Question

A glass of juice contains  $ {{9 gm}} $  of glucose. How many atoms of each kind are there in the glass of juice?

Answer 1

Hint: We know one mole of any compound or element contain  $ {{6}}{{.02 \times 1}}{{{0}}^{{{23}}}} $  molecules or atoms respectively. So we calculate the number of moles present in  $ {{9 g}} $  of glucose and find out the number of atoms present in the total weight of the glucose.

Complete answer:

Glucose molecule formula -  $ {{{C}}_{{6}}}{{H}}{ _{{{12}}}}{{{O}}_{{6}}} $ 

Molar mass of carbon =  $ {{12}}{{.01 g/mol}} $ 

Molar mass of hydrogen =  $ {{1}}{{.008 g/mol}} $ 

Molar mass of oxygen =  $ {{16}}{{.0 g/mol}} $ 

 $ {{Molecular mass of glucose = 6(12}}{{.01) + 12(1}}{{.008) + 6(16}}{{.0)}} $ 

 $  = 72.06 + 12.096 + 96 $ 

 $ {{ = 180}}{{.156 g/mol }} \approx {{180 g/mol}} $ 

One mole of glucose contains  $ 6.02 \times {10^{23}} $ atoms.

Molecular mass of  $ {{{C}}_{{6}}}{{{H}}_{{{12}}}}{{{O}}_{{6}}}{{ = 180 g/mol}} $ 

 $ {{9 g}} $  of  $ {{{C}}_{{6}}}{{{H}}_{{{12}}}}{{{O}}_{{6}}} $ =?

 $ {{Number of molecules in 9g of }}{{{C}}_{{6}}}{{{H}}_{{{12}}}}{{{O}}_{{6}}}{{ = }}\dfrac{{{{9 \times 6}}{{.023 \times 1}}{{{0}}^{{{23}}}}}}{{{{180}}}}{{ = 3}}{{.01 \times 1}}{{{0}}^{{{22}}}}{{ molecules}} $ 

Let’s calculate the number of each atom in nine grams of glucose.

Carbon atoms:

 $ {{Number\; of\; carbon\; atoms \; in \; 9g \; of\; glucose = 6 \times 3}}{{.01 \times 1}}{{{0}}^{{{22 }}}}{{ = 18}}{{.06 \times 1}}{{{0}}^{{{22}}}} $ 

Hence,  $ {{18}}{{.06 \times 1}}{{{0}}^{{{22}}}} $  of carbon atoms present in the  $ {{9g}} $  of glucose.

Oxygen atoms:

 $ {{Number\; of \; oxygen\; atoms\; in \; 9g \; of \; glucose = 6 \times 3}}{{.01 \times 1}}{{{0}}^{{{22 }}}}{{ = 18}}{{.06 \times 1}}{{{0}}^{{{22}}}} $ 

Hence,  $ {{18}}{{.06 \times 1}}{{{0}}^{{{22}}}} $  of oxygen atoms present in the  $ {{9g}} $  of glucose.

Hydrogen atoms:

 $ {{Number\; of\; hydrogen\; atoms \; in \; 9g \; of \; glucose = 12 \times 3}}{{.01 \times 1}}{{{0}}^{{{22 }}}}{{ = 36}}{{.12 \times 1}}{{{0}}^{{{22}}}} $ 

Hence,  $ {{36}}{{.12 \times 1}}{{{0}}^{{{22}}}} $  of hydrogen atoms present in the  $ {{9g}} $  of glucose.

Additional Information:

Moles are the number of molecular mass units present in a particular weight of that compound.

in chemistry it is very less likely we deal with single atom or single molecule so the concept of mole is very important and we can easily relate moles with atoms or molecules by formula that  $ {{1 mole}} $  contain Avogadro number of molecule i.e.  $ {{6}}{{.02 \times 1}}{{{0}}^{{{23}}}}{{ atoms}} $ .

The Avogadro value is a constant value for every element and compound. Avogadro number informs us about the number of molecules or atoms or electrons present in the bulk of the solution.

Note: We should pay special attention to the units of the molar masses used. The most frequently used unit s g/mol which is also the standard value and gives an exact answer in the standard unit system. We should avoid using values of unit kg/mol or a.m.u.