The 25 mL of a 0.15 M solution of lead nitrate, `Pb(NO_(3))_(2)` react with all of the aluminium sulphate , `Al_(2)(SO_(4))_(3)` , present in 20 mL of a solution . What is the molar concentration of the `Al_(2)(SO_(4))_(3)` ?

Options

A. `6.25xx10^(-2)M`
B. `2.421 xx 10^(-2) M`
C. `0.1875 M`
D. None of these

Answer

To find the molar concentration of aluminum sulfate (`Al₂(SO₄)₃`), we will follow these steps:

### Step 1: Write the balanced chemical equation
The reaction between lead nitrate (`Pb(NO₃)₂`) and aluminum sulfate can be represented as:
\[ 3 \, Pb(NO_3)_2 + Al_2(SO_4)_3 \rightarrow 3 \, PbSO_4 + 2 \, Al(NO_3)_3 \]
This equation shows that 3 moles of lead nitrate react with 1 mole of aluminum sulfate.

### Step 2: Calculate the number of moles of lead nitrate
We know the molarity and volume of the lead nitrate solution:
- Molarity of `Pb(NO₃)₂` = 0.15 M
- Volume of `Pb(NO₃)₂` = 25 mL = 0.025 L

Using the formula for molarity:
\[ \text{Moles} = \text{Molarity} \times \text{Volume (L)} \]
\[ \text{Moles of } Pb(NO_3)_2 = 0.15 \, \text{mol/L} \times 0.025 \, \text{L} = 0.00375 \, \text{moles} \]

### Step 3: Use stoichiometry to find moles of aluminum sulfate
From the balanced equation, we see that 3 moles of lead nitrate react with 1 mole of aluminum sulfate. Therefore, the number of moles of aluminum sulfate can be calculated as:
\[ \text{Moles of } Al_2(SO_4)_3 = \frac{1}{3} \times \text{Moles of } Pb(NO_3)_2 \]
\[ \text{Moles of } Al_2(SO_4)_3 = \frac{1}{3} \times 0.00375 \, \text{moles} = 0.00125 \, \text{moles} \]

### Step 4: Calculate the molar concentration of aluminum sulfate
We know the volume of the aluminum sulfate solution is 20 mL, which is 0.020 L. Now we can find the molarity:
\[ \text{Molarity} = \frac{\text{Moles}}{\text{Volume (L)}} \]
\[ \text{Molarity of } Al_2(SO_4)_3 = \frac{0.00125 \, \text{moles}}{0.020 \, \text{L}} = 0.0625 \, \text{mol/L} \]

### Final Answer
The molar concentration of aluminum sulfate is:
\[ 0.0625 \, \text{M} \, \text{or} \, 6.25 \times 10^{-2} \, \text{M} \]

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