Find the mass of urea (CH4N2O) needed to prepare 50.9 g of a solution in water in which the mole fraction of urea is 7.69×10−2.

Well, this question seems to be a chemistry problem, and I must admit that chemistry isn't really my strong suit. But hey, I'm here to help, so let's give it a shot!

To find the mass of urea needed, we need to use the mole fraction and the total mass of the solution. The mole fraction is given as 7.69×10−2, and the total mass of the solution is 50.9 g.

Now, to be honest, I don't exactly know what mole fraction means. It sounds vaguely like something you would find at a mole party, but I'm pretty sure it's not quite that. However, I can tell you that it represents the ratio of the moles of solute to the total moles in the solution.

So, let's try to find the moles of urea first. To do that, we can use the mole fraction and the total moles in the solution. Since the total moles of the solution aren't given, we can't calculate the exact moles.

But that won't stop us from making a mole-mentary calculation! We can assume that the total mass of the solution is approximately equal to the mass of urea. This is because the mass of water is much larger compared to the mass of urea. So, we can say that the total moles in the solution are approximately equal to the moles of urea.

Now, we can calculate the mass of urea needed using the mole fraction. We can multiply the mole fraction by the total mass of the solution (which we assumed to be the mass of urea).

But before we do that, let me ask you a question: What did one mole say to the other mole? "We better make a solution together, or else we won't be as effective!"

Okay, enough with the mole jokes, let's get back to business.

Mass of urea needed = Mole fraction of urea x Total mass of solution

Mass of urea needed = 7.69×10−2 x 50.9 g

Now, let's calculate this expression.

To find the mass of urea needed to prepare the solution, we'll need to use the mole fraction and the total mass of the solution.

Step 1: Find the mass of water in the solution.
Since the mole fraction of urea is given, we can calculate the mole fraction of water using the equation:

Mole fraction of water = 1 - Mole fraction of urea

Mole fraction of water = 1 - 7.69×10−2
Mole fraction of water = 0.9231

Step 2: Calculate the mass of water in the solution.
Since the mole fraction of water is equivalent to its mole fraction, we can use this value to find the mass of water.
Let's assume the total mass of the solution is M.

Mass of water = M × Mole fraction of water
Mass of water = M × 0.9231

Step 3: Calculate the mass of urea in the solution.
Since the mole fraction of urea is given, we can calculate the mass of urea using this equation:

Mass of urea = M × Mole fraction of urea
Mass of urea = M × 7.69×10−2

Step 4: Combine equations from Step 2 and Step 3.

Mass of water + Mass of urea = M

M × 0.9231 + M × 7.69×10−2 = M

Step 5: Solve for M.

Dividing both sides of the equation by M:

0.9231 + 7.69×10−2 = 1

0.9231M + 0.0769M = M

0.999M = M

Step 6: Solve for M.

Dividing both sides of the equation by 0.999:

M = M/0.999
M = 1

Since the total mass of the solution, M, is equal to 1, the mass of urea needed to prepare the solution is:

Mass of urea = M × Mole fraction of urea
Mass of urea = 1 × 7.69×10−2
Mass of urea = 7.69×10−2 grams

Therefore, the mass of urea needed to prepare the solution is 7.69×10−2 grams.

To find the mass of urea needed to prepare a solution with a given mole fraction, we'll follow these steps:

Step 1: Determine the moles of solute (urea) and solvent (water) in the solution.
Step 2: Calculate the total moles of solute and solvent in the solution.
Step 3: Use the mole fraction equation to find the moles of urea.
Step 4: Convert the moles of urea to grams using the molar mass of urea.

Let's start with Step 1:

Step 1: Determine the moles of solute (urea) and solvent (water) in the solution.
- The mole fraction (X) is defined as the ratio of the moles of one component to the total moles of all components in the solution.
- In our case, the mole fraction of urea (CH4N2O) is given as 7.69×10^−2.
- We'll assume water is the solvent, so the mole fraction of water will be (1 - 7.69×10^−2).

Now, let's move to Step 2:

Step 2: Calculate the total moles of solute and solvent in the solution.
- The total moles of solute and solvent can be calculated by dividing their respective masses by their molar masses.
- First, let's calculate the moles of water.
- The molar mass of water (H2O) is approximately 18.015 g/mol.
- We'll use the formula: moles = mass / molar mass.
- Substitute the values: moles of water = 50.9 g / 18.015 g/mol.
- Calculate the moles of water.
- Next, let's calculate the moles of urea.
- The molar mass of urea (CH4N2O) is approximately 60.055 g/mol.
- We'll use the same formula: moles = mass / molar mass.
- Substitute the values: moles of urea = ? (since it's what we'll be finding).

Now, let's proceed to Step 3:

Step 3: Use the mole fraction equation to find the moles of urea.
- The mole fraction equation is: X = moles of component / total moles of all components.
- In our case, the mole fraction of urea (X) is given as 7.69×10^−2, and the total moles of all components are the moles of water + the moles of urea.
- Setting up the equation: 7.69×10^−2 = moles of urea / (moles of urea + moles of water).
- Simplify the equation by multiplying both sides by (moles of urea + moles of water):
- 7.69×10^−2 * (moles of urea + moles of water) = moles of urea.
- Now, we have an equation with one unknown (moles of urea), which we can solve for.

Finally, let's move to Step 4:

Step 4: Convert the moles of urea to grams using the molar mass of urea.
- Now that we have the moles of urea, simply multiply it by the molar mass of urea to get the mass of urea.
- Substitute the values: mass of urea = moles of urea * molar mass of urea.
- Calculate the mass of urea, which will give you the answer to the question.

Note: I haven't performed the actual calculations since the information given is incomplete (the mass of water is not provided). However, the steps provided above will guide you in finding the mass of urea needed to prepare the solution. Make sure to substitute the correct values, perform the calculations accurately, and consider the appropriate significant figures in the final answer.

Let mass urea = X

mass H2O = 50.9-X

mols urea = X/molar mass urea = ?
mols H2O = (50.9-X)/molar mass H2O = ?
Total mols = X + (50.9-X)/molar mass H2O
Substitute and solve for X. I believe X is approx 11 grams.
Then mols urea/total mols = 0.769