Question

In 0.1 mole fraction glucose solution find % (w/w) of water in the sample (in nearest integer)​

Answer 1

Answer :

Mole fraction of glucose = 0.1

We have to find %(w/w) of water in the solution$.$

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$\circ\sf\:X_{Glucose}+X_{Water}=1$

$\circ\sf\:X_{Water}=1-0.1$

$\circ\bf\:X_{Water}=0.9$

Therefore,

• Moles of Water = 0.9
• Moles of Glucose = 0.1

፨ Molar mass of Gulcose = 180g/mol

፨ Molar mass of water = 18g/mol

◈ Mass of water in solution :

• w₁ = moles × molar mass
• w₁ = 0.9 × 18
• w₁ = 16.2 g

◈ Mass of glucose in solution :

• w₂ = moles × molar mass
• w₂ = 0.1 × 180
• w₂ = 18 g

◈ %(w/w) of water :

➝ %(w/w) = w₁ / (w₁ + w₂) × 100

➝ %(w/w) = 16.2/(16.2+18) × 100

➝ %(w/w) = 1620/34.2

➝ %(w/w) = 47.36%

Answer 2

Answer:

$\bigstar \purple{\boxed{\mathtt{\% \dfrac{w}{w} =47.36}}}$

Solution :

As per the given question ,

$\rightarrow \mathtt{X_g = 0.1 \: mole }$

we know that ,

$\rightarrow \mathtt{X_g + X_w = 1}$

$\rightarrow \mathtt{0.1 + X_w = 1}$

$\rightarrow \mathtt{ X_w = 1 - 0.1}$

$\rightarrow \mathtt{ X_w =0.9}$

___________________

moles of glucose = 0.1 moles

moles of water = 0.9 moles

we know that ,

$\star \boxed { \mathtt{n = \dfrac{w}{mol.wt} }}$

here ,

• n = moles
• w = weight
• mol.wt = molecular weight _g

______________

Glucose :

$\implies \mathtt{n_g = \dfrac{w_g}{mol.wt_g} }$

here ,

• ng = moles of glucose=0.1
• mol weight of glucose = 180 g

$\implies \mathtt{w_g = 0.1 \times 180}$

$\implies \mathtt{w_g = 18 \: g }$

______________

Water :

$\implies \mathtt{n_w= \dfrac{w_w}{mol.wt_w} }$

here ,

• ng = moles of glucose=0.9
• mol weight of glucose = 18 g

$\implies \mathtt{w_g = 0.9 \times 18}$

$\implies \mathtt{w_g = 16.2 \: g}$

______________

we need to find % w / w of water in the sample

we know that ,

$\star \boxed { \mathtt{\% \dfrac{w}{w} = \dfrac{w_w}{w_g + w_w} \times 100 }}$

$\implies\mathtt{\% \dfrac{w}{w} = \dfrac{16.2}{18+ 16.2} \times 100 }$

$\implies\mathtt{\% \dfrac{w}{w} = \dfrac{16.2}{34.2} \times 100 }$

$\implies\mathtt{\% \dfrac{w}{w} =0.4736 \times 100}$

$\implies \red{\boxed{\mathtt{\% \dfrac{w}{w} =47.36}}}$