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QuestionFind the mass of glucose (C6H12O6)\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right) in grams with 1.00×10121.00 \times 10^{12} hydrogen atoms. Round to 3 sig. figs.

Studdy Solution

STEP 1

Assumptions1. The molecular formula of glucose is C6H126\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{}_{6}, which means each molecule of glucose contains6 carbon atoms,12 hydrogen atoms, and6 oxygen atoms. . The number of hydrogen atoms we are interested in is 1.00×10121.00 \times10^{12}.
3. The atomic mass of hydrogen (H) is approximately1 g/mol.
4. Avogadro's number is 6.022×10236.022 \times10^{23} atoms/mol, which is the number of atoms in one mole of a substance.

STEP 2

First, we need to find the number of moles of hydrogen atoms in 1.00×10121.00 \times10^{12} atoms. We can do this by dividing the number of atoms by Avogadro's number.
Moles of H atoms=Number of H atomsAvogadro’s number\text{Moles of H atoms} = \frac{\text{Number of H atoms}}{\text{Avogadro's number}}

STEP 3

Now, plug in the given values to calculate the moles of hydrogen atoms.
Moles of H atoms=1.00×10126.022×1023\text{Moles of H atoms} = \frac{1.00 \times10^{12}}{6.022 \times10^{23}}

STEP 4

Calculate the moles of hydrogen atoms.
Moles of H atoms=1.00×10126.022×1023≈1.66×10−12 mol\text{Moles of H atoms} = \frac{1.00 \times10^{12}}{6.022 \times10^{23}} \approx1.66 \times10^{-12} \, \text{mol}

STEP 5

Now that we have the moles of hydrogen atoms, we can find the moles of glucose molecules that contain this many hydrogen atoms. Since one molecule of glucose contains12 hydrogen atoms, we divide the moles of hydrogen atoms by12.
Moles of glucose=Moles of H atoms12\text{Moles of glucose} = \frac{\text{Moles of H atoms}}{12}

STEP 6

Plug in the values to calculate the moles of glucose.
Moles of glucose=1.66×10−12 mol12\text{Moles of glucose} = \frac{1.66 \times10^{-12} \, \text{mol}}{12}

STEP 7

Calculate the moles of glucose.
Moles of glucose=1.66×10−12 mol12≈1.38×10−14 mol\text{Moles of glucose} = \frac{1.66 \times10^{-12} \, \text{mol}}{12} \approx1.38 \times10^{-14} \, \text{mol}

STEP 8

Now that we have the moles of glucose, we can find the mass of glucose. The molar mass of glucose is approximately180 g/mol, so we multiply the moles of glucose by the molar mass.
Mass of glucose=Moles of glucose×Molar mass of glucose\text{Mass of glucose} = \text{Moles of glucose} \times \text{Molar mass of glucose}

STEP 9

Plug in the values to calculate the mass of glucose.
Mass of glucose=.38×−14 mol×180 g/mol\text{Mass of glucose} =.38 \times^{-14} \, \text{mol} \times180 \, \text{g/mol}

STEP 10

Calculate the mass of glucose.
Mass of glucose=.38×10−14 mol×180 g/mol≈2.48×10−12 g\text{Mass of glucose} =.38 \times10^{-14} \, \text{mol} \times180 \, \text{g/mol} \approx2.48 \times10^{-12} \, \text{g}The mass of glucose that contains a trillion hydrogen atoms is approximately 2.48×10−122.48 \times10^{-12} g.

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