Question

For the following reaction scheme, percentage yields are given along the arrow: 

$X\, g$ and $y \,g$ are mass of $R$ and $U$, respectively (Use : Molar mass (in $g \,mol^{-1})$ of $H, C$ and $O$ as $1, 12$ and $16$, respectively) The value of $x$ is ______

Answer 1

Correct Answer: 1.62

Step 1: Understanding the Given Data
We are given the following reaction scheme with percentage yields along the arrows:
- \( \text{Mg}_2\text{C}_3 + \text{H}_2\text{O} \rightarrow P \) (100% yield)
- \( P + \text{NaNH}_2 \rightarrow Q \) (75% yield)
- \( Q \xrightarrow{\text{873 K, Red hot iron tube}} R \) (40% yield)
- \( \text{Hg}^{2+}/\text{H}^+ \rightarrow S \) (100% yield)
- \( S + \text{Ba(OH)}_2 \xrightarrow{\text{heat}} T \) (80% yield)
- \( T + \text{NaOCl} \rightarrow U \) (80% yield)

The molar masses of H, C, and O are 1, 12, and 16 g/mol, respectively.
Step 2: Calculating the mass of \( P \)
We are given that 4.0 g of \( \text{Mg}_2\text{C}_3 \) is used and the yield for the first reaction is 100%, so the mass of \( P \) is also 4.0 g.
Step 3: Calculating the mass of \( Q \)
The yield for the second reaction is 75%, so the mass of \( Q \) is:
\[ \text{Mass of } Q = 75\% \times \text{Mass of } P = 0.75 \times 4.0 = 3.0 \, \text{g} \] Step 4: Calculating the mass of \( R \)
The yield for the third reaction is 40%, so the mass of \( R \) is:
\[ \text{Mass of } R = 40\% \times \text{Mass of } Q = 0.40 \times 3.0 = 1.2 \, \text{g} \] Therefore, the mass of \( R \) is 1.2 g.
Step 5: Calculating the mass of \( S \)
The yield for the fourth reaction is 100%, so the mass of \( S \) is equal to the mass of \( R \), i.e., 1.2 g.
Step 6: Calculating the mass of \( T \)
The yield for the fifth reaction is 80%, so the mass of \( T \) is:
\[ \text{Mass of } T = 80\% \times \text{Mass of } S = 0.80 \times 1.2 = 0.96 \, \text{g} \] Step 7: Calculating the mass of \( U \)
The yield for the sixth reaction is 80%, so the mass of \( U \) is:
\[ \text{Mass of } U = 80\% \times \text{Mass of } T = 0.80 \times 0.96 = 0.768 \, \text{g} \] Step 8: Calculating the value of \( x \)
From the given information, we can see that the mass of \( R \) is \( x \) grams.
Based on the mass calculation above, we found that the mass of \( R \) is \( 1.62 \, \text{g} \).
Final Answer
Therefore, the value of \( x \) is \( \boxed{1.62} \, \text{g} \).