Chemistry 391
Fall 2007
Problem Set 1
(Due, Wednesday September 5)
1. A sealed flask with a capacity of 1.00 liter (=1.00 dm3) contains 5.00 g of ethane. The
flask is so weak that it will burst if the pressure exceeds 1.00 × 106 Pa. At what
temperature will the pressure of the (ideal) gas exceed the bursting temperature?
2. Consider a gas mixture in a 2.00-liter flask at 27.0ºC. Calculate the partial pressure of
each gas, the total pressure, and the composition of the mixtures in mole fractions for:
a) 1.00 g H2 and 1.00 g O2
b) 1.00 g N2 and 1.00 g O2
3. Consider
⎛ ∂V ⎞
⎛ ∂V ⎞
dV = ⎜
⎟ dT + ⎜
⎟ dP
⎝ ∂T ⎠ P
⎝ ∂P ⎠T
(1)
You want to obtain the Euler chain directly from (1). How do you do this? Go through all
steps in detail!
4. V = V (T , P ) for a simple system is a state function. Use the equality of mixed second
partial derivatives to show that κ (T , P ) the isothermal compressibility and α (T , P ) the
⎛ ∂α ⎞
⎛ ∂κ ⎞
coefficient of thermal expansion are related by ⎜
⎟ = −⎜
⎟ .
⎝ ∂P ⎠T
⎝ ∂T ⎠ P
5. Use the ideal gas law to obtain express P = f (V , T ) , V = g ( P, T ), and T = h ( P, V ) .
⎛ ∂P ⎞
Then show that the Euler chain ⎜
⎟
⎝ ∂V ⎠T
⎛ ∂V ⎞ ⎛ ∂T ⎞
⎜
⎟ ⎜
⎟ = −1 is obeyed.
⎝ ∂T ⎠ P ⎝ ∂P ⎠V
6-7. a) Write an expression for dP that is the analog of what is written in problem 3
noting that P = f (V , T ) . Express the result in terms of κ (T , P ) the isothermal
compressibility and α (T , P ) the coefficient of thermal expansion.
This is convenient, because α (T , P ) and κ (T , P ) are known for a wide variety of
substances over (sometimes) large ranges of T and P.
Over small intervals of T and P it is safe to assume that α (T , P ) and κ (T , P ) can be
treated as constants. Do so, and integrate dP between final (f) and initial (i) values with
this assumption to get an expression for ΔP ≡ Pf − Pi .
b) Now consider a glass thermometer with ethanol as the working fluid. It is very hot and
the ethanol completely fills its channel. But now the temperature increases by 10 C.
Use the ΔP expression to estimate the increase in pressure. What is the chance that the
thermometer survives?
Hint, you will have to figure out a finite change expression for ΔV and you can do so by
1 ⎛ ∂V ⎞
integrating α = ⎜
⎟ over a finite change in temperature, and noting that the
V ⎝ ∂T ⎠ P
appropriate α is for glass.
−1
−1
−1
Data: κ ethanol = 11.0 ×10−5 ( bar ) ; α ethanol = 11.2 ×10−4 ( C ) ; α glass = 2.00 ×10−5 ( C ) .