Note: To solve the problem completely, we need the mass of the ice and the initial and final temperatures. Please provide those values so I can help you solve the problem accurately.