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states that pressure is indirectly proportional to volume when the temperature and moles of the gas are constant.

This relationship can be modelled by the equation:

##P_1V_1=P_2V_2##

where:

##P_1=##initial pressure

##V_1=##initial volume

##P_2=##final pressure

##V_2=##final volume

When pressure is indirectly proportional to volume this means that

say for example if the pressure was increased by a factor the volume would decrease by the ##color(red)(same)## factor.

Similarly if the volume was increased by a factor the pressure would decrease by the ##color(red)(same)## factor.

For example if the initial pressure was ##color(blue)2## ##color(blue)(atm)## the initial volume was ##color(blue)4## ##color(blue)L## and the pressure decreased by a factor of ##color(blue)(1/2)## the volume would increase by a factor of ##color(blue)2##.

Algebraically we can solve for the final volume using Boyle’s Law formula assuming that the temperature and moles of the gas are constant:

##P_1V_1=P_2V_2##

##(2atm)(4L)=(1atm)(V_2)##

##V_2=((2color(red)cancelcolor(black)(atm))(4L))/((1color(red)cancelcolor(black)(atm)))##

##V_2=8## ##L##

Thus the volume has increased from ##4## ##L## to ##8## ##L##.

Graphically the relationship between pressure and volume can be represented as: