Use the ideal gas law to show that \(28.0 \mathrm{~g}\) of nitrogen gas and \(4.00 \mathrm{~g}\) of helium gas occupy the same volume at any temperature and pressure.

Understanding how to calculate molar mass is crucial when dealing with chemical substances and gases. It represents the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). For elements, the molar mass can be found directly on the periodic table as the atomic weight. For example, helium (He) has a molar mass of approximately 4 g/mol.

For compounds, such as nitrogen gas (N2), the molar mass is the sum of all the atomic masses of the atoms in the molecule. Since nitrogen is diatomic, we take the atomic mass of a single nitrogen atom (approximately 14 g/mol) and multiply it by two, yielding a molar mass of 28 g/mol for N2.

Calculating the molar mass allows you to convert between the mass of a substance and the number of moles, which is a key step in many chemical problems and essential for utilizing the ideal gas law.

The mole is a fundamental unit in chemistry used to quantify the amount of substance. When it comes to gases, the mole concept allows us to compare different volumes of gases under the same conditions of temperature and pressure. This is rooted in Avogadro's hypothesis, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules.

To find the moles of gas, you simply divide the mass of the gas by its molar mass. For example, with 28.0 g of N2, we divide by its molar mass (28 g/mol) to find that we have 1 mole of N2. Similarly, 4.00 g of He divided by its molar mass (4 g/mol) gives us 1 mole of He.

Understanding moles of gas is vital, as it serves as a bridge between the physical world (mass of a sample) and the chemical world (calculating reaction yields, for instance), and is a central element in the application of the ideal gas law.

The ideal gas law, represented by the equation PV=nRT, is a cornerstone of gas laws, linking pressure (P), volume (V), moles of gas (n), the ideal gas constant (R), and temperature (T). This equation allows us to predict how a gas will behave under different conditions.

For the gases in question, nitrogen and helium, their behavior under any given set of conditions can be determined using this equation. If we keep the temperature (T) and pressure (P) constant, and since the number of moles (n) of each gas is the same (as we calculated before), the volume (V) occupied by each gas will also be the same. This is because R is a constant value and does not change with the identity of the gas.

The ability to use the ideal gas law hinges on the assumption that the gas behaves ideally, which means the gas particles are considered to have no volume and do not exert attractive or repulsive forces on each other. While this is never completely true for real gases, the ideal gas law provides a good approximation under many conditions.