A plasma-screen TV contains thousands of tiny cells filled with a mixture of Xe, Ne, and He gases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell, 0.900 mm * 0.300 mm * 10.0 mm, contains 4% Xe in a 1:1 Ne:He mixture at a total pressure of 66.66 kPa. Calculate the number of Ne atoms in the cell and state the assumptions you need to make in your calculation.

Verified step by step guidance

1. Convert the dimensions of the plasma cell from millimeters to meters to find the volume in cubic meters.
2. Calculate the total volume of the plasma cell using the formula: \( V = \text{length} \times \text{width} \times \text{height} \).
3. Use the ideal gas law \( PV = nRT \) to find the total number of moles of gas in the cell, assuming ideal gas behavior.
4. Determine the mole fraction of Ne in the mixture. Since the mixture is 4% Xe and a 1:1 Ne:He mixture, calculate the mole fraction of Ne.
5. Calculate the number of Ne atoms by multiplying the moles of Ne by Avogadro's number (\(6.022 \times 10^{23}\) atoms/mol).

Key Concepts

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 calculating the number of gas particles in a given volume under specific conditions. In this problem, it will help determine the number of moles of the gas mixture in the plasma cell, which can then be converted to the number of atoms.

Partial Pressure

Partial pressure is the pressure that each gas in a mixture would exert if it occupied the entire volume alone. According to Dalton's Law of Partial Pressures, the total pressure of a gas mixture is the sum of the partial pressures of its individual components. This concept is crucial for calculating the contribution of neon (Ne) to the total pressure in the plasma cell, allowing for the determination of its mole fraction.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of the number of moles of that component to the total number of moles of all components. In this scenario, knowing the mole fraction of neon in the gas mixture will enable the calculation of the total number of Ne atoms present in the plasma cell, based on the total number of moles derived from the Ideal Gas Law.