Answer to Question #286860 in General Chemistry for Vale

Question

Your space shuttle must land on Earth. You hope your shuttle can survive the landing, but the oxygen tank worries you. The gauge in your 50.0 L O2 tank indicates a pressure of 4000 kPa. The temperature is currently -137.0 ° C, but you would expect it to rise to 695 ° C when it re-enters the atmosphere. The tank was created to withstand a pressure of 7000 kPa. What% of O2 can we keep?

Answer 1

The volume of the tank is constant. Apply the combined gas law to find how the pressure of 4000 kPa at -137 will increase at 695°C:

$$P_1T_2=P_2T_1,\\\space\\ P_2=P_1T_2/T_1,\\ P_2=4000(695+273)/(-137+273)=28471\text{ kPa}.$$

So, the tank will blow up.

Therefore, we need to find the volume of oxygen the tank should contain in order for the pressure not to exceed 7000 kPa and the final volume of oxygen is 50 L. Apply the combined gas law:

$$\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2},\\\space\\ \dfrac{4000·V_1}{(-137+273)}=\dfrac{7000·50}{(695+273)},\\\space\\ V_1=12.3\text{ L},$$

or 24.6% of the tank volume.