A compressed air tank carried by scuba divers has a volume of 8.0 L and a pressure of 140 atm at 20 °C. What is the volume of air in the tank in liters at STP?

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Step 1: Identify the given values. The volume (V1) is 8.0 L, the pressure (P1) is 140 atm, and the temperature (T1) is 20 °C. Convert the temperature to Kelvin by adding 273 to the Celsius temperature, so T1 = 293 K. The conditions at STP are a pressure (P2) of 1 atm and a temperature (T2) of 273 K.

Step 2: Use the combined gas law, which states that the ratio of the product of pressure and volume to temperature is constant for a given amount of gas. The formula is (P1*V1)/T1 = (P2*V2)/T2.

Step 3: Rearrange the formula to solve for the unknown volume at STP (V2). The rearranged formula is V2 = (P1*V1*T2) / (P2*T1).

Step 4: Substitute the given values into the formula. P1 is 140 atm, V1 is 8.0 L, T2 is 273 K, P2 is 1 atm, and T1 is 293 K.

Step 5: Calculate the value of V2. This will give you the volume of the air in the tank at STP in liters.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is essential for understanding how gases behave under different conditions, allowing us to calculate changes in volume or pressure when temperature or the amount of gas changes.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is defined as a temperature of 0 °C (273.15 K) and a pressure of 1 atm. At STP, one mole of an ideal gas occupies 22.4 liters. Understanding STP is crucial for converting gas volumes from one set of conditions to another, as it provides a reference point for calculations.

Gas Volume Conversion

Gas volume conversion involves using the Ideal Gas Law to determine how the volume of a gas changes with variations in pressure and temperature. By applying the combined gas law (P1V1/T1 = P2V2/T2), we can find the volume of gas at STP based on its initial conditions, which is key to solving the given problem.