You notion (1) is just wrong. 

With notion (2) You have the right idea. You'd need to make some assumptions  to solve the problem. So state your assumption and solve the problem from there. 

I had a wonderful high school teacher who was a stickler for answers to include any assumptions. At the time it was painful, but in retrospect it was wonderful training. 

So back to the problem, let's go down the rabbit hole! Given no other information you have to make several assumptions.


1. Does the sealed flask initially contain 40 ml of air or not?

* For instance the apparatus could contain two chambers. One 60 ml to be completely filled with liquid acetonitrile and a 40 ml chamber which is evacuated. Then when the experiment starts the chambers are first connected and then heated. 

* Alternatively the apparatus could contain one 100 ml chamber into which 60 ml of liquid acetonitrile is poured. 

2. What is the starting temperature?
 
 * This is more important if the flask initially contains 40 ml of air. 

3. Can the partial pressure of acetonitrile at the starting temperature be ignored?

 * If yes, then just state the assumption.

 * If no, then you'll need the partial pressure of acetonitrile at the starting temperature, and you'll have to assume that the 40 ml gaseous phase is equilibrium with the liquid phase. 

4. What is density of liquid(?) acetonitrile at the starting temperature?

 * Since the problem states "60 ml acetonitrile" you'd be led to assume that the acetonitrile was initially a liquid. 

 * I'd probably assume whatever temperature I could find a density for liquid acetonitrile. 

5. Since 140 °C is above the atmospheric boiling point, which does the acetonitrile do?

 * Totally vaporize?
 
 * Form gas and a liquid phases?

 * Turn into a supercritical fluid?

6. Does gaseous acetonitrile act as if it is a perfect gas?

 * If yes, then PV = nRT will work.

 * If no, then some more "advanced" model needs to be chosen and the additional constants that it needs to better fit the gas phase behavior...

6. Number of significant figures for the answer?

 * It would seem to be 2, so this feeds back into assumptions 2, 3, 4, and 6.  

Given the above assumptions, the problem should be easy to solve using PV = nRT. 

---------------------

OK, we've beat this to death and you're not getting it....

Let's assume:

1. The sealed flask initially contain 40 ml of air.

3. The partial pressure of acetonitrile is [$\pu{73 mm Hg at 68 ^\circ F}$](https://pubchem.ncbi.nlm.nih.gov/compound/Acetonitrile#section=Vapor-Pressure&fullscreen=true)

4. Density of liquid acetonitrile is [$\pu{0.787 g/ml at 68 ^\circ F}$](https://pubchem.ncbi.nlm.nih.gov/compound/Acetonitrile#section=Density&fullscreen=true)

2. The starting temperature is $\pu{68 ^\circ F = 20 ^\circ C = 293 ^\circ K}$

5. Since $\pu{140 ^\circ C = 413 ^\circ K}$ is above the atmospheric boiling point, the acetonitrile totally vaporizes. 

6. The gaseous acetonitrile acts as if it is a perfect gas.

7. 2 significant figures are needed for the answer.

OK, let's check some our our assumptions. 

$$\pu{0.787 g/ml}\times \pu{60 ml} = \pu{47.22 grams}\tag{1}$$

$$\dfrac{\pu{47.22 grams}}{\pu{41.053 grams/mole}} = \pu{1.150 moles} \tag{2}$$

One mole of a gas at STP occupies $\pu{22.711 L/mol at 0 °C and 100 kPa}$. Since the assumption is that only two significant figures are needed for the answer, the approximately 0.040 L of the gas phase (air + acetonitrile) can just be ignored. 

$$n_{\mathrm{air}} = \dfrac{PV}{RT} = \dfrac{\pu{100 kPa}\times \pu{0.040 L}}{\pu{8.314 L\cdot kPa} \cdot \pu{^\circ K^{-1}} \times \pu{293 ^\circ K} } = \pu{0.0016 moles}\tag{3}$$

So using the ideal gas equation:

$$P = \dfrac{nRT}{V} = \dfrac{\pu{1.150 moles}\times \pu{8.314 L\cdot kPa} \cdot \pu{^\circ K^{-1}} \cdot \pu{mole^{-1}} \times \pu{413 ^\circ K} }{\pu{0.100 L}} = \pu{39,487 kPa} \ce{->[round]} \pu{3.9\times10^{4} kPa}\tag{4}$$