Question

A compound $X$ decomposes by reactions done independently under different reaction conditions as follows:
$X\to 2Y+Z\dots \dots \text{(i)}$
$3X\to 4W+2V\dots \dots \text{(ii)}$
Assume the percentage yield of reaction (i) to be $40\%$ and that of reaction (ii) to be $60\%$. If $4$ moles of $Y$ were formed and a total of $15$ moles of $X$ were taken initially, the moles of $W$ formed will be:

• A. $11.25$ mol
• B. $7.99$ mol
• C. $5.00$ mol
• D. $3.65$ mol

Answer 1

The correct option is B $7.99$ mol

Let us assume that $‘a^{\prime }$ mol of $X$ was taken in reaction (i).
As per stoichiometry,
$1$ mol of $X$ gives $2$ mol of $Y$
So, $a$ mol of $X$ gives $2a$ mol of $Y$
But, as the yield of the reaction is $40\%$.
Thus number of moles of $Y$ obtained = $\frac{40}{100}\times 2a$
Actual yield of $Y$ is given as $4$.
So, $\frac{40}{100}\times 2a=4$
On solving, $a=5\text{mol}$
Hence moles of $X$ taken in reaction (ii) $=15–5=10$ mol
In reaction (ii),
$3$ mol of $X$ gives $4$ mol of $W$
$10$ mol of $X$ will give $=\frac{4}{3}\times 10=13.33$ mol of $W$
But, the yield given is $60\%$
Actual number of moles of $W$ obtained $=0.60\times 13.33=7.998$ mol