Question

A pre-weighed vessel was filled with oxygen at NTP and weighed. It was then evacuated, filled with \(\mathrm{SO}_{2}\) at the same temperature and pressure, and again weighed. The mass of oxygen will be (a) the same as that of \(\mathrm{SO}_{2}\) (b) half that of \(\mathrm{SO}_{2}\) (c) twice that of \(\mathrm{SO}_{2}\) (d) one-fourth of \(\mathrm{SO}_{2}\)

Short answer

The mass of oxygen will be half that of \text{SO}_2.

Step-by-step solution

Understanding Conditions

Since the vessel is filled with gases at NTP (Normal Temperature and Pressure), we know that both gases, oxygen (O2) and sulfur dioxide (SO2), are at the same conditions of temperature and pressure. This implies that the volume of both gases within the vessel will be the same due to Avogadro's law, which states that equal volumes of gases at the same temperature and pressure contain an equal number of molecules.

Applying the Molar Mass Concept

The molar mass of oxygen gas (O2) is 32 g/mol and the molar mass of sulfur dioxide (SO2) is 64 g/mol. Since they occupy the same volume under the same conditions and contain an equal number of molecules (1 mole each under NTP conditions), the mass of each gas will be directly proportional to its molar mass.

Determining the Mass Relationship

The mass of oxygen gas will be half that of sulfur dioxide because the molar mass of oxygen (32 g/mol) is half that of sulfur dioxide (64 g/mol). For the same number of moles, the mass is directly proportional to the molar mass, so when comparing equal volumes of these two gases at NTP, the mass of SO2 will be twice that of O2.

Key concepts

NTP Conditions

Normal Temperature and Pressure (NTP) conditions are a commonly used standard set of conditions for the measurement and documentation of experiments involving gases. Specifically, NTP is defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (101.325 kPa). These conditions provide a uniform baseline that allows scientists and students to compare different gas-related experiments and calculations under standardized conditions.

Under NTP conditions, one mole of any ideal gas occupies a volume of 22.4 liters. This is vital information when solving problems involving gas comparisons, like in our exercise, where oxygen and sulfur dioxide are compared. Remembering the volume of a mole under NTP simplifies problem-solving because it's consistent across all ideal gases according to Avogadro's law. This uniformity is crucial for students to grasp, as it underpins many calculations in chemistry and physics related to gases.

Molar Mass

Molar mass is a fundamental concept in chemistry defined as the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a physical property that is characteristic of every pure substance. The molar mass can be calculated by summing the atomic masses of all atoms in a molecule, which are listed on the periodic table of elements.

For instance, the molar mass of oxygen gas (\(O_2\)) is 32 g/mol because one mole of oxygen consists of two oxygen atoms, each with an atomic mass of approximately 16. Similarly, sulfur dioxide (\(SO_2\)) has a molar mass of 64 g/mol, calculated by adding one sulfur atom (approximately 32 g/mol) to two oxygen atoms. Understanding molar mass is crucial for students since it allows them to relate the mass of a substance to the amount of substance (moles) present, thereby providing a bridge between the macroscopic scale of the material you can weigh and the microscopic scale of atoms and molecules.

Gas Laws

Gas laws are a set of mathematical relationships between the volume, temperature, pressure, and amount of a gas. These laws are key to understanding how gases behave under different conditions. Avogadro's law, in particular, is directly applied in our exercise. This law states that equal volumes of all gases, at the same temperature and pressure, contain the same number of molecules.

To solve various problems, students need to be familiar with additional gas laws such as Boyle's Law, Charles's Law, and the Ideal Gas Law. Boyle's Law states that pressure and volume are inversely proportional at a constant temperature, while Charles's Law states that volume and temperature are directly proportional at a constant pressure. The Ideal Gas Law combines these relationships into one equation, making it a powerful tool for problem-solving. Integrating these laws allows for a comprehensive approach to predicting and quantifying the behavior of gases in a wide range of chemical and physical processes.