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# 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?

The new pressure is ##"18.6 atm"##.

This appears to be a problem.

##(P_1V_1)/T_1 = (P_2V_2)/T_2##

##P_1 = "3 atm"; V_1 = "500 mL"; T_1 = "(27 + 273.15) K = 300.15 K"##

##P_2 = "?";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 ##"18.6 atm"##.