Solid carbon dioxide (dry ice) goes from solid to gas at -78C. The molar heat of sublimation is 25.3 kj/mol. In one experiment 34.5g of dry ice are placed in an insulated isolated container with 500 g of water at 25C. What temp of the water is expected after all bubbles are gone? Specific heat of water is 4.184 J/g*C ??
I suppose we assume that the gas, after forming, does not cool the water on its way out of the system.
moles CO2 = 34.5g/44 = ??
?? moles CO2 x 25.3 kJ/mol = xx kJ to sublime the dry ice. Convert to joules.
[mass water x specific heat water x (Tfinal-25)] + xxJOULES = 0
Solve for Tfinal.
To find the final temperature of the water after the dry ice has completely sublimated, we need to calculate the amount of heat transferred from the water to the dry ice during the sublimation process.
Step 1: Calculate the moles of CO2 in 34.5g of dry ice.
To do this, we need to know the molar mass of carbon dioxide (CO2), which is approximately 44 g/mol.
molar mass of CO2 = 44 g/mol
moles of CO2 = mass of dry ice / molar mass of CO2
moles of CO2 = 34.5 g / 44 g/mol
Step 2: Calculate the amount of heat transferred during sublimation.
The molar heat of sublimation is given as 25.3 kJ/mol, which means 25.3 kJ of heat is required to convert 1 mole of solid CO2 to its gaseous state.
Heat transferred (Q) = moles of CO2 * molar heat of sublimation
Q = moles of CO2 * 25.3 kJ/mol
Step 3: Calculate the change in temperature of the water.
The heat transferred during sublimation will cause the water to lose heat until the temperature equalizes.
Q = m * Cp * ΔT
Where:
Q = heat transferred
m = mass of water
Cp = specific heat of water
ΔT = change in temperature
We need to solve for ΔT, so rearrange the equation:
ΔT = Q / (m * Cp)
Step 4: Substitute the given values into the equation.
mass of water = 500 g
Cp (specific heat of water) = 4.184 J/g*C
Q = (moles of CO2 * 25.3 kJ/mol) converted to J
First, convert the molar heat of sublimation from kJ/mol to J/mol:
25.3 kJ/mol * 1000 J/kJ = 25,300 J/mol
Now, substitute the values into the equation:
ΔT = (moles of CO2 * 25,300 J/mol) / (mass of water * Cp)
Step 5: Calculate the moles of CO2 and substitute the values.
moles of CO2 = 34.5 g / 44 g/mol
Substitute the value into the equation:
ΔT = ((34.5 g / 44 g/mol) * 25,300 J/mol) / (500 g * 4.184 J/g*C)
Step 6: Perform the calculation.
Calculate the value in parentheses first:
(34.5 g / 44 g/mol) * 25,300 J/mol = 20,042 J/mol
Now, substitute the calculated values:
ΔT = (20,042 J/mol) / (500 g * 4.184 J/g*C)
Perform the multiplication:
ΔT = 20,042 J / (2092 J*C/g)
Finally, divide the values:
ΔT = 9.58 C
Step 7: Calculate the final temperature of the water.
To find the final temperature of the water, subtract the change in temperature (ΔT) from the initial temperature of the water.
Final temperature = Initial temperature - ΔT
Final temperature = 25 C - 9.58 C
Final temperature of the water is approximately 15.42 C.
Therefore, the expected temperature of the water after all the bubbles are gone is approximately 15.42°C.