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Answer 1 · 2017-05-13T23:01:31

$-129 ^oC$

This question involves the pressure-temperature relationship of gases, and is illustrated by Gay-Lussac's law:

$(P_1)/(T_1) = (P_2)/(T_2)$

Remember that the temperature is the absolute temperature, so you have to convert the Celsius temperature to Kelvin:

$15 ^oC + 273 = 288 K$

We can rearrange this equation to solve for the final temperature, $T_2$ :

$T_2 = (T_1)(P_2)/P_1$

Plug in known variables:

$T_2 = 288 K(225 mm Hg)/(450 mm Hg) = 144 K$

Finally, we convert the Kelvin temperature back to Celsius:

$144 K - 273 = -129 ^oC$