Question

The volume of a sample of oxygen is 300.0 ml when the pressure is 1.00 atm and the temperature is 27°c. at what temperature is the volume 1.00 l and the pressure 0.500 atm?

Answer 1

Since the question has pressure, temperature, and volume as variables, in order to arrive at an answer the combined gas law will be needed to arrive at an answer. The Combined Gas Law is a combination of Boyle's Law (pressure and volume are inversely proportional when temperature is constant) and Charle's Law (volume and temperature are proportional when pressure is constant) and is used when neither volume, pressure nor temperature is constant.

Combine Gas Law Equation:   P₁V₁ ÷ T₁   =    P₂V₂ ÷ T₂

The following values are what is known from the question:
the initial pressure (P₁) = 1 atm; the final pressure (P₂) is 0.5 atm,
the initial volume (V₁) = 300 mL or 0.3 L; the final volume (V₂) = 1 L 
the initial temperature (T₁) = 27 °C
then we can substitute these into the equation to find the final temperature (T₂).

                                                     P₁V₁ ÷ T₁   =    P₂V₂ ÷ T₂

∴ by substituting the known values,   
                              
                              ⇒       (1 atm) (0.3 L )  ÷ (27 °C) =  (0.5 atm)(1 L) ÷ T₂                                                                
                              ⇒            T₂   = [ (0.5 atm) (1 L) (27 °C)  ] ÷ (1 atm) (0.3 L )

                              ⇒             T₂  =  [13.5 atm · L · °C] ÷ [0.3 atm · L]

                              ⇒             T₂  = 45 °C

        Thus the new temperature of the gas is 45 °C.