1. Given data

• Mass of water $= 900\,\text{g}$
• Mole fraction of urea $= 0.05$
• Density of solution $= 1.2\,\text{g cm}^{-3}$
• Molar mass of water $= 18\,\text{g mol}^{-1}$
• Molar mass of urea $= 60\,\text{g mol}^{-1}$

We need to find the molarity of the urea solution.

2. Calculate moles of water

$n_{\text{water}} = \frac{900}{18} = 50\,\text{mol}$

3. Use mole fraction relation

Let moles of urea be $n$.

Given:

$X_{\text{urea}} = \frac{n}{n+50} = 0.05$

Now solve:

$n = 0.05(n+50)$

$n = 0.05n + 2.5$

$0.95n = 2.5$

$n = \frac{2.5}{0.95} = 2.6316\,\text{mol}$

4. Calculate mass of urea

$m_{\text{urea}} = 2.6316 \times 60 = 157.896\,\text{g}$

5. Calculate total mass of solution

$m_{\text{solution}} = 900 + 157.896 = 1057.896\,\text{g}$

6. Calculate volume of solution using density

$\text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{1057.896}{1.2} = 881.58\,\text{cm}^3$

Convert to liters:

$V = 0.88158\,\text{L}$

7. Calculate molarity

$M = \frac{\text{moles of urea}}{\text{volume in liters}} = \frac{2.6316}{0.88158}$

$M \approx 2.985\,\text{mol L}^{-1}$

So, the molarity is

$\boxed{2.98}$

8. Comparison with stored answer

Stored correct answer: $2.98$

Our derived answer is $2.98$, so it matches.