# Question 46c7a

Jun 11, 2015

THe new volume of the gas will be 24.2 L.

#### Explanation:

For an an ideal gas, Boyle's Law establishes a relationship between volume and pressure if temperature and number of moles are kept constant.

More specifically, if those conditions are met, pressure and volume have an inverse relationship. If pressure increase, volume decreases, and if pressure decreases, volume increases.

Mathematically, this is written as

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

${P}_{1}$, ${V}_{1}$ - the pressure and volume at an initial state;
${P}_{2}$, ${V}_{2}$ - the pressure and volume at a final state.

In your case, pressure drops to approximately 1/4th of its initial value, so you can expect the new volume to be roughly 4 times bigger than the initial volume.

${P}_{1} {V}_{1} = {P}_{2} {V}_{2} \implies {V}_{2} = {P}_{1} / {P}_{2} \cdot {V}_{2}$

P_2 = (101cancel("kPa"))/(25.0cancel("kPa")) * "6.00 L" = "24.24 L"#

Rounded to three sig figs, the answer will be

${V}_{2} = \textcolor{g r e e n}{\text{24.2 L}}$