Amount (in g) of sample containing 80% NaOH required to prepare 60 litre of 0.5 M solution is

Options

A. 1000
B. 1200
C. 1500
D. 1600

Answer

To solve the problem of how much sample containing 80% NaOH is required to prepare 60 liters of a 0.5 M solution, we can follow these steps:

### Step 1: Understand the definition of molarity
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula is:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]

### Step 2: Calculate the number of moles required
Given that the molarity is 0.5 M and the volume of the solution is 60 liters, we can rearrange the formula to find the number of moles:
\[ \text{Number of moles} = \text{Molarity} \times \text{Volume} = 0.5 \, \text{mol/L} \times 60 \, \text{L} = 30 \, \text{moles} \]

### Step 3: Calculate the mass of NaOH required
Next, we need to calculate the mass of NaOH required. The molar mass of NaOH (sodium hydroxide) is calculated as follows:
- Sodium (Na) = 23 g/mol
- Oxygen (O) = 16 g/mol
- Hydrogen (H) = 1 g/mol
\[ \text{Molar mass of NaOH} = 23 + 16 + 1 = 40 \, \text{g/mol} \]

Now, we can calculate the mass of NaOH needed using the formula:
\[ \text{Mass} = \text{Number of moles} \times \text{Molar mass} = 30 \, \text{moles} \times 40 \, \text{g/mol} = 1200 \, \text{g} \]

### Step 4: Calculate the amount of sample required
Since the sample contains 80% NaOH, we need to find out how much of the sample is required to get 1200 g of NaOH. If the sample is 80% NaOH, then:
\[ \text{Mass of NaOH in the sample} = 0.80 \times \text{Mass of sample} \]
Let the mass of the sample be \( x \):
\[ 0.80x = 1200 \, \text{g} \]
Now, solving for \( x \):
\[ x = \frac{1200}{0.80} = 1500 \, \text{g} \]

### Final Answer
The amount of sample containing 80% NaOH required to prepare 60 liters of a 0.5 M solution is **1500 g**.

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