Imagine that 25.0 of ice at -3.0C is placed in a container holding water vapor at temperature of 120.0C . After a certain amount of time, the container has expanded slightly, but holds only water vapor at 110.0C. what is the final volume of the container? you may assume the water vapor is an ideal gas, and no heat is lost to the surroundings. some other information is useful: deltaH fus(H2O) = 6.01KJ/mol
delta H vap(H2O) = 40.66kJ/mol
Cp,m H2O solid =38.02J/mol K
Cp,m H2O liquid = 75.35J/mol K
Cp,m H2O gas = 33.60J/mol K
pressure= 1.000 atm
I would calculate the heat required to melt ice, raise T to 100 C, raise T to 110 (in 3 separate steps) and call that q. Then -q = mass water x specific heat water x (Tfinal-Tinitial) to calculate mass water. Convert 25 g ice to moles H2O, convert mass H2O originally in the container to moles, then use PV = nRT to solve for volume @ 110C. Post your work if you get stuck. Check my reasoning.
To find the final volume of the container, we can use the ideal gas law and the concept of heat transfer.
First, we need to determine the initial and final number of moles of water vapor in the container.
Step 1: Calculate the number of moles of ice:
Given mass of ice = 25.0 g
Molar mass of water = 18.015 g/mol
Number of moles of ice = mass of ice / molar mass of water
Step 2: Calculate the heat absorbed (Q) by the ice to melt at -3.0°C and reach 0°C:
The heat absorbed by the ice can be calculated using the formula:
Q = mass of ice * deltaH_fus(H2O)
Step 3: Calculate the number of moles of water at 0°C:
Since the ice melts at 0°C, the number of moles of water formed is equal to the number of moles of ice.
Step 4: Calculate the heat absorbed (Q) by the water to reach 100°C:
Q = mass of water * Cp,m H2O liquid * deltaT
where:
mass of water = number of moles of water * molar mass of water
deltaT = final temperature - initial temperature
Step 5: Calculate the number of moles of water vapor at 100°C:
The heat absorbed by the water will be used to vaporize it at 100°C.
The number of moles of water vapor formed is given by:
number of moles of water vapor = Q / deltaH_vap(H2O)
Step 6: Calculate the volume of the water vapor using the ideal gas law:
The ideal gas law equation is:
PV = nRT
where:
P = pressure = 1.000 atm
V = volume (unknown)
n = number of moles of water vapor
R = gas constant = 0.0821 L*atm/(mol*K)
T = temperature = 110.0°C + 273.15 (convert to Kelvin)
Rearranging the ideal gas law equation: V = nRT / P
Step 7: Calculate the final volume:
Substitute the values into the equation obtained in step 6, and calculate the final volume of the container.
Note: Make sure to convert all temperatures to Kelvin before performing calculations.
Follow these steps to find the final volume of the container.