An aqueous solution of urea containing 18 g urea in 1500 of the solution has a density equal to 1.052. If the molecular weight of urea is 60, the molality of the solution is:
A. 0.200 m
B. 0.192 m
C. 0.100 m
D. 1.200 m
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Hint: Molality is the ratio of number of moles of solute to the mass of solvent in kilograms.
We will first find the moles of urea, which is the ratio of mass to molar mass.
Complete step by step answer:
- As we know that density is the ratio of mass to volume.
- We are provided with density = 1.052 g/ml, so we can say that 1500 ml of solution corresponds to $1.052 g/ml\times 1500 ml = 1578 g$
- Molar mass of urea is 60 g/mol
- We will find the number of moles of urea, which is the ratio of mass to molar mass. It is:
\[\begin{align}
& \frac{18g}{60g/mol} \\
& =0.3mol \\
\end{align}\]
- We know that molality is the ratio of number of moles of solute to the mass of solvent. Hence, we can write, mass of water = 1575 g - 18 g = 1560 g
We will convert 1560 gram to kilogram= 1.560 kg, as (1 kg = 1000 g)
-Now, we will calculate molality as:
\[Molality=\frac{number\text{ }of\text{ }moles\text{ }of\text{ }urea}{mass\text{ }of\text{ }water\text{ }in\text{ }kg}\]
\[Molality=\frac{0.3} {\begin{align}
&1.560 \\ \end{align}}\] $= 0.192 m$
Hence, we can conclude that the correct option is (B), that is the molality of the solution is 0.192 m.
Note: We must not forget to write units after solving any question, here the unit of molality is m. We must convert the mass of the solvent given in grams into kilograms. We should not get confused in the terms molality and molarity. Molality is the ratio of number of moles of solute to the mass of solvent in kilograms. Whereas, molarity is the moles of a solute per litres of solution.
We will first find the moles of urea, which is the ratio of mass to molar mass.
Complete step by step answer:
- As we know that density is the ratio of mass to volume.
- We are provided with density = 1.052 g/ml, so we can say that 1500 ml of solution corresponds to $1.052 g/ml\times 1500 ml = 1578 g$
- Molar mass of urea is 60 g/mol
- We will find the number of moles of urea, which is the ratio of mass to molar mass. It is:
\[\begin{align}
& \frac{18g}{60g/mol} \\
& =0.3mol \\
\end{align}\]
- We know that molality is the ratio of number of moles of solute to the mass of solvent. Hence, we can write, mass of water = 1575 g - 18 g = 1560 g
We will convert 1560 gram to kilogram= 1.560 kg, as (1 kg = 1000 g)
-Now, we will calculate molality as:
\[Molality=\frac{number\text{ }of\text{ }moles\text{ }of\text{ }urea}{mass\text{ }of\text{ }water\text{ }in\text{ }kg}\]
\[Molality=\frac{0.3} {\begin{align}
&1.560 \\ \end{align}}\] $= 0.192 m$
Hence, we can conclude that the correct option is (B), that is the molality of the solution is 0.192 m.
Note: We must not forget to write units after solving any question, here the unit of molality is m. We must convert the mass of the solvent given in grams into kilograms. We should not get confused in the terms molality and molarity. Molality is the ratio of number of moles of solute to the mass of solvent in kilograms. Whereas, molarity is the moles of a solute per litres of solution.