A gas has a volume of 2.84 L at 1.00 atm and 0 °C. At what temperature does it have a volume of 7.50 L at 520 mmHg?

Guida verificata passo dopo passo

Step 1: Identify the gas law to use. Since the problem involves changes in pressure, volume, and temperature, use the combined gas law:

\frac{P_{1}}{V_{1}} / T_{1} = \frac{P_{2}}{V_{2}} / T_{2}

Step 2: Convert all given values to appropriate units. Ensure temperature is in Kelvin (K) by adding 273.15 to the Celsius value. Convert pressure from mmHg to atm using the conversion factor:

1

atm =

760

mmHg.

Step 3: Rearrange the combined gas law to solve for the unknown temperature,

T_{2}

T_{2} = \frac{P_{2} V_{2} T_{1}}{P_{1} V_{1}}

Step 4: Substitute the known values into the rearranged equation. Use the converted values for pressure, volume, and temperature. Ensure all units are consistent.

Step 5: Perform the calculation to find

T_{2}

. If needed, convert the result back to Celsius by subtracting 273.15 from the Kelvin temperature.

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Ideal Gas Law

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Charles's Law states that the volume of a gas is directly proportional to its temperature when pressure is held constant. Mathematically, it can be expressed as V1/T1 = V2/T2. This principle is crucial for understanding how changes in temperature affect the volume of a gas, which is essential for solving the given problem.

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Pressure conversion is the process of changing pressure units from one system to another, such as from atmospheres (atm) to millimeters of mercury (mmHg). In this case, 1 atm is equivalent to 760 mmHg. Understanding how to convert between these units is necessary to apply the Ideal Gas Law and Charles's Law correctly in the context of the problem.

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