If the density of water is 1.00 g/mL and the density of mercury is 13.6 g/mL, how high a column of water in meters can be supported by standard atmospheric pressure? By 1 bar?

Video transcript

Hi everyone. This problem reads the density of mercury is 13.534 g per cubic centimeter. While that of glycerol is 1.261 g per cubic centimeter, calculate the height and meters of a column of glycerol in a barometer at standard atmospheric pressure. So, our goal here is to calculate the height in meters of a column of glycerol. Ok, So there's an equation that we're going to need to know in order to solve this. And it's that the pressure exerted by a liquid is equal to density times gravity times height. And we want to calculate the height. So what that means is we need to rearrange this equation that we're so that we're solving for height. So we'll go ahead and divide both sides by density times gravity. So we get height is equal to pressure over density times gravity. Okay. And we're told that it is at standard atmospheric pressure. Okay, So let's recall that one atmosphere is equal to 101, pascal's and this is equal to 101, kg over meters times seconds squared. Ok. And let's recall that gravity is equal to 9.81 meters per second squared. Alright, so, for glycerol, we know that height is going to equal pressure over density times gravity. So let's go ahead and plug in what we know we know that the pressure. We're going to write down the one that's in the units of kilograms over meters times seconds squared. So we have 100 and kg over meters times seconds squared. Okay. And this is going to be divided by density times gravity. So our density is given in the problem. It is 1.261 g per cubic centimeter. But that is not the correct units that we need. So we need to convert this. So we have 1.261 g per cubic centimeter. And what we want to do here is we want to go from grams per cubic centimeter two kg per cubic meter because it's asking us for the height and meters and we need our units to match. Right now. We're in grams and we need it in kilograms because our pressure is in kilograms. And we also need it in meters. So we need to convert this. So let's go ahead and do that. So we have 1.261 g per cubic centimeter. So we first want to go from grams to kilograms. So we know that in one kg there is 1000 g. Okay, so our units of grams cancel. And now we're in units of kilograms. Next we want to go from kilograms Or excuse me, We want to go from cubic centimeter to cubic meter. Okay, So in one cc There is 10 to the - m3. Okay, So cubic centimeters cancel. And we're left with cubic meters. And these are the units that we want We want kilograms per cubic meter. That was our road map that we're following to get. So now let's go ahead and do the calculation. When we do the calculation, we get 1261 kg per cubic meter. So let's go ahead and plug that in for our density. So we have 1261 kilograms per cubic meter. And gravity we said, is 9.81 m/s squared. So now we have everything plugged in for our height. So now we just need to do the calculation. So once we do the calculation, we get height is equal to 8. m and this is going to be the final answer. This is the height of a column of glycerol and a barometer at standard atmospheric pressure. That is it for this problem? I hope this was helpful