4.17 How to Identify When We Should Use the Ideal Gas Law?

[vuongnaomi1L]

A technician carries out the reaction 2SO2(g)+O2(g)→SO3(g)at 25 °C and 1.00 atm in a cylinder fitted with a piston and maintained at constant pressure. Initially, 0.030 mol SO2 and 0.030 mol O2 are present in the cylinder. The technician then adds a catalyst to initiate the reaction. (a) Calculate the volume of the cylinder containing the reactant gases before reaction begins. (b) What is the limiting reactant? (c) Assuming that the reaction goes to completion and that the temperature and pressure of the reaction remain constant, what is the final volume of the cylinder (include any excess reactant)? (d) How much work takes place, and is it done by the system or on the system? (e) How much enthalpy is exchanged, and does it leave or enter the system? (f) From your answers to parts (d) and (e), calculate the change in internal energy accompanying the reaction.

for part A) we use the ideal gas law and set nRT/P = V, but how do we know that we should use the gas law? do we just look at our givens and use the equation because it fits what we are given? or is there an easier way to know when we should use the ideal gas law?

[Sophia Hu 1A]

The way I typically approach the problem is looking at the givens. For part a it asks us for the volume and although we definitely have a lot of equations that use volume, the easiest way to find volume is through PV = nRT. When looking at the givens we are given P = 1 atm, n = 0.060 mol and T = 298.15 K.

I have also noticed some problems ask us to calculate the work for a reversible reaction which requires the equation w = - nRT ln(V2/V1), but they do not give moles directly. Instead they give the initial volume, pressure, and temperature the reaction occurs at and we have to use the ideal gas law to find the number of moles.

I think it can definitely be difficult to know when to identify just because we have been given so many equations. However, I always try to identify what is given and then understand what the problem is asking and how I can use the givens to find the solution. Also identifying if a parameter is missing in what you need to solve, and then understanding if parameters could be used in the ideal gas law to find the parameter.

I know this wasn't a completely clear answer, but I hope it helped!

[Kailani_Dial_2K]

Hi so my first inclination to use the ideal gas law is when the question says treat something like an ideal gas or the gas that is mentioned is an ideal gas.

Also, when I start doing an equation like work where w=-nRTln(V1/V2) and I am given a temperature, pressure, and initial volume, but not moles, then I know that I will have to use PV=nRT to solve for moles.

Most of the time if you are given all the information to solve PV= nRT but not the one piece of information that you need like the final pressure, final volume, moles, or temperature, then you can probably bet on using the ideal gas law to solve for whatever you need.

[Victor Qiu 1C]

I think if you are dealing with a chemistry problem, you can assume that the gas is an idea gas, and you can apply ideal gas law for most of the times. Nevertheless, the real characteristics of ideal gas should include:

(1) the collisions between gas molecules are elastic and conservation of energy occurs among the molecules;
(2) the total volume of the individual molecules is negligible comparing with the volume the gas occupies;
(3) no intermolecular forces exist among the molecules or between molecules and their surroundings;
(4) the molecules are in constant motion, and the distance between two molecules is much larger than the size of an individual molecule.

[Jacob Schwarz-Discussion 3I]

This is a very good question because there is not one exactly correct answer that I could give you. In my experience, what I like to do is set up the problem using the given equations(ex: w=-nRTln(V1/V2). In this case I am trying to find the amount of work done. However, sometimes after setting this up I am given everything EXCEPT for n(moles). From here I would then use the Ideal Gas Law(PV=nRT) to solve for the amount of moles and would then plug moles back into the work equation. My recommendation is to plug in everything given to you and if you are missing something then use the Ideal Gas Law.