# What pressure is required to compress 196.0 liters of air at 1.00 atmosphere into a cylinder whose volume is 26.0 liters?

Jul 2, 2014

Boyle studied the relationship between the pressure of a trapped gas and its volume. The data obtained by him shows that the product of pressure and volume for the trapped air sample is constant at a constant temperature.

if volume of the gas increases, its pressure decreases, and vice versa. mathematically, if the volume of the gas is ${V}_{1}$ and its pressure is ${P}_{1}$. Let us suppose that its volume has been increased to ${V}_{2}$, the as per the Boyle's law its pressure will decrease and let us assume the new pressure is ${P}_{2}$.

${P}_{1}$ ${V}_{1}$ =${P}_{2}$${V}_{2}$

${P}_{1}$ = 1 atm
${V}_{1}$ = 196 L
${P}_{2}$ = ?
${V}_{2}$= 26 L substitute the values;

1 atm x 196 L = ${P}_{2}$ x 26 L

${P}_{2}$ = 1 atm x 196 L / 26 L

${P}_{2}$ = 196 atm L / 26 L = 7.53 atm