b. 50 cm³ of gasoline are mixed with 50 cm³ of water. What is the average density of the mixture?

Video transcript

Hi everyone. In this practice problem, we're being asked to calculate the mean density of the mixture. We will have equal volumes free of ethanol with row of 789 kg per meter cube and cooking oil with row of 915 kg per meter cube. Both are accidentally mixed. We're being asked to calculate the mean density of the mixture. And the options given are a at 152 kg per meter cube. B 100 and 26 kg per meter cube. C 726 kg per meter cube and D 426 kg per meter cube. So deme density which is the average density is going to be found from the um mass to which will be equal to the mass of ethanol, which I will denote with the subscript of E and mass of cooking oil with the subscript of C. So the mass of ethanol can be calculated by multiplying row of ethanol with the volume of ethanol row E multiplied by ve and um concurrently, the ma uh mass of the cooking oil can be calculated by multiplying row of cooking oil row C with the volume of cooking oil, VZ PC. So now the row mean or the mean density of the mixture can be calculated by taking row eve plus row CV C or essentially what we're looking at is the total mass divided by the total volume. So the total mass from our equation earlier is row E ce plus row CV C and divide it with a total volume, which is going to be the volume of ethanol plus the volume of cooking oil. So we know from the problem statement that they both have equal volume, which is going to be V. So let's uh substitute that with within our expression here. So we'll get row E multiplied by V plus row C multiplied by V divide that with fe plus P. So simply find out we will have row E plus row C in parentheses multiplied by V, divide it with two fees to P and we can cross out the P so that we have the equation for row mean which is just going to be row E plus row C divided by two. So let's substitute the values that we have. Row of ethanol is 789 kg per meter cube plus row of cooking oil is kg per meter cube and divide that with two and we will have the mean density of the mixture to then be equal to kg. Per meter cube. So there we have the final answer for this practice problem which will correspond to option a with the mean density of the mixture being 852 kg per meter cube. So answer A will be the answer to this particular practice problem and that'll be it for this video. If you guys still have any sort of confusion, please feel free to check out our other la videos on similar topics available on our website. But other than that, that will be it for this one and thank you so much for watching. Bye bye.