Question

Aerosol cans have a label that warns the user not to use them above a certain temperature and not to dispose of them by incineration. Even an empty can contains residual gaseous propellant. For example, the residual pressure in a can is 1.51 atm when it is sitting on a shelf at 23 ∘C. If the can is placed on top of the furnace where the temperature reaches the boiling point of water, what is the pressure inside the can? Express your answer with the appropriate units. View Available Hint(s) nothing nothing

Answer 1

Answer:

1.90 atm

Explanation:

Using ideal gas equation as:

$PV=nRT$

where,  

P is the pressure

V is the volume

n is the number of moles

T is the temperature  

R is Gas constant having value = 0.0821 L atm/ K mol  

According to above equation, at constant Volume and number of moles, pressure is directly proportional to the temperature. So,

$\frac {P_1}{T_1}=\frac {P_2}{T_2}$

Given ,  

P₁ = 1.51 atm

P₂ = ?

T₁ = 23 °C

T₂ = 100 °C  ( boiling point of water )

The conversion of T( °C) to T(K) is shown below:

T(K) = T( °C) + 273.15  

So,  

T₁ = (23 + 273.15) K = 296.15 K  

T₂ = (100 + 273.15) K = 373.15 K  

Using above equation as:

$\frac{1.51}{296.15}=\frac{P_2}{373.15}$

$P_2=\frac{1.51\cdot \:373.15}{296.15}\ atm$

New Pressure = 1.90 atm