1. From data below, calculate the total heat (in J) associated with the conversion of 0.514 mol ethanol gas (C2H6O) at 451°C and 1 atm to liquid ethanol at 25.0°C and 1 atm. (Pay attention to the sign of the heat.)
Boiling point at 1 atm 78.5°C
cgas 1.43 J/g°C
cliquid 2.45 J/g°C
H°vap 40.5 kJ/mol
2. A 0.75 L bottle is cleaned, dried, and closed in a room where the air is 20°C and 42% relative humidity (that is, the water vapor in the air is 0.42 of the equilibrium vapor pressure at 20°C). The bottle is brought outside and stored at 0.0°C.
What mass of water condenses inside the bottle?
What volume of CH4 at 0 °C and 1.20 atm contains the same number of molecules as 0.16 L of N2 measured at 23 °C and 1.50 atm?
To calculate the total heat associated with the conversion of ethanol gas to liquid ethanol, we need to consider the heat required to change the temperature of the gas, the heat required for condensation, and the heat released during cooling.
1. Calculate the heat required to change the temperature of the gas:
The heat required to change the temperature of a substance can be calculated using the formula:
q = m * c * ΔT
where q is the heat, m is the mass, c is the specific heat, and ΔT is the change in temperature.
Given:
m(gas) = 0.514 mol
c(gas) = 1.43 J/g°C
ΔT(gas) = 25.0°C - 451°C (negative because we are cooling)
First, convert the mass of the gas to grams:
m(gas) = 0.514 mol * molar mass of ethanol
The molar mass of ethanol (C2H6O) can be calculated as follows:
molar mass of C2H6O = (2 * atomic mass of C) + (6 * atomic mass of H) + atomic mass of O
Now, calculate the heat:
q(gas) = m(gas) * c(gas) * ΔT(gas)
2. Calculate the heat released during condensation:
The heat released during condensation can be calculated using the formula:
q(condensation) = n * ΔH°vap
where n is the number of moles and ΔH°vap is the molar enthalpy of vaporization.
Given:
n = 0.514 mol
ΔH°vap = 40.5 kJ/mol
Convert ΔH°vap to joules:
ΔH°vap = 40.5 kJ/mol * 1000 J/1 kJ
Now calculate the heat:
q(condensation) = n * ΔH°vap
3. Calculate the heat released during cooling:
The heat released during cooling can be calculated using the same formula as in step 1:
q(cooling) = m(liquid) * c(liquid) * ΔT(cooling)
Given:
c(liquid) = 2.45 J/g°C
ΔT(cooling) = 25.0°C
Calculate the mass of liquid ethanol:
m(liquid) = n * molar mass of ethanol
Now calculate the heat:
q(cooling) = m(liquid) * c(liquid) * ΔT(cooling)
4. Calculate the total heat:
Total heat = q(gas) + q(condensation) + q(cooling)
Add up the values obtained from each step to get the total heat associated with the conversion of ethanol gas to liquid ethanol.
Now, to determine the mass of water that condenses inside the bottle, we need to consider the change in temperature and the water vapor in the air.
1. Calculate the equilibrium vapor pressure at 20°C:
Look up the equilibrium vapor pressure of water at 20°C from a table. Let's assume it is X atm.
2. Calculate the actual vapor pressure at 20°C:
actual vapor pressure = X atm * 0.42
3. Calculate the saturation vapor pressure at 0.0°C:
Look up the saturation vapor pressure of water at 0.0°C from a table. Let's assume it is Y atm.
4. Calculate the difference in vapor pressure:
difference in vapor pressure = actual vapor pressure - saturation vapor pressure at 0.0°C
5. Multiply the difference in vapor pressure by the volume of the bottle to get the mass of water condensing inside the bottle. Remember to convert the volume to liters if necessary.
Note: These calculations assume ideal behavior and do not account for any other factors influencing humidity.