An ideal gas at a pressure of 152 kPa is contained in a bulbof unknown volume. A stopcock is used to connect thisbulb with a previously evacuated bulb that has a volumeof 0.800 L as shown here. When the stopcock is opened,the gas expands into the empty bulb. If the temperatureis held constant during this process and the final pressureis 92.66 kPa, what is the volume of the bulb that wasoriginally filled with gas?

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Convert the initial pressure from kPa to atm using the conversion factor: 1 atm = 101.325 kPa.

Use the combined gas law, which states that P1 * V1 = P2 * V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume.

Let V1 be the unknown volume of the initially filled bulb and V2 be the total volume after the stopcock is opened (V1 + 0.800 L).

Substitute the known values into the combined gas law equation: (P1 * V1) = (P2 * (V1 + 0.800 L)).

Solve for V1 by isolating it on one side of the equation.

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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 is a fundamental equation in chemistry that relates the pressure (P), volume (V), temperature (T), and number of moles (n) of an ideal gas. It is expressed as PV = nRT, where R is the ideal gas constant. This law allows us to predict the behavior of gases under various conditions, making it essential for solving problems involving gas expansion and compression.

Boyle's Law

Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature and the amount of gas are held constant. Mathematically, it can be expressed as P1V1 = P2V2. This principle is crucial for understanding how gases behave when they expand or compress, particularly in scenarios like the one described in the question.

Pressure Units and Conversion

Pressure is commonly measured in various units, including atmospheres (atm), pascals (Pa), and kilopascals (kPa). Understanding how to convert between these units is vital for solving gas-related problems. In this question, the initial pressure is given in kPa, while the diagram shows pressure in atm, necessitating conversion for accurate calculations.

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