Calculate the concentration of glucose labelled …

10% w/w solution of glucose in water means that 10 g of glucose in present in 100 g of the solution i.e., 10 g of glucose is present in (100 - 10) g = 90 g of water.
Molar mass of glucose {tex}\left( {{C_6}{H_{12}}{O_6}} \right) = (6 \times 12 )+( 12 \times 1) +( 6 \times 16 )= 180{\rm{ }}g{\rm{ }}mo{l^{ - 1}}{/tex}
Then, number of moles of glucose = {tex}\frac{{10}}{{180}}mol{/tex}
= 0.056 mol
Molality of solution = {tex}\frac{{0.056\,mol}}{{0.09\,kg}}{/tex} = 0.62
Number of moles of water = {tex}\frac{{90\,g}}{{18\,g\,mo{l^{ - 1}}}}{/tex}
= 5 mol
Mole fraction of glucose {tex}({x_g}) = \frac{{0.056}}{{0.056 + 5}}{/tex}
= 0.011
And, mole fraction of water {tex}{x_w} = 1 - {x_g}{/tex}
= 1 - 0.011
= 0.989
If the density of the solution is {tex}1.2\,g\,m{l^{ - 1}}{/tex}, then the volume of the 100 g solution can be given as:
{tex} = \frac{{100\,g}}{{1.2\,g\,m{l^{ - 1}}}}{/tex}
= 83.33 mL
{tex} = 83.33 \times {10^{ - 3}}L{/tex}
{tex}\therefore {/tex} Molarity of the solution = {tex}\frac{{0.056\,mol}}{{83.33 \times {{10}^{ - 3}}L}}{/tex}
=0.67 M