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QUESTION

What does Boyle's Law state?

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: