 In this video we are going to look at two concentration terms and how they are related. So let's start with our first term which is molarity which is denoted by this capital M here and it is defined as the number of moles of the solute divided by the volume of the solution in liters. This part of having the volume in liters is important because sometimes in labs we use solutions in mls that is milliliters so you cannot directly plug in the value in ml here you have to convert it into liters before you calculate the molarity and the other concentration term to consider is the strength of a solution which is defined as the mass of the solute in grams divided by the volume of the solution in liters and apart from these two you would have also heard about mole fraction or maybe molality or mass percent so then the question is why do we have so many measures of concentration is it only to complicate exams well the reason why we have so many measures of concentrations is based on the application for which they are used let me take an example here we have a glass of water and for this water to be drinkable that is for it to be of good quality we know that the total amount of impurities which is also called dissolved solids should be less than 300 milligrams in one liter of water so we know of this number from the different studies that have been carried out on drinking water and now let's rearrange this unit a little bit so we can write this 300 milligrams per liter as 300 times 10 to the power minus 3 grams per liter and because we know that the density of water is one that is one gram will have a volume of one cc or one ml we can write this as 300 into 10 to the power minus 3 grams divided by 1000 grams so instead of this one liter i know that the mass of one liter of water will be 1000 grams and so we can simplify this and we see the units have gone off and we get 300 into 10 to the power minus 6 10 to the power 6 is called a million so if you think of this 10 to the power minus 6 you can take it down to the denominator so then it becomes per million so we can write this as 300 ppm or parts per million so what i've done is if we rearrange this unit of milligrams per liter in case of water we can write this as ppm or parts per million and you can realize how small this quantity is because let's say we have one ppm of something what it means is out of one million units of that particular thing we are picking out one unit another example is of carbon monoxide in air different studies have shown that if the concentration of carbon monoxide in air exceeds 35 ppm it becomes poisonous for us so when we're dealing with these very small concentration limits like in the case of pollutants ppm is a convenient measure of concentration to use on the other hand if we consider industrial usage so let's take an example that an industrial tank will be around 50 000 liters and the amounts of solute that is added to this solution can be in the order of tons so now in both of these cases where on one hand we're dealing with very dilute concentrations which are in ppm's and on the other hand we have extremely large quantities of weight by volume measurements using only one standard measure of concentration is difficult which is why we have so many different measures of concentration which conventionally come from the applications they are used in and coming back to our experiments that we do in the lab the gram per liter measure of a strength of a solution is a sensible scale to use for the amount of quantities that we work with in labs so now let's go back to the original comparison that we were making and let's see if we can find a relationship between molarity and strength of a solution so to get the relationship between molarity and strength of the solution let's start with the definition of molarity which is given by a number of moles of the solute divided by the volume of the solution in liters and we know that the number of moles of a substance is defined as its mass divided by its molar mass so we can plug this in here instead of the number of moles and we get the molarity to be equal to mass divided by the molar mass of solute into the volume of the solution but if we look at this expression we know that this quantity that is mass divided by volume of solution is what we defined as the strength of a solution so in that case we can write the molarity to be equal to the strength of the solution in gram per liter divided by the molar mass of the solute so now with this relation if we have the molar mass of the solute and the molarity we can calculate the strength of the solution and vice versa