Find the total number of atoms in a sample of cocaine hydrochloride, C 17 H 22 ClNO 4 , of mass 23.5 mg.

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

Ch.3 - Molecules, Compounds & Chemical Equations

All textbooks

Tro 4th Edition

Ch.3 - Molecules, Compounds & Chemical Equations

Problem 137

Chapter 3, Problem 137

Find the total number of atoms in a sample of cocaine hydrochloride, C₁₇H₂₂ClNO₄, of mass 23.5 mg.

Verified step by step guidance

Convert the mass of the cocaine hydrochloride from milligrams to grams. Remember that 1 mg equals 0.001 grams.

Calculate the molar mass of cocaine hydrochloride, C17H22ClNO4. Use the atomic masses of carbon (C), hydrogen (H), chlorine (Cl), nitrogen (N), and oxygen (O) from the periodic table to find the sum.

Use the molar mass to convert the mass of the cocaine hydrochloride sample from grams to moles. Use the formula: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass}} \).

Calculate the total number of molecules in the sample by using Avogadro's number, which is approximately \(6.022 \times 10^{23}\) molecules per mole. Multiply the number of moles by Avogadro's number.

Determine the total number of atoms in a molecule of cocaine hydrochloride. Since the formula is C17H22ClNO4, add up the atoms: 17 carbon atoms, 22 hydrogen atoms, 1 chlorine atom, 1 nitrogen atom, and 4 oxygen atoms. Multiply the total number of molecules by the total number of atoms per molecule to find the total number of atoms in the sample.

Verified Solution

Video duration:

This video solution was recommended by our tutors as helpful for the problem above.

Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molecular Formula

The molecular formula of a compound provides the types and numbers of atoms present in a molecule. For cocaine hydrochloride, C17H22ClNO4, the formula indicates it contains 17 carbon (C) atoms, 22 hydrogen (H) atoms, 1 chlorine (Cl) atom, 1 nitrogen (N) atom, and 4 oxygen (O) atoms. Understanding the molecular formula is essential for determining the total number of atoms in a given mass of the substance.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). To find the total number of atoms in a sample, one must first calculate the molar mass of cocaine hydrochloride by summing the atomic masses of all atoms in its molecular formula. This value allows for the conversion of the sample's mass into moles, which is crucial for further calculations.

Avogadro's Number

Avogadro's number, approximately 6.022 x 10^23, is the number of particles (atoms, molecules, etc.) in one mole of a substance. Once the number of moles of cocaine hydrochloride is determined from the sample's mass and its molar mass, Avogadro's number can be used to calculate the total number of individual atoms in the sample. This concept is fundamental in bridging the macroscopic and microscopic worlds in chemistry.