The mole fraction of glucose in 0.15 M solution (density= 1.10 g mL-1 ) is

# The mole fraction of glucose in 0.15 M solution (density= 1.10 g mL-1 ) is

1. A

2.40 x 10-3

2. B

2.0 x 10-3

3. C

2.82 x 10-3

4. D

2.40 X 10-2

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### Solution:

Let we have

Amount of glucose, n2 = 0.15 mol;   Volume of solution, V = 1000 mL

Mass of glucose, m2 = n2M2 = (0.15 mol) (180 g mol -1) = 27.0 g.

Mass of solution, m = V$\rho$ = (1000 mL) (1.10 g mL-1 ) = 1100 g

Mass of water, m1 = m1 - m2 = 1100 g - 27 g = 1073 g

Amount of water, ${n}_{1}=\frac{{m}_{1}}{{M}_{1}}=\frac{10/3\mathrm{g}}{18\mathrm{g}{\mathrm{mol}}^{-1}}=59.61\mathrm{mol}$

Mole fraction of glucose, ${x}_{2}=\frac{{n}_{2}}{{n}_{1}+{n}_{2}}=\frac{0.15\mathrm{mol}}{\left(59.61+0.15\right)\mathrm{mol}}=0.002$

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