The value of p,q , r and s in balanced chemical equation :
`pBaCl_(2)+qAl_(2)(SO_(4))_(3)torAlCl_(3)+sBaSO_(4)` are respectively

Options

A. 3,2,2,3
B. 3,1,2,3
C. 3,1,3,3
D. 3,1,3,2

Explanation

To solve the problem of balancing the chemical equation \( p \text{BaCl}_2 + q \text{Al}_2(\text{SO}_4)_3 \rightarrow r \text{AlCl}_3 + s \text{BaSO}_4 \), we will follow these steps:

### Step 1: Write the unbalanced equation
The unbalanced equation is:
\[ p \text{BaCl}_2 + q \text{Al}_2(\text{SO}_4)_3 \rightarrow r \text{AlCl}_3 + s \text{BaSO}_4 \]

### Step 2: Identify the number of atoms of each element
- On the left side (reactants), we have:
- Barium (Ba): \( p \)
- Chlorine (Cl): \( 2p \)
- Aluminum (Al): \( 2q \)
- Sulfate (SO₄): \( 3q \)

- On the right side (products), we have:
- Aluminum (Al): \( r \)
- Chlorine (Cl): \( 3r \)
- Barium (Ba): \( s \)
- Sulfate (SO₄): \( s \)

### Step 3: Set up equations based on the conservation of mass
From the above counts, we can set up the following equations:
1. For Aluminum: \( 2q = r \)
2. For Chlorine: \( 2p = 3r \)
3. For Barium: \( p = s \)
4. For Sulfate: \( 3q = s \)

### Step 4: Solve the equations
From equation 3, we can express \( s \) in terms of \( p \):
\[ s = p \]

Substituting \( s \) in equation 4 gives:
\[ 3q = p \]
Thus, we can express \( q \) in terms of \( p \):
\[ q = \frac{p}{3} \]

Now substituting \( q \) in equation 1:
\[ 2\left(\frac{p}{3}\right) = r \]
\[ r = \frac{2p}{3} \]

Now substituting \( r \) in equation 2:
\[ 2p = 3\left(\frac{2p}{3}\right) \]
This simplifies to:
\[ 2p = 2p \]
This is always true, so we can choose a value for \( p \).

### Step 5: Choose a suitable value for \( p \)
Let’s choose \( p = 3 \) (to keep \( q \) as a whole number):
- Then, \( q = \frac{3}{3} = 1 \)
- From \( r = \frac{2p}{3} = \frac{2 \times 3}{3} = 2 \)
- And \( s = p = 3 \)

### Final values
Thus, we have:
- \( p = 3 \)
- \( q = 1 \)
- \( r = 2 \)
- \( s = 3 \)

### Conclusion
The values of \( p, q, r, \) and \( s \) in the balanced chemical equation are:
- \( p = 3 \)
- \( q = 1 \)
- \( r = 2 \)
- \( s = 3 \)