# If the pressure of a 2.00 L sample of gas is 50.0 kPa, what pressure does the gas exert if its volume is decreased to 20.0 mL?

##### 1 Answer
Jul 2, 2016

The gas exerts a pressure of 5.00 MPa.

#### Explanation:

This appears to be a Boyle's Law problem.

Boyle's Law is

$\textcolor{b l u e}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} {P}_{1} {V}_{1} = {P}_{2} {V}_{2} \textcolor{w h i t e}{\frac{a}{a}} |}}} \text{ }$

${P}_{1} = \text{50.0 kPa"; V_1 = "2.00 L}$
${P}_{2} = \text{?";color(white)(mmmll) V_2 = "20.0 mL" = "0.0200 L}$

We can rearrange Boyle's Law to get

P_2 = P_1 × V_1/V_2

${P}_{2} = \text{50.0 kPa" × (2.00 color(red)(cancel(color(black)("L"))))/(0.0200 color(red)(cancel(color(black)("L")))) = "5000 kPa" = "5.00 MPa}$