 We're now going to take a look at gases that do not exist as a single component but rather we'll be looking at gases that are in what we call gas mixtures. We're now going to be looking at what we refer to as being gas mixtures whereby you could have two different gases mixed together. For example, let's say you have a natural gas that consists of ethane and methane and different percentages. What we need to do is develop the mechanisms by which or the procedures by which we can evaluate the properties of these gas mixtures and this is actually taking us towards gas vapor mixtures which is what we will look at in the next few lectures after this one as well we'll eventually move into combustion and when we look at combustion we're looking at chemical reactions of different species and consequently we need the tools and techniques to be able to handle gas mixtures which is what this lecture will cover. So when we're looking at gas mixtures we quite often use mass and mole fractions so I will introduce those now and we use a certain form of subscripting so it's good to go through that so that we're consistent. Now whenever you see a subscript m that will denote the mixture so it's a gas mixture that we're talking about and whenever you see a subscript i that will denote one of the individual components in that mixture. So let's start with the simplest and let's take a look at the mass of a mixture and this one is somewhat obvious we can say the mass of a mixture is equal to the summation of the mass of each individual component in that mixture. So that makes sense you have a number of different components you add up the individual masses and that will give you the mass of the mixture. Now what we'll do is we'll take a look at the way of quantifying the number of moles within a mixture and in a like manner similar the number of moles in a mixture is going to be each of the components the number of moles of each component sum together and that will give us a value in kilomoles. Now having defined both the mass of the mixture as well as the number of moles what we can do is we can divide that summation by the total mass of the mixture and that introduces or brings us to what we call a mass fraction and the symbol for mass fraction is going to be little m little f and then subscript i because this will be the mass fraction for a given component in our mixture it will be the mass of that component divided by the mass of the total mixture and recall with this what that means we can say if we were to sum over all of the individual components all of the mass fractions that will have to equal one because you would have all the different components added together so that is the mass fraction and in a similar way we also have another term and it is called the mole fraction mole fraction is given the symbol little y subscript i to indicate each of the individual components and that would be the number of moles of an individual component in the mixture divided by the total number of moles in the mixture and just like for the mass fraction if we sum up all of the individual mole fractions they will have to total one so we'll be using both mass fraction and mole fraction and evaluating the properties which we'll get to in today's lecture another thing that i should write out and then this one is more obvious we quite often define it the mass is defined as being the number of moles times the molar mass you'd have seen this in freshman physics courses or perhaps chemistry courses and so with this what we can do we can write out our nomenclature the mass is equal to the number of moles will be capital N and molar mass will be capital M and with that we can define the molar mass as being the mass divided by the total number of moles that will give us something kilograms per kilo mole and with this what we can now do is come up with an expression for the molar mass of a mixture we can look up molar mass in the back of the book for individual components but if we want to know the molar mass of a mixture we need an expression for that and so that's what this can help us with so given our definition of molar mass we can say that it's the mass of the mixture divided by the number of moles in the mixture we can substitute with the mass as being the summation of each individual component in the mixture the mass of each individual component again divided by the total number of moles in the mixture and what we'll do is we'll substitute our relationship that we just looked at between mass number of moles and molar mass for the summation in the numerator and we can say that the mass is going to be the number of moles of that component times the molar mass of that component and then we divide by the total number of moles in the mixture what I'm going to do now is I'm going to pull these two out and that is as we saw earlier the definition of mole fraction so if you know the mole fraction of your components and if you know the individual molar mass as you can then determine by the summation the molar mass of your mixture and another thing that we'll be using if we use the ideal gas equation we often use the gas constant well for a mixture and we can look up the gas constant in the back of the book for for different components but if we have a mixture the way to determine the gas constant for the mixture will be to take the universal gas constant and divide by the molar mass of the mixture and the units here are going to be kilojoules per kilogram kelvin and the universal gas constant is 8.314 kilojoules per kilomole kelvin and sometimes there are different ways of representing the universal gas constant depending upon the units that you're using but it's 8.314 if you're using kilojoules per kilomole kelvin so those are some things that we're going to be using what we'll do next is we'll take a look at kind of a simple example problem to demonstrate some of these concepts and then we'll continue working on towards trying to evaluate the property values for different mixtures using these concepts