Question

What volume does 0.118 mol of helium gas at a pressure of 0.97 atm and a temperature of 305 \(\mathrm{K}\) occupy? Would the volume be different if the gas was argon (under the same conditions)?

Short answer

The volume of the helium gas is approximately 3.05 L. The volume would be the same if the gas was argon, given that it behaves ideally and is under the same conditions.

Step-by-step solution

Identify Given Values

List the given values. The amount of helium gas is 0.118 mol, the pressure is 0.97 atm, and the temperature is 305 K.

Use the Ideal Gas Law Equation

Apply the Ideal Gas Law, which is given by the equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.

Choose the Ideal Gas Constant

Select the value of R based on the units of pressure. Since the pressure is given in atm, use the gas constant in the units of L·atm/(mol·K), which is 0.0821 L·atm/(mol·K).

Rearrange Ideal Gas Law to Solve for Volume

Rearrange the Ideal Gas Law to solve for Volume (V): V = \( \frac{nRT}{P} \).

Substitute Known Values

Substitute the known values into the rearranged Ideal Gas Law: V = \( \frac{(0.118 \, \text{mol})(0.0821 \, \text{L·atm/mol·K})(305 \, \text{K})}{0.97 \, \text{atm}} \).

Calculate the Volume

Perform the calculation to find the volume V = \( \frac{(0.118)(0.0821)(305)}{0.97} \) L.

Consider the Noble Gas

Determine if the type of noble gas would affect the volume. Since the Ideal Gas Law doesn't consider the type of gas but only the fact that it behaves ideally, the volume would be the same for argon under the same conditions.

Key concepts

Gas Volume Calculation

Understanding how to calculate the volume of gas is a fundamental aspect of chemistry and involves capturing the interplay between pressure, temperature, and amount of gas. In our exercise, we calculate the volume occupied by a known amount of helium, which involves identifying the given values such as moles of gas, pressure, and temperature. To provide a clearer explanation, we apply the Ideal Gas Law which encapsulates the relationship between these variables. The simplicity of this calculation is intriguing; by plugging the values into an equation, one can swiftly find the volume occupied by a gas at certain conditions.

It's critical to remember that in these calculations, temperature must always be in Kelvin for the equation to work appropriately. Temperature in Celsius may mislead your result, as the Kelvin scale directly relates to the kinetic energy of the particles involved. The pressure must also be consistent with the unit of the gas constant used. In the context of our exercise, the volume of helium or any other ideal gas can be determined efficiently using these principles.

PV=nRT Equation

At the heart of gas volume calculations lies the PV=nRT equation; an essential tool in the chemist's arsenal known as the Ideal Gas Law. The riddle of various gas behavior is solved by this deceptively simple relationship which states that the product of pressure (P) and volume (V) of a gas equals the number of moles (n) times the ideal gas constant (R), times the temperature (T). This equation is pivotal because it assumes that gases act ideally, meaning their particles have negligible volume and there are no intermolecular forces affecting them.

To calculate volume, you simply rearrange the equation to solve for V:
V = \( \frac{nRT}{P} \). From this equation, determining the volume becomes a straightforward task of substituting values for n, R, T, and P, and solving the algebraic formula. Using this equation provides a foundational understanding of how gases will react in different conditions which is an essential concept in both chemistry and physics. The universality of this equation makes it adaptable to various problems, as demonstrated in the step-by-step solutions for finding the volume of helium.

Noble Gases Properties

Noble gases, such as helium and argon mentioned in the exercise, possess a set of properties that make them unique contenders in the realm of chemistry. They are known for their inertness; they rarely engage in chemical reactions due to their complete valence electron shells. Superior stability is the pride of these elements, making them relatively predictable when it comes to their behavior under different conditions.

When using the Ideal Gas Law for noble gases, the assumption of ideal behavior fits these gases quite well at standard conditions. This is because their atomic structure leads to very weak interatomic forces, allowing them to approximate the behavior of an ideal gas more closely than many other gases. In terms of the exercise, this means the volume of helium would be equivalent to that of argon when measured under the same conditions of pressure and temperature. This ideal behavior is also why noble gases are commonly used in experiments and applications requiring controlled, non-reactive environments. Despite their unique characteristics, when it comes to the Ideal Gas Law, the type of noble gas under identical conditions of pressure, temperature, and volume doesn't influence the outcome of calculations.