63g of a compound (Mol.Wt.=126) was dissolved in 500g of distilled water.The density of the resultant solution is 1.126g/ml. The molarity of the solution is
- 1.25M
- 1.0M
- 0.75M
- 1.1M
The Correct Option is B
Approach Solution - 1
Given:
- Mass of compound = 63 g
- Molecular weight of compound = 126 g/mol
- Mass of water = 500 g
- Density of solution = 1.126 g/ml
First, let's find the volume of the solution. The density formula is \( \text{density} = \frac{\text{mass}}{\text{volume}} \), so the volume of the solution is:
\[ \text{Volume of solution} = \frac{\text{mass of solution}}{\text{density of solution}} = \frac{63 g + 500 g}{1.126 g/ml} \]
\[ \text{Volume of solution} = \frac{563 g}{1.126 g/ml} \]
\[ \text{Volume of solution} = 500 ml \]
Since the density of water is 1 g/ml, the mass of water in the solution is 500 g. This means the mass of the compound in the solution is \( 63 \text{ g} \). Since the compound's molecular weight is 126 g/mol, the number of moles of the compound in the solution is:
\[ \text{Moles of compound} = \frac{\text{Mass of compound}}{\text{Molecular weight of compound}} \]
\[ \text{Moles of compound} = \frac{63 \text{ g}}{126 \text{ g/mol}} \]
\[ \text{Moles of compound} = 0.5 \text{ mol} \]
Now, the molarity of the solution is given by the formula:
\[ \text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \]
Since we have 0.5 moles of compound and the volume of the solution is 500 ml (0.5 liters), the molarity is:
\[ \text{Molarity} = \frac{0.5 \text{ mol}}{0.5 \text{ L}} \]
\[ \text{Molarity} = 1.0 \text{ M} \]
Therefore, the molarity of the solution is 1.0 M.
The correct answer is option (B): 1.0M
Approach Solution -2
Given:
- Mass of solute = 63 g
- Molar mass = 126 g/mol
- Mass of water = 500 g
- Density of solution = 1.126 g/mL
Step 1: Calculate moles of solute
\[ \text{Moles} = \frac{63}{126} = 0.5\ \text{mol} \]
Step 2: Calculate total mass of solution
\[ \text{Total mass} = 63\ \text{g (solute)} + 500\ \text{g (solvent)} = 563\ \text{g} \]
Volume of solution:
\[ \text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{563}{1.126} \approx 500\ \text{mL} = 0.5\ \text{L} \]
Step 3: Calculate molarity
\[ M = \frac{\text{moles of solute}}{\text{volume of solution in L}} = \frac{0.5}{0.5} = 1.0\ \text{M} \]
Final Answer: 1.0 M
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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:
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- 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:
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