Question

Calculate the mole fraction of ethanol in solution prepared by dissolving 46 g of ethanol in 90 g of water. [Molar mass of ethanol = 46 u] ​

Answer 1

Answer:

• Mole fraction of ethanol is 0.167

Given:

1. Mass of ethanol dissolved = 46 g
2. Mass of water = 90 g

Explanation:

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Let's find the moles of ethanol and water.

Ethanol:

We know,

$\bigstar\;\underline{\boxed{\sf n_{1}=\dfrac{W_{1}}{M_{1}}}}$

Here,

• n₁ Denotes moles.
• W₁ Denotes dissolved mass.
• M₁ Denotes molecular mass.

Substituting the values,

$\longrightarrow\sf n_{1}=\dfrac{46}{46}\\\\\\\longrightarrow\sf n_{1}=1\\\\\\\longrightarrow\underline{\underline{n_{1}=1\;mole}}$

Water:

We know,

$\bigstar\;\underline{\boxed{\sf n_{2}=\dfrac{W_{2}}{M_{2}}}}$

Here,

• n₂ Denotes moles.
• W₂ Denotes mass of water present.
• M₂ Denotes molecular mass.

Substituting the values,

$\longrightarrow\sf n_{2}=\dfrac{90}{18}\\\\\\\longrightarrow\sf n_{2}=5\\\\\\\longrightarrow\underline{\underline{n_{2}=5\;mole}}$

∴ We got moles of Ethanol & Water respectively.

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Now, lets find the mole fraction of ethanol.

$\bigstar\;\underline{\boxed{\sf \chi =\dfrac{n_{1}}{n_{1}+n_{2}}}}$

Here,

• X Denotes Mole fraction.
• n₁ Denotes moles of ethanol.
• n₂ Denotes moles of Water.

Substituting the values,

$\longrightarrow\sf \chi=\dfrac{1}{1+5}\\\\\\\longrightarrow\sf \chi=\dfrac{1}{6}\\\\\\\longrightarrow\sf \chi=0.167\\\\\\\longrightarrow \large{\underline{\boxed{\red{\sf \chi=0.167}}}}$

∴ Mole fraction of ethanol is 0.167 .

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