What is the total charge of all the electrons in 1.0 L of liquid water?

Video transcript

Hi, everyone. Let's take a look at this practice problem dealing with the electrical charge. This problem says if you have a container with 3 L of water at room temperature and atmospheric pressure, what would be the total electrical charge of electrons in the water? We're also given that the molar mass of water is 18.015 g per mole. We're given four possible choices as our answers A is negative 1.6 multiplied by 10 to the negative 19 columns. Choice B is negative 1.6 multiplied by 10 to the eight columns. Point C is 1.6 multiplied by 10 to the negative 19 columns. And choice D 1.6 multiplied by 10 to the eight columns. Now, in order to figure out the total electrical charge in the water, I need to figure out the number of electrons that I have in the water since the charge of the electron is quantized. In order to figure that out, I need to figure out the number of molecules that I have in the water. And to find that I could use that uh molar mass of water that was given to the problem. But I first need to figure out the mass of the water that I was given. So let's start there. So I need to figure out the mass of the water. But the only thing that I was given is the volume of water. So volume and uh mass are related through density. So we're gonna start there. Recall your definition of density. We have row is equal to M divided by V or row is gonna be the density M is the mass and V is the volume. I'm gonna solve this for M. So I have M as equal to row V and I was given the volume and I know the density of water it's constant. So I can solve this for our mass. We have M is equal to the density of water. I'm gonna want to use um the one that has grams and milliliters. So that is 1 g per milliliter and that gets multiplied by the volume which is 3 L. But I'll convert that into milliliters. I need to multiply by the conversion factor of 1000, no leaders divided by 1 L. This gives me a mass equal to 3000 grams. And the reason why I wanted to use grams is because that's the um mass unit in my molar mass. So now that I have the mass, I can calculate the number of moles of water that I actually have that will use our definition of molar mass to recall that the molar mass capital M is equal to little M divided by N where little M is the mass and N is the number of moles. So if I solve this for the number of moles I'll have N is equal to little M divided by capital M. And I can plug in values for both of those, we have little N is equal to, for the mass will have the 3000 g that gets divided by the molar mass, which is the 18.015 g per mole. And this gives me uh value for N equal to 166.5 moles. But now I have the number of moles. I need to figure out the number of molecules of water that I have. So recall to convert moles into a number, we have capital N which is gonna be the number of molecules of water. We have gonna be equal to Avogadro's number in a multiplied by the number of moles which is little N. So I can plug in values I have capital N equal to here, I have Avogadro's number which is 6.022 multiplied by 10 to the 23 that is molecules thermo then multiply that by N which is the number of moles, which is 100 and 66.5 moles. So this gives me an end value equal to 1.00 multiplied by 10 to the 26 molecules. If I don't have the number of molecules, I can calculate the total charge to recall that charge. Here, in this case, with electrons is quantized my total charge you gonna be equal to the number of electrons multiplied by the charge of the electron. Now, here I have the number of molecules of water and each water molecule has 10 electrons. So the 10 electrons eight come from the oxygen atom and one from each of the hydrogen. So the total number of electrons I'll have will be just 10 multiplied by the number of water water molecules which is N and we need to multiply that by the charging the electron which is E so you can plug in values of Q is equal to 10, multiplied by the 1.00 multiplied by 10 to the 26. And that gets multiplied by the charge electron which is a negative 1.602 multiplied by 10 to the negative 19 coulombs. So when we multiply those together we get Q is equal to a negative 1.6 multiplied by 10 to the eight kos. And that corresponds with answer B so quick little recap of what we did. Here, we started off by using our definition of the density to calculate the mass of the water. And once we have the mass of water, we use the molar mass of water to calculate the number of moles and then we use a goos numbers and the number of moles to calculate the number of water molecules. And once we had the number of water molecules, we noticed that we had 10 electrons per water molecule. And so we just multiplied the number of electrons why they charge you the electron to get the total charge of the electrons. So I hope that this has been useful and I'll see you in the next video.