A can of diet soda contains 180 mg of the low-calorie sugar substitute aspartame (C14H18N2O5). How many molecules of aspartame are in the can of soda? (LO 3.4) (a) 3.7 * 10^23 (b) 3.7 * 10^20 (c) 3.2 * 10^25 (d) 1.2 * 10^22

Video transcript

welcome back everyone in this example, we're working with sink in in which is a naturally occurring alkaloid with anti malarial properties and we need to find the total number of atoms in our sink in in sample that has a mass of 51.6 mg. So our first step is to figure out our formula mass from our molecular formula given in the prompt of sinking in. And according to our prompt, we have the molecular formula C 19 H 22 N two. And then oh, Where we would recognize that we have the atoms carbon, hydrogen, nitrogen and oxygen. And according to our periodic tables, we would recall that carbon has a molar mass of 12.01 g per mole hydrogen. We would recall has a molar mass of 1.1 g per mole Nitrogen. We should recall has a molar mass of 14.01 g per mole from the periodic table. And then lastly oxygen on the periodic table has a molar mass of 16.0 g per mole. So we can use this information to calculate our formula formula mass. So to find the formula mass, We're going to take our number of atoms of each type of element. We have multiplied by its molar mass. So we would say that we have the sum of 1st 19 of our carbon atoms multiplied by the molar mass of 12.01 g per mole. This is then going to be added to our second quantity, which is our atoms of hydrogen Multiplied by their molar mass of 1.01 g per mole. And just to make more room. We're just going to move this a bit over so we'll just do this below here actually. So added onto this, we have our Two atoms of nitrogen multiplied by their molar mass of 14.01 g per mole. And then lastly added to this, we have for our one atom of oxygen. Well, we're just going to say oxygen here. Or rather we'll just plug in since it's just one unit. Its molar mass being 16.00 g per mole for oxygen. And so this would complete our some here. And what we would get for our formula mass is a value equal to 294.43 g per mole as our formula mass of our sink in. In based on its molecular formula. And the next step that we want to take is adding up our atoms in our formula. So our total atoms Would be equal to 19 plus 22 plus our two atoms of nitrogen and then plus r one atom of oxygen. And this is going to give us a total number of atoms equal to for total atoms. So now that we have our formula mass and our total atoms, we want to go ahead and recall from the prompt that they give us our mass of sinking in as 51.6 mg. But we want to convert from milligrams to grams. So we should recall that our prefix milli tells us that for one mg, which is our larger unit, that gives us 10 to the negative third power grams. And so now that we have this conversion factor laid out, we can go ahead and get into finding our total number of atoms in our sample. So beginning with the info from the prompt, we have our 51. milligrams which we're going to convert to grams. So we can just do that conversion here where we have milligrams, which we will multiply by our conversion factor above. Where we said for one mg, Graham's leaving us with Graham So far where we now want to cancel out grams by utilizing our formula mass from above. Where we would plug in our 294. g of our sinking in. For one mole of are sinking in. So now we can go ahead and show our cancelation of our gramps and now moving from moles of sinking in. We want to cancel out moles next and go into adam's of sinking in. So we have moles of sinking in. Well, just write its name out since it's easier to our moller atoms of sink in in in the Molecular formula that we calculated above. So we would see that for one mole of our sinking in. We counted a total of 44 mol atoms making up our molecular compound. So canceling out our units here, we're going to get rid of our moses sinking in. And now we want to cancel out mole atoms by multiplying by Our one mole of sinking in in the denominator. For our avocados number, which we should recall is 6.22 times 10 to the 23rd power atoms for one mole of sunken in. And so we can cancel out our moles of sinking in. And we're left with our atoms of just sinking in. Which we would get a final value for a quotient above equal to 4.6, 4 times 10 to the 21st power atoms of sinking in. And so for our final answer, we have this value here in units of atoms and this is going to correspond to choice a in our multiple choice as our final answer. So I hope that everything that I explained was clear. If you have any questions, please leave them down below. And I will see everyone in the next practice video