In 2014, a major chemical leak at a facility in West Virginia released 28,390 L of MCHM (4-methylcyclohexylmethanol, C8H16O) into the Elk River. The density of MCHM is 0.9074 g/mL. (a) Calculate the initial molarity of MCHM in the river, assuming that the first part of the river is 2.00 m deep, 90.0 m wide, and 90.0 m long.

Video transcript

Hey everyone, we're told that a chemical spill happened on a lake near a herbicide factory. It was discovered that 15,634 liters of Atrazine contaminated the lake through a broken pipeline, calculate the polarity of Atrazine in the lake. If the density of Atrazine is 1.187 g per cubic centimeters And the lake has a diameter of three km and an average depth of 10 m. To answer this question, we first need to calculate the volume of a lake and we're going to think of this as if it were a cylinder. So our volume is going to be equal to pI times r radius square times our height. Looking at the values they've given us, They told us we had a diameter of 3.00 km. So this means our radius must be equal to 1. km And we want to convert this into meters. So we know that one km contains 10 to the 3rd m. So this gives us a radius of 1500 m. And for our height we're going to use our debt. So that's going to be 10 m. So, plugging in our values, we have a volume that is equal to pI times r squared, which was 1500 m squared Times 10 m. This gets us to a value of 70,650, cubic meters. And to convert this into leaders, we're going to use dimensional analysis. Now we know that 10 to the negative one m Is equivalent to one decimate er And since we're in cubic meters we need to cube each of these values. And lastly we know that one cubic decimate er is equivalent to one leader. So when we calculate this out, we end up with a volume Of 7.06, 5 times 10 to the 10 leaders. Now let's go ahead and calculate the moles of Atrazine. Taking our density of 1.187 g over cubic cm. We're first going to use dimensional analysis to get two g to get to our molar mass and then finally to our moles. So we know that we have 10 cm per one decimate er and since we are in cubic centimeters we need to cube each of these values. And again we know that one cubic desi meter is equivalent to one leader And we're going to multiply this by our 15,634 L. So when we calculate this out, We end up with a mass of 1.856 times 10 to the seven g. So taking our mass of 1.856 times 10 to the seven g, we can calculate the molar mass of Atrazine and we find it to be 215.72 g per one mole And this will get us to 86,037.46 mol. Now to calculate our polarity, taking that value of 86,037 0. mol and dividing that by our leaders, which we calculated to be 7.65 times 10 to the 10 leaders. We end up with a polarity of 1.218 times 10 to the negative six Mohler. And this is going to be our final answer. Now, I hope that made sense and let us know if you have any questions.