For the reaction
`2x+3y+4z rarr 5w`
Initially if 1 mole of x, 3 mole of y and 4 mole of z is taken. If 1.25 mole of w is obtained then % yield of this reaction is

Options

A. `50%`
B. `60%`
C. `70%`
D. `40%`

Answer

To calculate the percentage yield of the reaction \(2x + 3y + 4z \rightarrow 5w\), we will follow these steps:

### Step 1: Identify the Limiting Reagent
From the initial amounts given:
- Moles of \(x = 1\)
- Moles of \(y = 3\)
- Moles of \(z = 4\)

The stoichiometric coefficients from the balanced equation indicate that:
- 2 moles of \(x\) are required for every 5 moles of \(w\).
- Thus, for 1 mole of \(x\), the theoretical yield of \(w\) can be calculated.

### Step 2: Calculate Theoretical Yield of \(w\)
Using the stoichiometry of the reaction:
- From the balanced equation, \(2 \text{ moles of } x\) produce \(5 \text{ moles of } w\).
- Therefore, \(1 \text{ mole of } x\) will produce:
\[ \text{Theoretical yield of } w = \left(\frac{5 \text{ moles of } w}{2 \text{ moles of } x}\right) \times 1 \text{ mole of } x = 2.5 \text{ moles of } w \]

### Step 3: Determine Actual Yield of \(w\)
According to the problem, the actual yield of \(w\) obtained is \(1.25\) moles.

### Step 4: Calculate Percentage Yield
The percentage yield can be calculated using the formula:
\[ \text{Percentage Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100 \]
Substituting the values:
\[ \text{Percentage Yield} = \left(\frac{1.25}{2.5}\right) \times 100 = 50\% \]

### Final Answer
The percentage yield of the reaction is **50%**.

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