Some physical properties of water are shown below:
melting point 0.0°C
boiling point 100.0°C
specific heat solid 2.05 J/g·°C
specfic heat liquid 4.184 J/g·°C
specific heat gas 2.02 J/g·°C
ΔH° fusion 6.02 kJ/mol
ΔH° vaporization 40.7 kJ/mol
80.0 kJ of heat are added to 20.5 g of ice at -24.3°C.
(a) What will be the final temperature of the system (in °C)?
(b) What mass will be in each phase after the heating?
i.solid - 0
ii. liquid - 0
iii. gas -
I need help with a and with b.iii
My Work:
q = m * c * (change in temperature)
q = 20.5 * 2.05 * (0+24.3) = 1021.2 J
q = 20.5 * 4.184 * (100-0) = 8577.2 J
80,000 J - (1021.2+8577.2) = 70401.6 J left for the final phase
How do I find both the final mass and final temperature if they are both variables?
q = m * c * (change in temperature)
q = 20.5 * 2.05 * (0+24.3) = 1021.2 J right and I would make that 1.02 kJ.
Then you need to melt the ice.
q = (20.5/18)*6.02 = ?
q = 20.5 * 4.184 * (100-0) = 8577.2 J right and I would make that 8.68 kJ.
Then you need to vaporize the water.
(20.5/18) x 40.7 = ? kJ.
80,000 J - (1021.2+8577.2) = 70401.6 J left for the final phase Not right since I've added some steps you left out.
80 - each of the above = ?kJ left and I would change that back to J.
Then q(in J) = 20.5 x specific heat steam x (Tfinal - Tinitial).
Tf is the unknown. Ti is 100 C
Well, it seems like you're in quite a "phases" of confusion! Don't worry, I'll help you out with your questions.
First, let's tackle part (a), finding the final temperature of the system. You've already calculated the heat absorbed by the ice correctly, which is 1021.2 J. However, you need to consider the heat required for the phase changes as well. Let's break it down:
1) Heat required to melt the ice:
q = m × ΔH° fusion
q = 20.5 g × (6.02 kJ/mol) × (1 mol/18.015 g)
q = 20.5 g × 0.33494 kJ/g
q ≈ 6.87 kJ
2) Heat required to heat the liquid water:
q = m × c × ΔT
q = 20.5 g × 4.184 J/g·°C × (final temperature - 0°C)
Now, if the ice is completely melted, the final temperature will be the melting point of water, which is 0.0°C. So we can write:
q = 20.5 g × 4.184 J/g·°C × (0.0 - 0.0°C)
q = 0
Now, let's add up all the heats:
1021.2 J + 6.87 kJ + 0 J = 7021.2 J
Since no more heat is applied after this, we know that the final temperature is 0.0°C.
Now onto part (b): What mass will be in each phase (solid, liquid, and gas) after the heating?
We know that the ice has completely melted, so the mass in the solid phase will be 0 grams. The gas phase will start once the temperature reaches the boiling point of water, which is 100.0°C. Since the final temperature is 0.0°C, we can calculate the mass in the gas phase using the equation:
q = m × ΔH° vaporization
7021.2 J = m × (40.7 kJ/mol) × (1 mol/18.015 g)
m = 7021.2 J × (1 mol/40.7 kJ) × (18.015 g/mol)
m ≈ 32.37 g
Therefore, after the heating, there will be 0 grams in the solid phase, 20.5 - 32.37 grams (which is negative, indicating no liquid water), and 32.37 grams in the gas phase.
I hope this helps you "phase" out the confusion!
To find the final temperature of the system, you can apply the principle of heat conservation. The heat added to the system is equal to the heat absorbed by each phase during the heating process.
First, calculate the heat absorbed by the ice during the heating process:
q_ice = m_ice * c_ice * (T_final - T_initial)
You know that the initial temperature (T_initial) of the ice is -24.3°C. Assume that the final temperature (T_final) is the same for both the ice and water phases.
Using the heat equation, q = m * c * ΔT, you can calculate the heat absorbed by the ice using the specific heat of ice (c_ice) as 2.05 J/g·°C.
Next, calculate the heat absorbed by the resulting liquid water:
q_water = m_water * c_water * (T_final - T_initial)
For this calculation, you can use the specific heat of liquid water (c_water) as 4.184 J/g·°C.
Now, since the total heat added to the system is 80,000 J, you can set up the equation:
80,000 J = q_ice + q_water + q_gas
Substitute the calculated values for q_ice and q_water, and solve for the heat absorbed by the gas phase (q_gas).
Finally, use the equation:
q_gas = m_gas * c_gas * (T_final - T_initial)
Substitute the known values for q_gas and solve for the mass of the gas phase (m_gas).
So, to summarize:
(a) To find the final temperature (T_final) of the system, solve for T_final in the equations q_ice = m_ice * c_ice * (T_final - T_initial) and q_water = m_water * c_water * (T_final - T_initial), with known values for q_ice, c_ice, q_water, and c_water.
(b) To find the mass of the gas phase (m_gas), substitute the calculated value of q_gas into the equation q_gas = m_gas * c_gas * (T_final - T_initial), with known values for q_gas and c_gas.
To find the final temperature and mass in each phase, we can use the concept of energy conservation. The total heat absorbed by the system will be equal to the sum of the heat needed to raise the temperature of the ice to its melting point, the heat required to melt the ice, and the heat needed to raise the temperature of the resulting liquid water to the final temperature.
Let's break down the steps to find the answers to the questions:
(a) Final temperature of the system in °C:
1. Calculate the heat required to raise the temperature of the ice to its melting point:
q1 = mass * specific heat solid * (melting point - initial temperature)
q1 = 20.5 g * 2.05 J/g·°C * (0.0°C - (-24.3°C))
2. Calculate the heat required to melt the ice:
q2 = mass * ΔH° fusion
q2 = 21.5 g * 6.02 kJ/mol
3. Calculate the heat required to raise the temperature of the resulting liquid water to the final temperature:
q3 = mass * specific heat liquid * (final temperature - melting point)
q3 = 20.5 g * 4.184 J/g·°C * (final temperature - 0°C)
4. The total heat absorbed by the system is the sum of q1, q2, and q3:
total heat absorbed = q1 + q2 + q3
5. Set up and solve the equation:
80,000 J = (q1 + q2 + q3)
Plug in the respective values for q1, q2, and q3, and solve for the final temperature.
(b) Mass in the gas phase:
To find the mass of water in the gas phase after heating, we need to account for the heat absorbed during the phase change from liquid to gas. As you calculated, there is 70,401.6 J remaining for the final phase.
1. Calculate the heat required for vaporization:
q4 = mass * ΔH° vaporization
q4 = ? * 40.7 kJ/mol
2. Set up and solve the equation:
70,401.6 J = q4
Plug in the respective values for q4 and solve for the mass in the gas phase.
Remember, the total mass will be the sum of the masses in each phase.