When 0.583 g of neon is added to an 800 cm³ bulb containing a sample of argon, the total pressure of the gases is 1.17 atm at a temperature of 295 K. Find the mass of the argon in the bulb.

Verified step by step guidance

1. Use the ideal gas law, PV = nRT, to find the number of moles of neon. First, convert the mass of neon to moles using its molar mass (20.18 g/mol).
2. Calculate the number of moles of neon: n_{Ne} = \frac{0.583 \text{ g}}{20.18 \text{ g/mol}}.
3. Convert the volume from cm³ to liters: 800 \text{ cm}^3 = 0.800 \text{ L}.
4. Use the ideal gas law to find the total number of moles of gas in the bulb: n_{total} = \frac{PV}{RT}, where P = 1.17 \text{ atm}, V = 0.800 \text{ L}, R = 0.0821 \text{ L atm/mol K}, and T = 295 \text{ K}.
5. Subtract the moles of neon from the total moles to find the moles of argon: n_{Ar} = n_{total} - n_{Ne}. Convert the moles of argon to mass using its molar mass (39.95 g/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 understanding how gases behave under varying conditions and is crucial for solving problems involving gas mixtures, such as the one presented.

Dalton's Law of Partial Pressures

Dalton's Law states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of each individual gas. This concept is vital for determining the contribution of argon to the total pressure when neon is added to the system.

Molar Mass and Mass Calculations

Understanding molar mass is crucial for converting between grams and moles of a substance. In this problem, knowing the molar mass of argon allows for the calculation of its mass based on the number of moles derived from the total pressure and volume of the gas mixture.