Urea forms a ideal solution in water. Determine the vapour pressure in an aqua solution containing 10 percent bymass at 40degree Celsius
To determine the vapor pressure of an aqueous solution of urea at 40 degrees Celsius and with a concentration of 10% by mass, you can use Raoult's Law.
Raoult's Law states that the vapor pressure of a component in a mixture is proportional to its mole fraction in the mixture. In this case, we need to convert the mass percentage of urea to its mole fraction.
1. Start by calculating the mole fraction of urea in the solution. The mole fraction of a component is the ratio of the moles of that component to the total moles of all components in the mixture.
Let's assume we have 100g of the solution. Since the concentration of urea is 10% by mass, we have 10g of urea.
The molar mass of urea (CO(NH2)2) is 60.063 g/mol. So, the moles of urea can be calculated as:
Moles of urea = mass of urea / molar mass of urea
= 10g / 60.063 g/mol
≈ 0.166 mol
The moles of water (H2O) can be calculated as:
Moles of water = total moles - moles of urea
Since we started with 100g of solution, and we have 10g of urea, we have 90g of water:
Moles of water = mass of water / molar mass of water
= 90g / 18.015 g/mol
≈ 4.994 mol
The total moles of all components in the solution is the sum of moles of urea and moles of water:
Total moles = moles of urea + moles of water
≈ 0.166 mol + 4.994 mol
≈ 5.16 mol
2. Now, we can calculate the mole fraction of urea in the solution:
Mole fraction of urea = moles of urea / total moles
= 0.166 mol / 5.16 mol
≈ 0.0321
The mole fraction of water can be calculated similarly:
Mole fraction of water = moles of water / total moles
= 4.994 mol / 5.16 mol
≈ 0.9679
3. Finally, we can use Raoult's Law to calculate the vapor pressure of urea in the solution. The vapor pressure of pure water at 40 degrees Celsius is 55.3 mmHg.
Vapor pressure of urea = mole fraction of urea * vapor pressure of pure water
= 0.0321 * 55.3 mmHg
≈ 1.777 mmHg
So, the vapor pressure of the aqueous solution containing 10% urea by mass at 40 degrees Celsius is approximately 1.777 mmHg.