Math

QuestionFind the number of boron atoms in 2.24 moles of BCl₃ and chlorine moles in 4.61×10224.61 \times 10^{22} BCl₃ molecules.

Studdy Solution

STEP 1

Assumptions1. The molecular formula of boron trichloride is BCl3, which means each molecule of boron trichloride contains one atom of boron and three atoms of chlorine. . Avogadro's number is 6.022×10236.022 \times10^{23}, which is the number of atoms in one mole.

STEP 2

First, we need to find the number of atoms of boron in2.24 moles of boron trichloride. We can do this by multiplying the number of moles by Avogadro's number.
Atomsofboron=NumberofmolestimesAvogadrosnumberAtoms\, of\, boron = Number\, of\, moles \\times Avogadro's\, number

STEP 3

Now, plug in the given values for the number of moles and Avogadro's number to calculate the atoms of boron.
Atomsofboron=2.24times6.022×1023Atoms\, of\, boron =2.24 \\times6.022 \times10^{23}

STEP 4

Calculate the atoms of boron.
Atomsofboron=2.24times6.022×1023=1.348928×1024Atoms\, of\, boron =2.24 \\times6.022 \times10^{23} =1.348928 \times10^{24}

STEP 5

Now, we need to find the number of moles of chlorine in 4.61×10224.61 \times10^{22} molecules of boron trichloride. We can do this by dividing the number of molecules by Avogadro's number and then multiplying by the number of atoms of chlorine in one molecule of boron trichloride (which is3).
Molesofchlorine=(Numberofmolecules/Avogadrosnumber)timesNumberofchlorineatomsinonemoleculeMoles\, of\, chlorine = (Number\, of\, molecules / Avogadro's\, number) \\times Number\, of\, chlorine\, atoms\, in\, one\, molecule

STEP 6

Now, plug in the given values for the number of molecules, Avogadro's number, and the number of chlorine atoms in one molecule to calculate the moles of chlorine.
Molesofchlorine=(4.61×1022/6.022×1023)times3Moles\, of\, chlorine = (4.61 \times10^{22} /6.022 \times10^{23}) \\times3

STEP 7

Calculate the moles of chlorine.
Molesofchlorine=(4.61×1022/6.022×1023)times3=2.294molesMoles\, of\, chlorine = (4.61 \times10^{22} /6.022 \times10^{23}) \\times3 =2.294 \,molesa. There are 1.348928×10241.348928 \times10^{24} atoms of boron in2.24 moles of boron trichloride. b. There are2.294 moles of chlorine in 4.61×10224.61 \times10^{22} molecules of boron trichloride.

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