Question

suppose the element X and Y combine to form two compound XY2 and X3Y2 . when 0.1 mole of XY2 weighs 10g and 0.05 mole of X3Y2 weighs 9g , the atomic weights of X and Y are

Answer 1

2X + Y = 10/0.1 -1
2X +3Y = 9/0.05 -2

Solve the above two equations. You will get the answer 40,30

Answer 2

Answer:

• Moles of XY₂ = 0.1 mole

• Moles of X₃Y₂ = 0.05 mole

• Mass of XY₂ = 10g

• Mass of X₃Y₂ = 9g

Let the atomic weight of X be 'a' and atomic weight of Y be 'b'.

• Compund XY₂:

$\footnotesize\longrightarrow\: Moles \: of \: XY_2 = \dfrac{Mass \: of \: XY_2}{Molar \: mass \: of \: XY_2}$

$\footnotesize\longrightarrow\:0.1 = \dfrac{10}{a + 2b}$

$\footnotesize\longrightarrow\:a + 2b = \dfrac{10}{0.1}$

$\footnotesize\longrightarrow\:a + 2b = \dfrac{10}{ \frac{1}{10} }$

$\footnotesize\longrightarrow\:a + 2b =100 \: ... \Bigg \lgroup \bf{Equation \: (i )}\Bigg \rgroup$

• Compund X₃Y₂ :

$\footnotesize\longrightarrow\: Moles \: of \: X_{3} Y_2 = \dfrac{Mass \: of \: X_{3}Y_2}{Molar \: mass \: of \: X_{3}Y_2}$

$\footnotesize\longrightarrow\:0.05 = \dfrac{9}{3a + 2b}$

$\footnotesize\longrightarrow\:3a + 2b= \dfrac{9}{0.05}$

$\footnotesize\longrightarrow\:3a + 2b= \dfrac{9}{ \frac{5}{100} }$

$\footnotesize\longrightarrow\:3a + 2b= \dfrac{9 \times 100}{ 5}$

$\footnotesize\longrightarrow\:3a + 2b= 9 \times 20$

$\footnotesize\longrightarrow\:3a + 2b= 180 \: \: ...\Bigg \lgroup \bf{Equation \: (i i)}\Bigg \rgroup$

Subtracting equation (ii) from equation (i), we get:

$\footnotesize\longrightarrow\:3a - a + 2b - 2b = 180 - 100$

$\footnotesize\longrightarrow\:2 a = 80$

$\footnotesize\longrightarrow\: a = \dfrac{80}{2}$

$\footnotesize\longrightarrow\: \red { \rm a = 40 \: g/mol}$

Substitue the value of a = 40 in equation (i)

$\footnotesize\longrightarrow\:40 + 2b =100$

$\footnotesize\longrightarrow\:2b =100 - 40$

$\footnotesize\longrightarrow\:2b =60$

$\footnotesize\longrightarrow\:b = \dfrac{60}{2}$

$\footnotesize\longrightarrow\: \purple { \rm b = 30 \: g/mol}$