Question

a gas - filled weather balloon with a volume of 65.0 l is released at sea level conditions of 745 torr and 25 °c. the ballon can expand to a maximum volume of 835 l. when the balloon rises to an altitude at which the temperature is - 5 °c and the pressure is 0.066 atm, will it reach its maximum volume?
○ yes
○ no

Explanation:

Step1: Convert units

First, convert the initial pressure from torr to atm. We know that $1\ atm = 760\ torr$, so $P_1=\frac{745\ torr}{760\ torr/atm}\approx0.980\ atm$. Convert the temperatures to Kelvin: $T_1 = 25 + 273.15 = 298.15\ K$, $T_2=- 5+273.15 = 268.15\ K$.

Step2: Apply combined gas law

The combined gas law is $\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$. We want to find $V_2$, so rearrange the formula to $V_2=\frac{P_1V_1T_2}{P_2T_1}$.
Substitute the values: $P_1 = 0.980\ atm$, $V_1 = 65.0\ L$, $T_2 = 268.15\ K$, $P_2 = 0.066\ atm$, $T_1 = 298.15\ K$.
$V_2=\frac{0.980\ atm\times65.0\ L\times268.15\ K}{0.066\ atm\times298.15\ K}\approx\frac{0.980\times65.0\times268.15}{0.066\times298.15}\ L$.
Calculate the numerator: $0.980\times65.0\times268.15\approx0.980\times17429.75\approx17081.165$.
Calculate the denominator: $0.066\times298.15\approx19.6779$.
Then $V_2\approx\frac{17081.165}{19.6779}\approx868\ L$.
Since $868\ L>835\ L$, the balloon will exceed its maximum volume, so the answer is Yes.

Answer:

Yes