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QuestionAn oxygen atom weighs 2.66×10−23 g2.66 \times 10^{-23} \mathrm{~g}; a glass of water weighs 0.050 kg0.050 \mathrm{~kg}.
1. Find the mass of 1 mole of oxygen atoms: □g\square \mathrm{g}.
2. How many moles of oxygen equal the mass of water? □\square.

Studdy Solution

STEP 1

Assumptions1. The mass of an oxygen atom is .66×10−23 g.66 \times10^{-23} \mathrm{~g} . The mass of a glass of water is 0.050 kg0.050 \mathrm{~kg} 3.1 mole of any element contains 6.022×10236.022 \times10^{23} atoms (Avogadro's number)
4. The mass of the glass of water needs to be converted from kilograms to grams before comparing it to the mass of the oxygen atoms

STEP 2

First, we need to find the mass of1 mole of oxygen atoms. We can do this by multiplying the mass of a single oxygen atom by Avogadro's number.
Massmole=Massatom×Avogadro′s numberMass_{mole} = Mass_{atom} \times Avogadro's\, number

STEP 3

Now, plug in the given values for the mass of an oxygen atom and Avogadro's number to calculate the mass of1 mole of oxygen atoms.
Massmole=2.66×10−23 g×6.022×1023Mass_{mole} =2.66 \times10^{-23} \mathrm{~g} \times6.022 \times10^{23}

STEP 4

Calculate the mass of1 mole of oxygen atoms.
Massmole=2.66×10−23 g×6.022×1023=16.0 gMass_{mole} =2.66 \times10^{-23} \mathrm{~g} \times6.022 \times10^{23} =16.0 \mathrm{~g}

STEP 5

Now, we need to convert the mass of the glass of water from kilograms to grams.
Masswater=0.050 kg×1000 g/kgMass_{water} =0.050 \mathrm{~kg} \times1000 \mathrm{~g/kg}

STEP 6

Calculate the mass of the glass of water in grams.
Masswater=0.050 kg×1000 g/kg=50.0 gMass_{water} =0.050 \mathrm{~kg} \times1000 \mathrm{~g/kg} =50.0 \mathrm{~g}

STEP 7

Now, we can find the number of moles of oxygen atoms that have a mass equal to the mass of a glass of water. We can do this by dividing the mass of the glass of water by the mass of1 mole of oxygen atoms.
Molesoxygen=Masswater/MassmoleMoles_{oxygen} = Mass_{water} / Mass_{mole}

STEP 8

Plug in the values for the mass of the glass of water and the mass of1 mole of oxygen atoms to calculate the number of moles.
Molesoxygen=50.0 g/16.0 gMoles_{oxygen} =50.0 \mathrm{~g} /16.0 \mathrm{~g}

STEP 9

Calculate the number of moles of oxygen atoms that have a mass equal to the mass of a glass of water.
Molesoxygen=50. g/16. g=3.125Moles_{oxygen} =50. \mathrm{~g} /16. \mathrm{~g} =3.125The mass of mole of oxygen atoms is16. g and there are3.125 moles of oxygen atoms in a glass of water.

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