Answer :
Answer:
To calculate the mole fraction of each component, we need to follow these steps:
1. Calculate the number of moles of urea and water:
- Moles of urea = mass of urea / molar mass of urea
- Moles of water = mass of water / molar mass of water
2. Calculate the total number of moles:
- Total moles = moles of urea + moles of water
3. Calculate the mole fraction of each component:
- Mole fraction of urea = moles of urea / total moles
- Mole fraction of water = moles of water / total moles
Given values:
- Mass of urea = 30 g
- Molar mass of urea = 60.06 g/mol
- Density of water = 1 g/ml
- Volume of water = 1 L = 1000 ml
- Mass of water = density x volume = 1 g/ml x 1000 ml = 1000 g
- Molar mass of water = 18.02 g/mol
Calculations:
- Moles of urea = 30 g / 60.06 g/mol = 0.50 mol
- Moles of water = 1000 g / 18.02 g/mol = 55.45 mol
- Total moles = 0.50 mol + 55.45 mol = 55.95 mol
- Mole fraction of urea = 0.50 mol / 55.95 mol = 0.0089 (or 0.89%)
- Mole fraction of water = 55.45 mol / 55.95 mol = 0.9911 (or 99.11%)
So, the mole fraction of urea is 0.0089 (or 0.89%) and the mole fraction of water is 0.9911 (or 99.11%).
To calculate the mole fraction of urea (\( X_{\text{urea}} \)) in the solution, we need to follow these steps:
1. **Calculate the moles of urea:**
Given:
- Mass of urea (\( m_{\text{urea}} \)) = 30 grams
- Molar mass of urea (\( M_{\text{urea}} \)) = 60.06 g/mol (approximate molar mass of urea)
Number of moles of urea (\( n_{\text{urea}} \)) can be calculated using the formula:
\[
n_{\text{urea}} = \frac{m_{\text{urea}}}{M_{\text{urea}}}
\]
\[
n_{\text{urea}} = \frac{30 \text{ g}}{60.06 \text{ g/mol}} \approx 0.4998 \text{ mol}
\]
2. **Calculate the moles of water:**
Volume of water (\( V_{\text{water}} \)) = 1 litre = 1000 ml
Density of water (\( \rho_{\text{water}} \)) = 1 g/ml (assuming water density is approximately 1 g/ml)
Mass of water (\( m_{\text{water}} \)) = Volume \(\times\) Density = \( 1000 \text{ ml} \times 1 \text{ g/ml} = 1000 \text{ g} \)
Number of moles of water (\( n_{\text{water}} \)) can be calculated using the formula:
\[
n_{\text{water}} = \frac{m_{\text{water}}}{M_{\text{water}}}
\]
\[
n_{\text{water}} = \frac{1000 \text{ g}}{18.015 \text{ g/mol}} \approx 55.51 \text{ mol}
\]
(Here, \( M_{\text{water}} \) is the molar mass of water, which is approximately 18.015 g/mol.)
3. **Calculate mole fraction of urea (\( X_{\text{urea}} \)):**
Mole fraction of urea in the solution is given by:
\[
X_{\text{urea}} = \frac{n_{\text{urea}}}{n_{\text{urea}} + n_{\text{water}}}
\]
Substitute the values we calculated:
\[
X_{\text{urea}} = \frac{0.4998 \text{ mol}}{0.4998 \text{ mol} + 55.51 \text{ mol}}
\]
\[
X_{\text{urea}} = \frac{0.4998}{56.0098}
\]
\[
X_{\text{urea}} \approx 0.0089
\]
Therefore, the mole fraction of urea in the solution is approximately \( 0.0089 \).
This means for every 100 moles of molecules in the solution, about 0.89 moles are urea molecules.