A ballon filled with 1.75 L of gas at 20°C has a pressure of 65 mmHg. If the gas pressure in the ballon is increased to 1 atm and the ballon will brust at a volume of up to 2 L, determine the temperature at which the ballon will brust.
a. 23°C
b. 26°C
c. 60°C
d. 117°C
e. 296°C
Assuming the gas behaves ideally, the final temperature which the balloon will burst, T_2, is
\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\Leftrightarrow T_2=T_1\frac{P_2V_2}{P_1V_1}=(293\textrm{ K})\times\frac{(1\textrm{ atm})(2\textrm{ L})}{(65\textrm{ mmHg})(1.75\textrm{ L})}\times\frac{760\textrm{ mmHg}}{1\textrm{ atm}}=3915.25\textrm{ K}
so, the balloon will burst at 3915.25 \textrm{ K} or roughly 3642.25^o\textrm{C}