# 500 mL of hydrogen at 27°C and 3 atmospheres pressure is compressed to 100 mL at 100°C. What is the new pressure in atmospheres?

Feb 25, 2016

The new pressure is $\text{18.6 atm}$.

#### Explanation:

This appears to be a combined gas law problem.

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

${P}_{1} = \text{3 atm"; V_1 = "500 mL"; T_1 = "(27 + 273.15) K = 300.15 K}$

${P}_{2} = \text{?";color(white)(mml) V_2 = "100 mL"; T_2 = "(100 + 273.15) K = 373.15 K}$

P_2 = P_1 × V_1/V_2 × T_2/T_1 = "3 atm" × (500 color(red)(cancel(color(black)("mL"))))/(100 color(red)(cancel(color(black)("mL")))) × (373.15 color(red)(cancel(color(black)("K"))))/(300.15 color(red)(cancel(color(black)("K")))) = "18.6 atm"

The new pressure is $\text{18.6 atm}$.