A scuba diver takes a 2.8 -L balloon from the surface, where...

A scuba diver takes a 2.8 -L balloon from the surface, where the pressure is 1.0 atm and the temperature is $34^{\circ} \mathrm{C}$, to a depth of $25 \mathrm{m},$ where the pressure is $3.5 \mathrm{atm}$ and the temperature is $18^{\circ} \mathrm{C} .$ What is the volume of the balloon at this depth?

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Key Concepts

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. It provides the foundation for understanding how a gas will behave under various conditions, assuming the gas behaves ideally. This law is crucial for solving problems where the state of a gas changes, as it shows that any change in pressure, volume, or temperature will affect the others when the number of moles remains constant.

Combined Gas Law

The combined gas law is derived from the ideal gas law for processes involving a fixed amount of gas. It relates the initial and final states of a gas with the equation (P1V1/T1 = P2V2/T2). This law is used to solve problems where a gas is subjected to simultaneous changes in pressure, volume, and temperature, such as the scenario of the scuba diver’s balloon.

Temperature Conversion

Temperature conversion, specifically converting from Celsius to Kelvin, is essential in gas law calculations because the ideal gas law requires absolute temperature values. To convert Celsius to Kelvin, 273.15 is added to the Celsius temperature. Using Kelvin ensures that the temperature values are on a scale where zero represents absolute zero, which is necessary for the proportional relationships in the ideal and combined gas laws to hold true.

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