The volume of a gas is 5.0 l when the temperature is 5.0ºc. if the temperature is increased to 10.0ºc without changing the pressure, what is the new volume? a. 2.5 l b. 4.8 l c. 5.1 l d. 10.0 l

  10 L (option D)

Solution:

The question notes that there is a change in temperature from 5 °C to 10 °C, that resulted in a change in volume from 5 L. Based on the question, it is evident that this question rests on the premise of Charle's Law, which note that as temperature increases, volume increases (once pressure remains constant) since the two are temperature is directly proportional. As such Charle's Gas Law Equation can be used to solve for the final volume.    

 Charle's Gas Law Equation:   V₁  ÷  T₁    =    V₂  ÷  T₂

Since the initial temperature ( T₁ ) is 5 °C, the final temperature ( T₂ ) is 10 °C and the initial volume ( V₁ ) is 5 °C, then these values can be substituted in the equation to solve for the final volume.

                                          V₁  ÷  T₁    =    V₂  ÷  T₂

                       ⇒   ( 5 L )   ÷   ( 5 °C)   =    V₂   ÷   ( 10 °C )

                       ⇒                          V₂   =    ( 10 °C ) ( 1 L · °C )

                      ⇒                           V₂  =  10 L

Thus the new volume is 10 L.

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