Question

A solution is prepared by adding 124 g of ethylene glycol (molar mass = 62 g mol\(^{-1}\)) to \( x \) g of water to get a 10 m solution. What is the value of \( x \) (in g)?

• A. 100
• B. 400
• C. 800
• D. 200

Hint:

Molality (m) is defined as moles of solute per kg of solvent: \( m = \frac{n_{\text{solute}}}{\text{mass}_{\text{solvent (kg)}}} \). Be careful to convert grams to kilograms in denominator!

Answer 1

The Correct Option is D

Step 1: Understand the given data

• Mass of solute (ethylene glycol) = 124 g
• Molar mass of ethylene glycol = 62 g/mol
• Molality (\( m \)) = 10 m
• Mass of solvent (water) = \( x \) g

Step 2: Use molality formula

\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \Rightarrow 10 = \frac{124/62}{x/1000} \]

Step 3: Solve for \( x \)

\[ 10 = \frac{2}{x/1000} \Rightarrow 10 = \frac{2000}{x} \Rightarrow x = 200 \text{ g} \]

Final Answer:

200 g