A 500 mL incandescent light bulb is filled with 1.5 * 10-5 mol of xenon to minimize the rate of evaporation of the tungsten filament. What is the pressure of xenon in the light bulb at 25 _x001F_C?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

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Step 1: Identify the known variables. We have the volume (V) of the bulb as 500 mL, the amount of xenon gas (n) as 1.5 \(\times\) 10^{-5} mol, and the temperature (T) as 25 \(\degree\) C.

Step 2: Convert the volume from milliliters to liters, since the ideal gas law requires volume in liters. 1 L = 1000 mL, so V = 500 mL = 0.500 L.

Step 3: Convert the temperature from Celsius to Kelvin, as the ideal gas law requires temperature in Kelvin. Use the formula T(K) = T(\(\degree\) C) + 273.15. Therefore, T = 25 + 273.15 = 298.15 K.

Step 4: Use the ideal gas law to find the pressure. The ideal gas law is given by PV = nRT, where R is the ideal gas constant (0.0821 L·atm/mol·K). Rearrange the formula to solve for pressure (P): P = \(\frac{nRT}{V}\).

Step 5: Substitute the known values into the rearranged ideal gas law equation: P = \(\frac{(1.5 \times 10^{-5}\) mol) \(\times\) (0.0821 L·atm/mol·K) \(\times\) (298.15 K)}{0.500 L}. Calculate to find the pressure of xenon in the light bulb.

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Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature in Kelvin. This law allows us to calculate the pressure of a gas when the other variables are known.

Molar Volume of a Gas

At standard temperature and pressure (STP), one mole of an ideal gas occupies approximately 22.4 liters. However, in this question, we are dealing with a specific volume of 500 mL (0.5 L). Understanding the concept of molar volume helps in determining how many moles of gas correspond to a given volume, which is essential for calculating pressure using the Ideal Gas Law.

Temperature Conversion

Temperature must be expressed in Kelvin when using the Ideal Gas Law. To convert Celsius to Kelvin, you add 273.15 to the Celsius temperature. In this case, 25 °C converts to 298.15 K. Accurate temperature conversion is crucial for ensuring that calculations involving gas laws yield correct results.