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Answer 1 · 2016-03-16T02:10:59

The pressure at maximum compression is 9.72 atm.

This is an example of a Combined Gas Laws problem.

$color(blue)(|bar(ul((P_1V_1)/T_1=(P_2V_2)/T_2)|)$

Your data are:

$P_1 = "1.00 atm"$ ; $V_1 = "400.0 cm"^3$ ; $T_1 = "(15 + 273.15) K" ="288.15 K"$

$P_2 = "?"$ ; $color(white)(mmmm) V_2 = "50.0 cm"^3$ ; $color(white)(ll)T_2 = "(77 + 273.15) K" = "350.15 K"$

Now. we insert these values into the Combined Gas Law.

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

$P_2 = P_1 × V_1/V_2 × T_2/T_1 = "1.00 atm" × (400 cancel("cm"^3))/(50.0 cancel("cm"^3)) × (350.15 cancel("K"))/(288.15 cancel("K")) = "9.72 atm"$

The maximum pressure is 9.72 atm.