Video: Completing a Set of Calculations and Identifying Which Does Not Yield Avogadro’s Number

Which of the following is not equal to Avogadro’s number? [A] The number of atoms in 4.48 L of CH₄ at STP. [B] The number of molecules in one mole of CO₂ [C] The number of Cl⁻ ions in 1 L of 1.0 M hydrochloric acid [D] The number of electrons with a combined charge of −96,500 coulombs [E] All of the other answers equal Avogadro’s number

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Video Transcript

Which of the following is not equal to Avogadro’s number? (A) The number of atoms in 4.48 liters of CH4 at STP. (B) The number of molecules in one mole of CO2. (C) The number of Cl− ions in one liter of 1.0-molar hydrochloric acid. (D) The number of electrons with a combined charge of negative 96,500 coulombs. (E) All of the other answers equal Avogadro’s number.

Avogadro’s number is equal to 6.022 times 10 to the 23. This number is equivalent to the number of entities that are in one mole of something. So, for example, one mole of molecules contains 6.022 times 10 to the 23 molecules. In this question, we need to figure out which answer choice is not equal to Avogadro’s number. And since Avogadro’s number is equivalent to the number of entities in one mole, we need to figure out which answer choice does not contain one mole.

So let’s take a look at our first answer choice, which is the number of atoms in 4.48 liters of CH4, or methane, at STP. STP stands for standard temperature and pressure, which is defined as zero degrees Celsius and one bar of pressure. To see if this answer choice contains one mole, we’re going to use the fact that at STP, all ideal gases have a molar volume equal to 22.4 liters per mole.

The molar volume is simply the volume that the gas occupies divided by the amount of gas particles in moles. We need to find the amount of CH4 particles that we have in 4.4 liters in moles, which we can do by dividing the volume that was given by the molar volume. So we’ll need to divide 4.48 liters by 22.4 liters per mole. This looks a little bit tricky, but 22.4 divided by 4.48 is equal to five. So we have one-fifth of a mole of methane molecules in 4.48 liters of methane.

Now, we need to figure out the number of atoms that are in this amount of methane. And as we can see from methane’s formula, for every one mole of methane molecules that we have, we would have one mole of carbon and four moles of hydrogen atoms. Which gives us a total of five moles of atoms for every one mole of methane molecules.

So now we just have to multiply one-fifth by five, which gives us one mole of atoms. So there’s one mole of atoms in 4.48 liters of CH4 at STP, which means that answer choice (A) is equal to an Avogadro’s number of atoms. So answer choice (A) does contain a mole. So it’s not the answer choice we’re looking for.

Our next answer choice is the number of molecules in one mole of CO2, or carbon dioxide. We don’t have to do any math for this answer choice, since one mole is an Avogadro’s number of molecules. So we would have one mole of carbon dioxide molecules. So answer choice (B) is equal to an Avogadro’s number.

Our next answer choice is the number of Cl− ions in one liter of 1.0-molar hydrochloric acid solution, which has the chemical formula HCl. When we have a solution of hydrochloric acid, it will disassociate into H+ ions and Cl− ions. Since molarity is defined as the amount of the substance in moles per liter of solution, we can find the amount of HCl that we have in moles by multiplying the concentration by the volume. So we have one mole of HCl in the solution.

As we can see from the stochiometric coefficients in our balanced chemical equation, every one mole of HCl will dissociate into one mole of Cl− ions. So since we have one mole of HCl, we’re going to end up with one mole of Cl− ions in the solution. So there’s one mole of Cl− ions in one liter of a 1.0-molar hydrochloric acid solution. Since we have a mole of Cl− ions, that means we have an Avogadro’s number. So this isn’t the correct answer choice either.

So, that just leaves us with our final answer choice, which is the number of electrons with a combined charge of negative 96,500 coulombs. To think about this statement, we’ll use Faraday’s constant, which tells us the magnitude of electric charge per mole of electrons. And it’s equal to 96,485 coulombs per mole.

Faraday’s constant tells us the magnitude of electric charge, which is why the constant is a positive value even though the electron has a negative charge. As we can see, this number is approximately equal to the negative 96,500 coulombs that we have in statement (D). Which means that the number of electrons that have a combined charge of negative 96,500 coulombs must be approximately one mole of electrons, which again is equal to an Avogadro’s number. So this statement is not the correct answer choice either.

Since all of the statements had one mole of particles, which means they were all equal to an Avogadro’s number, that means answer choice (E) must be the correct answer.

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