The solve the given question, we can use combined gas law .The formula for combined gas law is given by :
[tex]{\boxed{ \sf\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2} }} [/tex]
According to the question, we have: I have a bag that contains 976 mL of air at room temperature (25 °C) and has a pressure of 795 torr
Converting the temperature In Kelvins,
[tex]\sf T_1 = 25 + 273 [/tex]
[tex]\sf T_1 = 298 \ K [/tex]
Also, If I ascend a mountain and the bag does not break, what is the volume [tex]\sf (V_2) [/tex] in liters (L) when the pressure is 553 torr [tex]\sf(P_2) [/tex] and the temperature is 10. °C [tex]\sf (T_2) [/tex]
Converting the temperature In Kelvins:
[tex]\sf T_2 = 10 + 273 = 283 \ K [/tex]
To solve for Volume [tex]\sf (V_2) [/tex] , substitute the given values in the above formula for combined gas law:
[tex]\sf\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2} \\ \\ \sf\dfrac{795 \times 976 }{298} = \dfrac{553 \times V_2}{283 } \\ \\ \sf\dfrac{775920 }{298} = \dfrac{553 \times V_2}{283 } \\ \\ \sf 553 \times 298 \times V_2 = 283 \times 775920\\ \\ \sf 164794 \times V_2 = 219,585,360 \\ \\ \sf V_2 = \dfrac{219,585,360}{164794} \\ \\ \sf V_2 = 1331.83 \ mL [/tex]
converting in liters,
[tex]\sf V_2 = \dfrac {1331.83 }{1000} [/tex]
[tex]\sf V_2 = 1.33 \ L [/tex]
Hence, when the pressure is 553 torr and the temperature is 10. °C, the Volume will be 1.33 liters.
