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?

Verified step by step guidance

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.

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, 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.

Recommended video:

Guided course

02:10

Temperature Conversion Example

Related Practice

Textbook Question

You have a sample of gas in a container with a movable piston, such as the one in the drawing. b. Redraw the container to show what it might look like if the external pressure on the piston is increased from 1.0 atm to 2.0 atm while the temperature is kept constant.

Textbook Question

Consider the sample of gas depicted here. What would the drawing look like if the volume and temperature remained constant while you removed enough of the gas to decrease the pressure by a factor of 2? (a) It would contain the same number of molecules. (b) It would contain half as many molecules. (c) It would contain twice as many molecules. (d) There is insufficient data to say.

views

Textbook Question

Imagine that the reaction 2 CO1g2 + O21g2¡2 CO21g2 occurs in a container that has a piston that moves to maintain a constant pressure when the reaction occurs at constant temperature. Which of the following statements describes how the volume of the container changes due to the reaction: (a) the volume increases by 50%, (b) the volume increases by 33%, (c) the volume remains constant, (d) the volume decreases by 33%, (e) the volume decreases by 50%.

views