# If 32 L of a gas at room temperature exerts a pressure of 6 kPa on its container, what pressure will the gas exert if the container's volume changes to 2 L?

Feb 28, 2016

96kPa will be the pressure exerted by gas in container, if its volume changes to 2L.

#### Explanation:

Assume that temperature at two volumes (i.e. 32L and 2L) remains unchanged.

Case i :

${V}_{1} = 32 L$

${P}_{1} = 6000 P a$

case ii:

${V}_{2} = 2 L$

P_2=?

we know that

${V}_{1} \propto \frac{1}{{P}_{1}}$$- - - - - - \left(1\right)$

${V}_{2} \propto \frac{1}{{P}_{2}}$$- - - - - - \left(2\right)$

doing $\left(1\right) / \left(2\right)$

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

substitute given data above equation

$\frac{32}{2} = \frac{{P}_{2}}{6000}$

${P}_{2} = 16 \times 6000$

${P}_{2} = 96000 P a$