Question

Use the molar volume of a gas at STP to determine the volume (in L) occupied by 33.6 \(\mathrm{g}\) of neon at STP.

Short answer

The volume occupied by 33.6 \(\mathrm{g}\) of neon at STP is \(\frac{33.6 \, \mathrm{g}}{20.18 \, \mathrm{g/mol}} \times 22.4 \, \mathrm{L/mol} = 37.34 \, \mathrm{L}\).

Step-by-step solution

Recall the molar volume of a gas at STP

At standard temperature and pressure (STP), the molar volume of an ideal gas is 22.4 liters per mole. This means that one mole of any ideal gas occupies 22.4 liters at STP.

Calculate the number of moles of neon

Use the molar mass of neon (approximately 20.18 \(\mathrm{g/mol}\)) to convert the mass of neon to moles. This is done using the formula: number of moles = mass of substance (in grams) / molar mass (in \(\mathrm{g/mol}\)).

Perform the mole calculation

For 33.6 \(\mathrm{g}\) of neon, the number of moles is \(\frac{33.6 \, \mathrm{g}}{20.18 \, \mathrm{g/mol}}\).

Find the volume of neon at STP

Multiply the number of moles of neon by the molar volume of a gas at STP to find the volume. That is, volume = number of moles × molar volume at STP.

Calculate the final volume

Using the molar volume at STP (22.4 L/mol), calculate the volume occupied by the neon gas.

Key concepts

Standard Temperature and Pressure (STP)

Understanding the standard temperature and pressure (STP) conditions is essential for working with gases. STP refers to a set of conditions where the temperature is 0°C (273.15 K) and the pressure is 1 atmosphere (atm). These conditions are universally adopted to allow chemists and scientists to compare the behaviors of different gases under consistent conditions.

At STP, one mole of any ideal gas occupies a fixed volume of 22.4 liters. This property is rooted in the ideal gas law, which helps us establish a standard to compare various gases. In practical scenarios, not all gases behave perfectly ideally, but many gases come close enough that the ideal gas approximation at STP provides a very useful point of reference.

Mole Calculation

A mole is a fundamental unit in chemistry that represents a specific number of particles (6.022 x 10^23 particles, to be exact). It is the bridge between the microscale (atoms, molecules) and the macroscale (grams, liters) providing a way to convert between the number of particles and the mass. To calculate the number of moles from a given mass, we use the formula: \[\begin{equation}n = \frac{m}{M}\end{equation}\]where:

• (){n}) is the number of moles,
• (){m}) is the mass of the substance in grams, and
• (){M}) is the molar mass of the substance in grams per mole (g/mol).

By using this formula, you can easily calculate the amount of substance in moles, which is crucial for further gas law calculations and understanding chemical reactions.

Molar Mass of Neon

Each element has a unique molar mass, which is the mass of one mole of that element. For neon, a noble gas, the molar mass is approximately 20.18 grams per mole (g/mol). The molar mass acts like a conversion factor between grams and moles. This value is determined by averaging the masses of all isotopes of an element, each weighted by its natural abundance, and can be found on the periodic table.

The molar mass is vital because it allows us to convert between the mass of a substance and the number of moles, facilitating calculations involving chemical amounts. Knowing the molar mass of neon, or any other element, is fundamental when performing chemical calculations, such as determining the volume of a gas at STP, as highlighted in the exercise.

Gas Law Calculations

Gas law calculations are a set of mathematical techniques used to predict and explain the behavior of gases. These calculations derive from the ideal gas law, represented by the equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature (in Kelvin).

For calculations at STP, we often use the molar volume of 22.4 L/mol for an ideal gas. This simplifies the equation, allowing us to directly calculate the volume occupied by a gas given a number of moles, as demonstrated in our exercise solution. By mastering gas laws, students can not just solve textbook problems but also gain insights into how gases will behave under different conditions, which is crucial in laboratory work and industrial applications.