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 Xe, Ne, and He atoms in a ratio of 1:12:12, respectively, at a total pressure of 500 torr at 298 K. Calculate the number of Xe, Ne, and He atoms in the cell.

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 volume of the plasma cell using the formula for the volume of a rectangular prism: \( V = \text{length} \times \text{width} \times \text{height} \).
3. Use the ideal gas law \( PV = nRT \) to find the total number of moles of gas in the cell. Remember to convert pressure from torr to atm and use the appropriate value for the gas constant \( R \).
4. Determine the mole fraction of each gas using the given ratio of Xe:Ne:He = 1:12:12. Calculate the mole fraction for each gas.
5. Calculate the number of moles of each gas by multiplying the total moles by the respective mole fraction, and then convert moles to atoms using Avogadro's number.

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 scenario, it will help determine the total number of moles of gas present in the plasma cell, which can then be used to find the number of individual atoms.

Mole Ratio

Mole ratio is the proportion of different substances in a mixture, expressed in terms of moles. In this question, the gases Xe, Ne, and He are present in a ratio of 1:12:12. Understanding this ratio is crucial for calculating the individual amounts of each gas after determining the total number of moles, allowing for the accurate distribution of atoms based on their respective ratios.

Avogadro's Number

Avogadro's Number, approximately 6.022 x 10²³, is the number of particles (atoms, molecules, etc.) in one mole of a substance. This concept is vital for converting the number of moles of each gas into the actual number of atoms. By applying Avogadro's Number to the calculated moles of Xe, Ne, and He, one can find the total number of atoms present in the plasma cell.