Find the mass of urea needed to prepare 51.7 of a solution in water in which the mole fraction of urea is 7.80×10−2.
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To find the mass of urea needed to prepare the solution, we need to calculate the amount of urea required based on its mole fraction and the total mass of the solution.
First, let's define the given quantities:
- The mole fraction of urea is given as 7.80×10−2.
- The total mass of the solution is given as 51.7 g.
The mole fraction (X) of a component in a solution is the ratio of the moles of that component to the total moles of all components in the solution. Mathematically, mole fraction is expressed as:
X = (moles of component) / (total moles of all components)
We can rearrange this equation to solve for the moles of the component:
(moles of component) = X * (total moles of all components)
Since we are given the mole fraction of urea and the total mass of the solution, we need to determine the moles of urea.
To calculate the moles of urea, we first need to know the molar mass of urea. The molar mass of urea (CH4N2O) is approximately 60.06 g/mol.
Now, we can calculate the moles of urea using the following equation:
moles of urea = (mole fraction of urea) * (total moles of all components)
moles of urea = (7.80×10−2) * (total moles of all components)
However, the total moles of all components is equal to the moles of urea since urea is the only component in the solution. Therefore, we can simplify the equation as:
moles of urea = (7.80×10−2) * (moles of urea)
Simplifying further:
1 = 7.80×10−2
We can solve this equation to find that the moles of urea is equal to 0.078.
Now, to find the mass of urea, we can use the equation:
mass of urea = moles of urea * molar mass of urea
mass of urea = 0.078 * 60.06 g/mol
Calculating the result gives us:
mass of urea = 4.68348 g
Therefore, the mass of urea needed to prepare 51.7 g of a solution in which the mole fraction of urea is 7.80×10−2 is approximately 4.68 g.