Question

The number of moles of a sodium salt (A) is defined as m = ∫01 [1/1+x2 ]dx. Given that the sodium salt (A) reacts with concentrated sulphuric acid in the ratio 2:1 to produce a product B according to the equation

A + H2SO4 → B. Find the mass of the compound B that was produced (RMM of B= 20g/mol)

A. (π/4)g B. (20.5 +π/4)g

C. (5/3)m2 D. (5/2)π

Answer 1

$m = ∫^1_0 \dfrac{1}{1+x² } \ dx$

$m = ∫^1_0 \dfrac{1}{1+x² } \ dx =\dfracπ4$

$2NaCl (A)+ H_2SO_4 \to Na_2SO_4 + 2HCl\qquad(\approx B)$

ratio of moles = $2:1$

since the number of moles of A is $\dfracπ4$, then the number of moles of B is $\dfracπ4÷2 =\dfracπ8$

mass = number of moles × mass = $\dfracπ8×20 = \dfrac{5\pi}{2}$

Ans. d.