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# What are the steps to the Boyle's Law formula "P1 x V1 = P2 x V2"?

Boyle's law developed by Robert Boyle in 1662, states that if we keep the temperature of a gas constant in a sealed container. Its pressure (P) varies inversely with its volume (V). In other words at any given temperature. If we pressurize a gas its volume will be reduced proportionately to the pressure change. If we increase the volume of a gas its pressure will increase.

I am not sure what you mean by the steps, but I can help you identify a problem, and tell you how to solve it.

Boyle's Law is that Pressure, P is inversely related to volume, V at constant temperature and number of moles. The mathematical relationship is ##P = k*1/V## which rearranges to

##P*V=k##,

where ##k## is a constant.

Since ##PV=k##, you get ##P_1V_1=P_2V_2##.

You can tell a problem will be a Boyle's law problem, if there is a change in pressure or volume and it asks you about the other.

For example, you could be asked the following: If a gas at , has its container expand to three times its volume, what is the new pressure.

Solution ##P_1 = 760 mmHg## ##V_1 = V_1##

##P_2 = ?## ##V_2 = 3V_1## because the new volume is 3 times bigger.

##P_1V_1 = P_2V_2## Boyle's Law

##P_2 = (P_1V_1)/V_2## Divide both sides by ##V_2##

##P_2 = ((760 mmHg)V_1)/(3V_1)## Substitute givens.

##P_2 = (760mmHg)/3 = 253.3 mmHg##