\(250\) \(g\) solution of \(D-glucose\) in water contains 10.8% of carbon by weight. The molality of the solution is nearest to (Given: Atomic Weights are, \(H, 1 u; C, 12 u; O, 16 u\))
- 1.03
- 2.06
- 3.09
- 5.40
The Correct Option is B
Approach Solution - 1
To find the molality of the solution, we need to understand the details provided and make some calculations:
- First, determine the weight of carbon in the solution. Since the solution has 10.8% carbon by weight in a 250 g solution, the amount of carbon is calculated as: \(\frac{10.8}{100} \times 250 = 27 \, g\).
- Next, we need to find the molar mass of \(D\)-glucose, which is \(\text{C}_6\text{H}_{12}\text{O}_6\). Calculate its molar mass using atomic weights provided:
- Carbon (\(C\)): \(6 \times 12 = 72 \, u\)
- Hydrogen (\(H\)): \(12 \times 1 = 12 \, u\)
- Oxygen (\(O\)): \(6 \times 16 = 96 \, u\)
- Now, calculate the moles of carbon in the solution. Since each mole of glucose corresponds to 6 moles of carbon: \(\text{Moles of carbon} = \frac{27}{12} = 2.25 \, \text{moles}\).
- For the molality (\(m\)), which is moles of solute per kg of solvent, determine the moles of \(D\)-glucose based on carbon content: \[ \text{Moles of } D\text{-glucose} = \frac{2.25}{6} = 0.375 \, \text{moles} \]
- Finally, since glucose is the solute and water is the solvent, the weight of the solvent (water) is calculated as: \(250 - \frac{180 \times 0.375}{1} = 182.5 \, g\) or \(0.1825 \, kg\).
- The molality of the solution is given by: \[ m = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}} = \frac{0.375}{0.1825} = 2.06 \, \text{mol/kg} \]
Thus, the molality of the solution is nearest to 2.06.
Approach Solution -2
Weight of D-glucose in water =\( 250\) \(g\)
∴ Weight of carbon in D-glucose
= \(\frac{250}{180}×72 = 100\) \(g\)
Percentage of carbon in the aqueous solution of glucose is
= \(10.8\%\)
∴ Weight of the solution is = \(925.93\)
∴ Molality of D-glucose is
=\(\frac{\frac{ 250}{180}}{(925.93 - 250)}×1000\)
= \(\frac{250}{180×675.93} ×1000\)
= \(2.06\)
Hence, the correct option is (B): \(2.06\)
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Concepts Used:
Solutions
A solution is a homogeneous mixture of two or more components in which the particle size is smaller than 1 nm.
For example, salt and sugar is a good illustration of a solution. A solution can be categorized into several components.
Types of Solutions:
The solutions can be classified into three types:
- Solid Solutions - In these solutions, the solvent is in a Solid-state.
- Liquid Solutions- In these solutions, the solvent is in a Liquid state.
- Gaseous Solutions - In these solutions, the solvent is in a Gaseous state.
On the basis of the amount of solute dissolved in a solvent, solutions are divided into the following types:
- Unsaturated Solution- A solution in which more solute can be dissolved without raising the temperature of the solution is known as an unsaturated solution.
- Saturated Solution- A solution in which no solute can be dissolved after reaching a certain amount of temperature is known as an unsaturated saturated solution.
- Supersaturated Solution- A solution that contains more solute than the maximum amount at a certain temperature is known as a supersaturated solution.