Aerosol cans can be dangerous when they are heated because they can explode. Sup...

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September 2022 1 6 Report

Aerosol cans can be dangerous when they are heated because they can explode. Suppose a can of insecticide with a pressure of 4.0 atm at room temperature (28oC) is thrown into a fire. If the temperature of the gas inside the can reaches 400oC, what will be its pressure?

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Tokamak

$\tt{\huge{\blue{Explanation:}}}$

Gay-Lussac's law is given by

$\bold{\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2}}$

where:

P₁ = initial pressure

T₁ = initial temperature (in kelvin)

P₂ = final pressure

T₂ = final temperature (in kelvin)

Note: If the given temperature is in °C, we must convert it to kelvin (K) first before substituting into the formula.

$\tt{\huge{\red{Solution:}}}$

Listing the given values, we have

$\begin{aligned} P_1 & = \text{4.0 atm} \\ T_1 & = 28 + 273 = \text{301 K} \\ T_2 & = 400 + 273 = \text{673 K} \end{aligned}$

Arranging the equation, we can now solve for the final pressure of the gas. Therefore,

$\begin{aligned} P_2 & = \frac{P_1T_2}{T_1} \\ & = \frac{(\text{4.0 atm})(\text{673 K})}{\text{301 K}} \\ & = \boxed{\text{8.9 atm}}\end{aligned}$

Hence, the pressure will be 8.9 atm.

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