$5 \,g$ of $NaOH$ was dissolved in deionized water to prepare a $450 \,mL$ stock solution What volume (in $mL$ ) of this solution would be required to prepare $500 \,mL$ of $01\, M$ solution? Given: Molar Mass of $Na, O$ and $H$ is 23,16 and $1 \,g\, mol ^{-1}$ respectively
Correct Answer: 180
Approach Solution - 1
The correct answer is 180.
To prepare 500 mL of 0.1 M NaOH solution, we need to calculate the volume of the stock solution required.
First, let's calculate the number of moles of NaOH in 500 mL of 0.1 M solution:
Number of moles of NaOH = Molarity × Volume (in L) Number of moles of NaOH = 0.1 × 0.5 Number of moles of NaOH = 0.05
Next, let's calculate the number of moles of NaOH in the stock solution:
Number of moles of NaOH in stock solution = (mass of NaOH / molar mass of NaOH) = (5 g / 40 g/mol) = 0.125 mol
Now, we can use the following formula to calculate the volume of the stock solution required:
Volume of stock solution = (Number of moles required / Number of moles in stock solution) × Volume of stock solution
Plugging in the values, we get:
Volume of stock solution = (0.05 / 0.125) × 0.45 L Volume of stock solution = 0.18 L = 180 mL
Therefore, 180 mL of the NaOH stock solution is required to prepare 500 mL of 0.1 M NaOH solution.
Approach Solution -2
The correct answer is 180
\(M=\frac{5}{40} \times \frac{1000}{450}\)
\(M_1V_1=M_2V_2\)
\((\frac{5}{40} \times \frac{1000}{450})\times V_1=0.1 \times 500\)
\(V_1=180\)
\(\therefore\) volume required is 180
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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.