Question

A discarded spray paint can with a volume of 473 mL contains leftover propellant at a pressure of 101 kPa. If the can is run over by a garbage truck and flattened to 13.2 mL and does not spring a leak, what is the pressure of propellant in the can? (101.3 kPa = 1 atm) Provide an answer with values to the hundredths place (two spaces past the decimal).

A. 0.01 atm
B. 0.12 atm
C. 9.91 atm
D. 103.56 atm

Answer 1

Using Boyle's Law, the final pressure of the propellant after the can is flattened is calculated to be 2.70 atm, which does not match any of the provided multiple-choice options.

Step-by-step explanation:

To determine the pressure of the propellant after the can is flattened, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional if the temperature and the amount of gas remain constant. Boyle's Law is expressed as P1V1 = P2V2.

Given:

• Initial pressure (P1) = 101 kPa
• Initial volume (V1) = 473 mL
• Final volume (V2) = 13.2 mL

We need to find the final pressure (P2).

P1V1 = P2V2 can be rearranged to solve for P2:

P2 = P1V1 / V2

Substitute the given values:

P2 = (101 kPa)(473 mL) / 13.2 mL

P2 = 3613 kPa / 13.2 mL

P2 = 273.86 kPa

To convert the pressure from kPa to atm, we use the conversion factor (1 atm = 101.3 kPa).

P2 = 273.86 kPa / 101.3 kPa/atm

P2 = 2.70 atm (rounded to two decimal places)

However, none of the options (A. 0.01 atm, B. 0.12 atm, C. 9.91 atm, D. 103.56 atm) matches our calculated value. Therefore, either the options provided are incorrect, or there was a mistake in the calculation process.