Question

In an experiment 4 gm of $M_2{O}_x$ oxide is reduced to 2.8 gm of metal. If the atomic wt Of metal is 56 gm/mol. Find the number of oxygen atoms in the oxide.

• A. $1.513\times {10}^{22}$
• B. $0.413\times {10}^{31}$
• C. $0.413\times {10}^{29}$
  
• D. $0.513\times {10}^{32}$

Answer 1

The correct option is A $1.513\times {10}^{22}$

$\begin{array}{c}\text{As}{M}_2{O}_x\text{gives}=2M\\ (56\times 2+16x)g\equiv 112g\\ \text{4 g of}{M}_2{O}_x\equiv \left(\frac{112}{112+16x}\right)\times \text{4 g metal}\end{array}$

$\begin{array}{c}{M}_2{O}_x\text{reduces to}2.8g\text{of metal}\\ \text{Hence,}\frac{112\times 4}{112+16x}=2.8\\ \Rightarrow x=3\end{array}$

$\begin{array}{c}\Rightarrow x=3\\ \text{So, oxide is}{M}_2{O}_3\text{.}\\ \text{Mass of}\text{Oxygen in}{M}_2{O}_3=4-2.8\\ \text{Total atoms of}\text{Oxygen}=\frac{1.2}{3\times 16}\times 6.023\times {10}^{23}\\ =1.5\times {10}^{22}\text{atoms}\end{array}$