Question

All the steps please!It is dangerous for aerosol cans to be exposed to heat. If a can of hairspray at a pressure of 4 atmospheres and a room temperature of 27 ° C is thrown into a fire and the container reaches 402 ° C. What will its new pressure be? The can can explode if the internal pressure exerts 6080 mm Hg. How likely is it to explode?

Answer 1

The new pressure = 9 atm.

Since the new pressure of 6840 mmHg (9 atm) exceeds 6080 mmHg, then the can will likely explode.

Step-by-step explanation

Given:

Initial pressure P₁ = 4 atm

Initial temperature, T₁ = 27 °C = (27 + 273.15 K) = 300.15 K

Final temperature, T₂ = 402 °C = (402 + 273.15 K) = 675.15

What to find:

The new pressure at a temperature of 402 °C.

Step-by-step solution:

According to Amonton's law: The pressure of a given amount of gas is directly proportional to its absolute temperature, provided that the volume does not change, i.e:

`(P_1)/(T_1)=(P_2)/(T_2)`

Putting P₁ = 4 atm, T₁ = 300.15 K, and T₂ = 675.15 K into the formula, we have:

`\begin{gathered} (4atm)/(300.15K)=(P_2)/(675.15K) \\ \\ Cross\text{ }multiply \\ \\ P_2*300.15K=4atm*675.15K \\ \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }300.15K \\ \\ (P_2)/(300.15K)=(4atm*675.15K)/(300.15K) \\ \\ P_2=9\text{ }atm \end{gathered}`

The new pressure at a temperature of 402 °C = 9 atm.

According to the information in the question that the can explode if the internal pressure exerts 6080 mmHg, then we need to convert 9 atm to mmHg to know how likely is it to explode.

Conversion factor:

1 atm = 760 mmHg

So 9 atm = (9 atm/1 atm) x 760 mmHg = 6840 mmHg

Since 6840 mmHg pressure exceeds 6080 mmHg, then the can will likely explode.