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?

2 Answers
Hriman · Ernest Z.
Mar 6, 2018

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.

zhirou
Mar 6, 2018

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.

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