Question

The pressure exerted on walls of a \(3 \mathrm{~L}\) flask when \(7 \mathrm{~g}\) of \(\mathrm{N}_{2}\) is introduced into it at \(300 \mathrm{~K}\) should be (assume ideal behaviour of gas) (a) zero (b) \(2.05 \mathrm{~atm}\) (c) \(4.10 \mathrm{~atm}\) (d) \(207.85\) atm

Short answer

The pressure exerted is 4.10 atm.

Step-by-step solution

Calculate the number of moles of N2

First, calculate the number of moles of nitrogen gas (2) using its molar mass (28 g/mol). The formula for the number of moles is mass (m) divided by molar mass (M).

Use Ideal Gas Law

Use the Ideal Gas Law equation \(PV = nRT\), where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles of gas, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin. Solve for \(P\) (Pressure).

Insert Values and Calculate Pressure

Insert the calculated number of moles, given volume (3 L), temperature (300 K), and the value of \(R\) (0.0821 L atm / (mol K)) into the Ideal Gas Law equation and calculate the Pressure.

Check the Answer

Check the calculated pressure against the options provided to find the correct one.

Key concepts

Chemical Thermodynamics

Chemical thermodynamics is the study of the interrelation of heat and work with chemical reactions or with physical changes of state within the confines of the laws of thermodynamics. In the context of an ideal gas, it primarily deals with how the energy transformations involved in a chemical reaction can be understood and quantified.

For instance, when dealing with gases, the energy changes can be reflected in changes of state variables such as temperature, volume, and pressure. The Ideal Gas Law establishes a relationship between these variables for a gas that follows ideal behavior—meaning the gas particles do not attract or repel each other, and the volume of the gas particles is negligible.

Understanding the Ideal Gas Law allows us to calculate the work done by or on the gas when it expands or contracts, which is a fundamental concept in chemical thermodynamics and crucial for chemical engineers and chemists studying reactions involving gases.

Physical Chemistry

Physical chemistry is a branch of chemistry that deals with the physical properties and behavior of matter, as well as the changes that occur during chemical reactions. It is grounded in physics and thus provides an understanding of the principles that govern the physical aspects of chemical systems.

This includes studies of atomic and molecular structure, chemical bonding, and how matter interacts with energy. Among these topics, the behavior of gases holds significance, which is why equations like the Ideal Gas Law are so crucial.

Physical chemistry explains why and how chemical reactions occur, and the energy exchange involved. Without understanding the underlying physical principles, advanced chemical processes and material properties cannot be fully comprehended or manipulated in laboratory and industrial settings.

Gas Laws

Gas laws are a series of laws that relate the physical properties of gases, such as pressure, volume, and temperature. The Ideal Gas Law is a fundamental equation within this series, combining the simpler laws such as Boyle's law (pressure-volume relationship), Charles's law (volume-temperature relationship), and Avogadro's law (volume-mole relationship).

With the Ideal Gas Law, expressed as \(PV=nRT\), all of these relationships are brought together. It tells us how a gas will behave under different conditions and allows us to calculate one property if the others are known.

Understanding gas laws is essential for anyone studying chemistry or related fields because gases play a crucial role in many chemical reactions and industrial processes. For example, when predicting how much of a gas will be produced or consumed in a reaction, one must consider the conditions under which the gas is measured to accurately use stoichiometry.

Stoichiometry

Stoichiometry involves the calculation of the quantities of reactants and products in chemical reactions. It is based on the conservation of mass and the concept that reactions occur in whole-number ratios of moles. In exercises involving gases, stoichiometry applies these mole ratios to quantify the amount of gas involved in reactions.

The equation from step 1 in the solution, mass (m) divided by molar mass (M), provides the moles of gas, which is a key step in solving Ideal Gas Law problems. Stoichiometry is closely linked to the gas laws because it often requires the application of the Ideal Gas Law to find out the number of moles of gas at a given pressure, volume, and temperature.

This practice helps students develop the necessary skills to perform calculations pertinent to laboratory and industrial chemistry applications, where the quantitative analysis of gases is required to understand and manipulate chemical processes. Moreover, it aids in the comprehension of how substances will react and in what proportions, which is vital for all chemical experimentation and production.