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What is the combined gas law and how can we use it to solve problems?
The air in a 2 L balloon is at 0.998 atm and 34.0 °C. What will be its pressure if it is brought to a higher altitude where it now occupies 3.5 L and is at 12.0 °C?
Answer:
The combined gas law is the combination of Boyle's law, Charles's law, and Gay-Lussac's law. It allows us to relate the pressure, volume, and temperature of a gas when one or more of these properties change.
To solve this problem, we can use the formula of the combined gas law: [tex]\\frac{P_1V_1}{T_1}=\\frac{P_2V_2}{T_2}[/tex]
Given values:
- Initial pressure (P1) = 0.998 atm
- Initial volume (V1) = 2 L
- Initial temperature (T1) = 34.0 °C = 307.0K
- Final volume (V2) = 3.5 L
- Final temperature (T2) = 12.0 °C = 285.0K
By substituting these values into the formula, we can calculate the final pressure (P2) which is equal to 0.529 atm. This means that the pressure of the balloon at a higher altitude with a volume of 3.5 L and a temperature of 12.0 °C will be 0.529 atm.