A semiconductor `Y_(2)Ba_(2)Cu_(3)O_(7)` is prepared by a reaction involving `Y_(2)O_(3), BaO_(2)` and CuO. The ratio of their molar should be

Options

A. `1:2:4`
B. `1:2:3`
C. `3:2:1`
D. `1:1.5:2.5`

Answer

To determine the molar ratio of the reactants \( Y_2O_3 \), \( BaO_2 \), and \( CuO \) in the synthesis of the semiconductor \( Y_2Ba_2Cu_3O_7 \), we need to balance the chemical reaction. Here’s a step-by-step solution:

### Step 1: Write the unbalanced reaction
The unbalanced reaction for the formation of \( Y_2Ba_2Cu_3O_7 \) from its oxides is:
\[ Y_2O_3 + BaO_2 + CuO \rightarrow Y_2Ba_2Cu_3O_7 \]

### Step 2: Identify the number of atoms in the product
In the product \( Y_2Ba_2Cu_3O_7 \):
- Yttrium (Y): 2
- Barium (Ba): 2
- Copper (Cu): 3
- Oxygen (O): 7

### Step 3: Balance the yttrium (Y)
From the product, we see that we need 2 moles of \( Y_2O_3 \) to provide 2 yttrium atoms:
\[ 2Y_2O_3 \rightarrow 2Y_2Ba_2Cu_3O_7 \]

### Step 4: Balance the barium (Ba)
Next, we need 2 moles of \( BaO_2 \) to provide 2 barium atoms:
\[ 2BaO_2 \rightarrow 2Y_2Ba_2Cu_3O_7 \]

### Step 5: Balance the copper (Cu)
We need 3 moles of \( CuO \) to provide 3 copper atoms:
\[ 3CuO \rightarrow 2Y_2Ba_2Cu_3O_7 \]

### Step 6: Balance the oxygen (O)
Now, we count the total number of oxygen atoms:
- From \( 2Y_2O_3 \): \( 2 \times 3 = 6 \) oxygen atoms
- From \( 2BaO_2 \): \( 2 \times 2 = 4 \) oxygen atoms
- From \( 3CuO \): \( 3 \times 1 = 3 \) oxygen atoms

Total oxygen from reactants = \( 6 + 4 + 3 = 13 \) oxygen atoms.

In the product \( Y_2Ba_2Cu_3O_7 \), we have 7 oxygen atoms. To balance the reaction, we need to ensure that the total number of oxygen atoms is equal on both sides.

### Step 7: Final balanced equation
The balanced equation for the reaction is:
\[ 2Y_2O_3 + 2BaO_2 + 3CuO \rightarrow 2Y_2Ba_2Cu_3O_7 \]

### Step 8: Determine the molar ratio
From the balanced equation, we can see the molar ratio of the reactants:
- \( Y_2O_3 : BaO_2 : CuO = 2 : 2 : 3 \)

To simplify this, we can express it as:
\[ Y_2O_3 : BaO_2 : CuO = 1 : 1 : \frac{3}{2} \]

### Conclusion
Thus, the molar ratio of \( Y_2O_3 \), \( BaO_2 \), and \( CuO \) is:
\[ 1 : 1 : 1.5 \]