Moles and Avogadro's Number Practice Problems

Calculate the number of atoms in a 3.0 cm × 4.0 cm × 5.0 cm right rectangular prism of copper.

A spacecraft on a mission to explore a distant planet discovers a solid mineral with a mass density of 2300 kg/m  ³. The analysis reveals that the mineral's number density is 6.25 × 10 ²⁸ atoms/m³. Find the atomic mass number of the element comprising this mineral.

What is the total count of iron (Fe) atoms in a nail weighing exactly 4.0 g?

A scientist is comparing the number of atoms in a 50.0 g oxygen (O₂) sample to that in a nitrogen (N₂) sample of the same mass. How do these numbers compare?

Consider an ideal gas that has a pressure of 120 kPa and is at a temperature of 20°C. Calculate the number of molecules found in 1 cubic meter of this ideal gas.

What is the final volume of a 4.50 m³ nitrogen gas initially at STP if it is subjected to a pressure of 3.90 atm and the temperature increases to 40.0°C?

A tank contains 2.00 liters of ethanol at STP. Given that the density of ethanol at STP is 0.789 g/mL and the molar mass of ethanol (C₂H₅​OH) is 46.08 g/mol, how many moles and how many molecules of ethanol are present?

A gas cylinder contains 25.5 kg of oxygen gas (O₂) at 7.35 atm absolute pressure. At the same temperature, what will be the pressure if oxygen is replaced with methane (CH₄)?

A gauge pressure of 5.00 atm is recorded for a container filled with 20.0 kg of nitrogen gas (N₂). If this nitrogen is swapped out for argon gas (Ar) while maintaining the same temperature, how many kilograms of argon are necessary to achieve a gauge pressure of 6.50 atm? Use: molar mass of N₂=28 g/mol and molas mass of Ar=40 g/mol.

A steam boiler operates at a pressure of 1 atm and a temperature of 100°C, and the steam is used to drive a turbine in a power plant. Compare the density of steam at these conditions using the actual density (0.598 kg/m³) with the density predicted by the ideal gas law. Explain any differences observed. Use: molecular mass of water vapor = 18g/mol.

In a laboratory vacuum chamber that has a density of 5 molecules per cubic meter and maintains a temperature of 10 K, what is the pressure inside the chamber?

A pressurized canister containing CO₂ starts with a gauge pressure of 150 bar. After releasing some gas for industrial processes, its gauge pressure drops to 45 bar. Calculate what percentage of CO₂ remains based on initial conditions.

Consider a lecture hall with dimensions 20.0 meters in length, 15.0 meters in width, and 5.0 meters in height. Estimate the number of air molecules in the hall if the temperature is 27°C. How many moles does that correspond to? Assume the air is an ideal gas, and that the pressure is 1.0 atm.

Estimate the number of moles of ethanol that can be found in a lake. The lake covers 70% of a recreational area of 15 km² and has an average depth of 5 m. Assume that the density of ethanol is 789 kg/m³.

Estimate the number of molecules of methanol in a reservoir. The reservoir covers 80% of a recreational area of 10 km² to an average depth of 4 m. Assume the density of methanol is 792 kg/m³.

At some pressure and temperature, you have 0.025 m³ of gas in a vessel. To find the effect of compression on this gas, you exert a force that reduces its volume to 0.022 m³. This compression decreases the temperature of the gas by 7.0 K, and the pressure inside the vessel increases by 350 Pa. What was the initial temperature and pressure before this compression? [n = 4.0 mol]

A balloon filled with helium gas bursts, releasing the gas into the outside environment. What will the density of this helium gas be under standard temperature and pressure conditions? [Hint: Use the following constants - 1 atm = 101325 Pa, R = 8.314 J·mol^-1·K^-1, and the molar mass of helium = 4.0 g/mol.]

The atmospheric pressure at the surface of Mars is about 610 Pa. Given that the radius of Mars is approximately 3.39 million meters and the gravitational acceleration on Mars is 3.71 m/s², estimate the total number of carbon dioxide molecules in the Martian atmosphere. Assume the atmosphere is composed entirely of carbon dioxide, and the molar mass of CO₂ is 44.0 grams per mole.