Problem 29 - Chemistry Central Science

Question

(a) Write the ideal-gas equation, and give the units used for each term in the equation when \(R=0.0821 \mathrm{~L}-\mathrm{atm} / \mathrm{mol}-\mathrm{K}\). (b) What is an ideal gas?

Step-by-Step Solution

Answer

(a) The ideal-gas equation is \(PV = nRT\), where \(P\) has units of atm, \(V\) has units of L, \(n\) has units of mol, \(R\) is given as 0.0821 L atm / mol K, and \(T\) has units of K. (b) An ideal gas is a theoretical gas where particles move randomly and do not interact. It obeys the ideal-gas equation and serves as an approximation for real gas behavior under certain conditions, such as low pressures and high temperatures.

Step 1: (a) Ideal-gas equation and units

The ideal-gas equation is given by: \[PV = nRT\] where: - \(P\) is the pressure with units of atmospheres (atm) - \(V\) is the volume with units of liters (L) - \(n\) is the moles of the gas with units of moles (mol) - \(R\) is the gas constant, given in this case as 0.0821 L atm / mol K - \(T\) is the temperature with units of Kelvin (K)

Step 2: (b) Definition of an ideal gas

An ideal gas is a theoretical gas composed of a large number of randomly-moving, non-interacting particles, that obey the ideal-gas equation. It is an approximation of the behavior of real gases under certain conditions, especially at low pressures and high temperatures. In an ideal gas, the volume of the gas particles can be neglected, and it is assumed that there are no intermolecular forces between them. While no real gas behaves exactly like an ideal gas, this model helps to simplify calculations and can give reasonably accurate results under certain scenarios.