Question

A two-liter soft drink bottle can withstand apressure of

5 atm. Half a cup (approximately 120mL) of ethynlalcohol, C2H5OH,
(d=0.789 g/mL) is poured into a soft drink bottleat room
temperature. The bottle is then heated to 100C, changingthe liquid
alcohol to a gas. Will the soft drink bottle withstandthe pressure
or explode?

Answer 1

Step-by-step explanation:

According to the ideal gas equation, PV = nRT.

where, P = pressure, V = volume

n = no. of moles, R = gas constant

T = temperature

Also, density is equal to mass divided by volume. And, no. of moles equals mass divided by molar mass.

Therefore, then formula for ideal gas could also be as follows.

P =
`(mass)/(volume * molar mass) * RT`

or, P =
`\frac{density}{\text{molar mass}} * RT`

Since, density is given as 0.789 g/ml which is also equal to 789 g/L (as 1000 mL = 1 L). Hence, putting the given values into the above formula as follows.

P =
`\frac{density}{\text{molar mass}} * RT`

=
`(789 g/l)/(46.06 g/mol) * 0.0821 L atm/mol K * 373 K`

= 525 atm

As two-liter soft drink bottle can withstand a pressure of 5 atm and the value of calculated pressure is 525 atm which is much greater than 5 atm.

Therefore, the soft drink bottle will obviously explode.