The molecular mass of water (H₂O) is 18 u. How many protons are there in 1.0 L of liquid water?

Video transcript

Hey, everyone. So this problem is dealing with mold. Let's see what it's asking us. A chemist is studying a sample of liquid ethanol with the given chemical formula C two H H. And they tell us it has a molecular mass of 46 U. If the chemist has a 1.4 liter sample of this ethanol, how many protons are present within this given volume? Our multiple choice answers here are a 4.53 times 10 to the 24 B 4.41 times 10 to the 26 C 3.76 times 10 to the 26 or D 3.21 times 10 to the 24. So the first step here is looking at the chemical formula for liquid ethanol and determining how many protons we have for a molecule. So C two H five O H so C carbon has six protons per atom and we have two carbons. So that gives us for hydrogen, it has one proton per atom, six hydrogen atoms here give us six and oxygen has eight protons per atom, one oxygen adam here. And so we have eight. So when we sum this, we get 26 so that's 26 protons per molecule. So the next step is to find out how many molecules we have in this volume. And then we can multiply that by 26 to find our final answer. So we can recall that the number of molecules N is given by the equation N A or avocados, Avogadro's number multiplied by um the mass that we are working with divided by upper case M or our molar MS. We can further expand this mass term and recall that mass is equal to density multiplied by volume. And the equation becomes N A row V divided by M. And from here, we have everything we need to plug in to this equation. Avocado number is a constant. You can recall is 6.2 times to the 23. And that's units per mole multiplied by the density of ethanol is a constant 0.789 kg per liter multiplied by our volume, which was given in the problem as 1.4 liters. We divide all of that by our molar mass and a molecular mass of 46 U is 0.46 kg per mole. When we plug that into our equation, we get number of molecules of ethanol in this 1.4 liter volume of 1.45 times 10 to the 25. And then our last step is multiplying that by 26 protons per molecule and we get 3.76 times 10 to the 26 protons. And so that is the final answer for this problem and it aligns with answer choice C so that's all we have for this one. We'll see you in the next video.