The ΔHof of gaseous dimethyl ether (CH3OCH3) is –185.4 kJ/mol; the vapour pressure is 1.00 atm at –23.7oC and 0.526 atm at –37.8oC.
a) Calculate ΔHovap of dimethyl ether.
b) Calculate ΔHof of liquid dimethyl ether
Any idead how to calculate for the heat of formation?
To calculate the heat of formation (ΔHof) for a compound, you generally need to use known heat of formation values for the elements that make up the compound. However, in this case, you are given the ΔHof values directly, so you don't need to calculate them.
To answer your specific questions:
a) To calculate the heat of vaporization (ΔHovap) of dimethyl ether, you can use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance at two temperatures to its heat of vaporization.
The equation is: ln(P2/P1) = -ΔHovap/R * (1/T2 - 1/T1)
First, convert the temperatures to Kelvin:
-23.7oC = 249.5 K
-37.8oC = 235.3 K
R is the gas constant, which has a value of 8.314 J/(K⋅mol).
Using the given vapor pressure values:
P1 = 1.00 atm
P2 = 0.526 atm
T1 = 249.5 K
T2 = 235.3 K
Substituting these values into the Clausius-Clapeyron equation and solving for ΔHovap:
ln(0.526/1.00) = -ΔHovap/8.314 * (1/235.3 - 1/249.5)
Calculate ln(0.526/1.00) ≈ -0.526.
-0.526 = -ΔHovap/8.314 * (0.00425 - 0.00401)
Solve for ΔHovap: ΔHovap ≈ (-0.526 * 8.314) / (0.00425 - 0.00401)
b) To calculate the heat of formation of liquid dimethyl ether from the given ΔHof of gaseous dimethyl ether, you need to consider the enthalpy changes related to the phase changes.
ΔHovap (heat of vaporization) can be related to ΔHof (heat of formation) of liquid dimethyl ether as follows:
ΔHovap = ΔHof(gas) - ΔHof(liquid)
Given ΔHof of gaseous dimethyl ether = -185.4 kJ/mol, you now need to find the value of ΔHof of liquid dimethyl ether.
Rearranging the equation: ΔHof(liquid) = ΔHof(gas) - ΔHovap
Substitute the calculated ΔHovap value and the given ΔHof(gas) value into the equation to find ΔHof(liquid).