Question

A 2.0 liter bottle can withstand a pressure of 5.0 atm. 120 mL of liquid ethanol, `"C"_2"H"_5"OH"`, (density 0.789 g/mL), is poured into the bottle and sealed. The bottle is heated to 100 C, changing all the liquid to gas. Will the bottle explode?

Answer 1

Yes, the bottle will burst.

Explanation:

`120 cancel("mL C"_2"H"_5"OH")*(0.789cancel( "g C"_2"H"_5"OH"))/(cancel("mL C"_2"H"_5"OH"))*("mol C"_2"H"_5"OH")/(46.07cancel("g C"_2"H"_5"OH")) = 2.055 "mol C"_2"H"_5"OH"`

Alright, now we will use the Ideal gas law and solve for Pressure,

`P=(nRT)/V`

`(2.055 cancel("mol C"_2"H"_5"OH")*(0.082cancel(L)"atm")/(cancel("mol")cancel("K"))*373cancel( K))/ (2cancel(L))`= `31.4 "atm"`

Yes, the bottle will burst, in the calculation, 373 K was used because that's the temperature at which ethanol was all gas, and so, therefore, the gas law would be applied and then once it was a gas, it automatically occupied the volume of the bottle which was 2 L.

Answer 2

Yes.

Explanation:

(@Hi's answer was awesome—this answer just elaborates more on why they used the values and equation that they did.)

This is what we're given:

• `V`, or volume, of `"2.0 L"`. We consider this to be the volume of our gas, because a property of the gas phase is that its volume freely expands to fill up the container.
  In our case, our container was `"2.0 L"`, so the volume of gas will also be `"2.0 L"`
• `T`, or temperature, which is `100°C` or `100 + 273.15 = "373.15 K"`.
• The volume of `C_2H_5OH` as a liquid: `"120 mL"`.
• The density of `C_2H_5OH` as a liquid: `"0.789 g/mL"`.
• `R`, or the Ideal Gas Constant, which is `"0.08206 L atm/g mol"`. (Quick note: We always know the value of `R` because it's a constant.)

To determine if the bottle will explode, we need to find the pressure of gaseous `C_2H_5OH`.
If it exceeds `"5.0 atm"`, the bottle will explode. If it doesn't, the bottle won't explode.

We can use the Ideal Gas Law to find the pressure of `C_2H_5OH`:

`pV = nRT`

And rearrange this to have only `p`, pressure, on one side:

`p = (nRT)/V`

We already know `R`, `T` `V`, but a bit more work needs to be done to find the value of `n`, or the number of moles of gas.

To find moles, we first need to find mass.
We can use the density equation:

`"density" = "mass"/"volume"`

Therefore, `"mass" = "volume" xx "density"`.

Since density and volume were given in the question:

`"mass" = "120 mL" xx "0.789 g/mL" = 94.68 g"`

Then, we can use mass to find `n`:

`n = "mass"/"molar mass"`
`n = ("94.68 g")/((Cxx2+Hxx5+O+H)"g/mol")`
`n = ("94.68 g")/((12.01xx2+1.008xx5+16.00+1.008)"g/mol")`
`n = "2.055 mol"`

Finally, we can plug `V`, `n`, `R`, and `T`, into the Ideal Gas Law:

`p = ("2.055 mol" xx "0.08206 L atm/K mol" xx "373.15 K")/"2.0 L"`

`p = (2.055 cancel("mol") xx 0.08206 cancel("L") "atm/"cancel("K mol") xx 373.15 cancel("K"))/(2.0 cancel("L"))`

`p = "31.47 atm"`

Since the pressure exceeds `"5.0 atm"` (by a lot!), the bottle will (definitely) explode.